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University of Southern California
1.
Aslam, Kamran.
A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling.
Degree: PhD, Aerospace Engineering, 2012, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371 
► This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their…
(more)
▼ This dissertation describes the computational
formulation of probability density functions (pdfs) that facilitate
head-to-head match simulations in tennis along with ranking systems
developed from their use. A background on the statistical method
used to develop the pdfs, the
Monte Carlo method, and the resulting
rankings are included along with a discussion on ranking methods
currently being used both in professional sports and in other
applications. Using an analytical theory developed by Newton and
Keller that defines a tennis player’s probability of winning a
game, set, match and single elimination tournament, a computational
simulation has been developed in Matlab that allows further
modeling not previously possible with the analytical theory alone.
Such experimentation consists of the exploration of non-iid
effects, considers the concept the varying importance of points in
a match and allows an unlimited number of matches to be simulated
between unlikely opponents. The results of these studies have
provided pdfs that accurately model an individual tennis player’s
ability along with a realistic, fair and mathematically sound
platform for ranking them.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kanso, Eva (Committee Member), Fulman, Jason (Committee Member).
Subjects/Keywords: monte carlo; markov chain; tennis
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APA (6th Edition):
Aslam, K. (2012). A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371
Chicago Manual of Style (16th Edition):
Aslam, Kamran. “A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling.” 2012. Doctoral Dissertation, University of Southern California. Accessed February 23, 2020.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371.
MLA Handbook (7th Edition):
Aslam, Kamran. “A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling.” 2012. Web. 23 Feb 2020.
Vancouver:
Aslam K. A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling. [Internet] [Doctoral dissertation]. University of Southern California; 2012. [cited 2020 Feb 23].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371.
Council of Science Editors:
Aslam K. A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling. [Doctoral Dissertation]. University of Southern California; 2012. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371
2.
Auranen, Toni.
Computational Methods for Bayesian Estimation of Neuromagnetic Sources.
Degree: 2007, Helsinki University of Technology
URL: http://lib.tkk.fi/Diss/2007/isbn9789512289547/
► The electromagnetic inverse problem in human brain research consists of determining underlying source currents in the brain based on measurements outside the head. Solution to…
(more)
▼ The electromagnetic inverse problem in human brain research consists of determining underlying source currents in the brain based on measurements outside the head. Solution to the inverse problem is ambiguous, necessitating the use of prior information and modeling assumptions for obtaining reasonable inverse estimates. In this study, we create new and improve existing computational methods for estimating neuromagnetic sources in the human brain. One straightforward way of incorporating presumptions to this problem is to formulate it in a probabilistic Bayesian manner. Bayesian statistics is largely based on modeling uncertainties associated with parameters constituting the model by representing them with probability distributions. In this work, existing neuroscientific knowledge and information from anatomical and functional magnetic resonance imaging are used as prior assumptions in model implementation. The neuromagnetic inverse problem is resolved with two different approaches. First, we perform the analysis using distributed source current modeling and infer some arbitrary parameter choices and the source currents from the measurement data by using numerical sampling methods. We apply similar strategies to cortically constrained current dipole localization and suggest using functional magnetic resonance imaging data for guiding the sampling algorithm. The models are tested with simulated and measured data. The presented methods are rather automatic, yielding plausible and robust inverse estimates of cortical current sources. With the spatiotemporal dipole localization model, the inclusion of functional magnetic resonance imaging data improves performance of the numerical sampling method. However, apparent multimodality of the parameter posterior distribution causes complications especially with empirical data. We suggest using loose cortical orientation constraints for smoothing down the complicated posterior distribution instead of marginal improvements to the sampling scheme. This might help to overcome the somewhat limited mixing properties of the sampling algorithm and ease the inconvenient multimodality of the posterior distribution.
Ihmisaivojen tutkimukseen liittyvällä sähkömagneettisella käänteisongelmalla tarkoitetaan aivojen virtalähteiden paikantamista pään ulkopuolisten mittausten perusteella. Ongelmaan ei ole yksikäsitteistä ratkaisua, joten mallintamisessa on käytettävä ennakko-oletuksia järkevien ratkaisujen tuottamiseksi. Tässä tutkimuksessa kehitämme uusia ja parannamme olemassaolevia laskennallisia menetelmiä aivoissa syntyvien magneettikenttiä tuottavien lähteiden paikantamiseksi. Kenties yksinkertaisin tapa lisätä ennakko-oletuksia tähän ongelmaan on käyttää bayesilaista mallintamista. Bayesilainen tilastotiede perustuu pitkälti parametrien epävarmuuksien mallintamiseen ja esittämiseen todennäköisyysjakaumin. Työn mallien muodostamisessa käytetään apuna aivojen toiminnallisesta ja rakenteellisesta magneettikuvauksesta saatavaa neurotieteellistä ennakkotietoa. Sähkömagneettisen…
Advisors/Committee Members: Helsinki University of Technology, Department of Electrical and Communications Engineering, Laboratory of Computational Engineering.
Subjects/Keywords: inverse problem; magnetoencephalography; Markov chain Monte Carlo
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APA (6th Edition):
Auranen, T. (2007). Computational Methods for Bayesian Estimation of Neuromagnetic Sources. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2007/isbn9789512289547/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Auranen, Toni. “Computational Methods for Bayesian Estimation of Neuromagnetic Sources.” 2007. Thesis, Helsinki University of Technology. Accessed February 23, 2020.
http://lib.tkk.fi/Diss/2007/isbn9789512289547/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Auranen, Toni. “Computational Methods for Bayesian Estimation of Neuromagnetic Sources.” 2007. Web. 23 Feb 2020.
Vancouver:
Auranen T. Computational Methods for Bayesian Estimation of Neuromagnetic Sources. [Internet] [Thesis]. Helsinki University of Technology; 2007. [cited 2020 Feb 23].
Available from: http://lib.tkk.fi/Diss/2007/isbn9789512289547/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Auranen T. Computational Methods for Bayesian Estimation of Neuromagnetic Sources. [Thesis]. Helsinki University of Technology; 2007. Available from: http://lib.tkk.fi/Diss/2007/isbn9789512289547/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Ontario Institute of Technology
3.
McDougall, Robin.
Robotic radiation mapping using modelling and probabilistic analysis of sparse data.
Degree: 2015, University of Ontario Institute of Technology
URL: http://hdl.handle.net/10155/552
► An approach for generating radiation intensity maps, comprised of a mobile robotic platform and an integrated radiation model, is presented, and its ability to generate…
(more)
▼ An approach for generating radiation intensity maps, comprised of a mobile robotic platform and an integrated radiation model, is presented, and its ability to generate accurate radiation maps in simulation studies as well as real-life exposure scenarios are investigated.
The radiation intensity mapping approach described here consists of two stages. First, radiation intensity samples are collected using a radiation sensor mounted on a mobile robotic platform, reducing the risk of exposure to humans from an unknown radiation field. Next, these samples, which need only to be taken from a subsection of the entire area being mapped, are then used to calibrate a radiation model. This model is then used to predict the radiation intensity field throughout the rest of the area.
In this thesis, the technical details of both the prototype mobile robotic platform and the mathematical models for the radiation and map generation algorithms are presented in depth. The performance of the approach is evaluated in simulation studies and experiments in the lab. The sensitivity of the performance of the platform to changes in the number and orientation of the locations where the robot gathers samples from to calibrate the model for the given exposure scenario is analyzed quantitatively.
The results show that the developed system is effective at achieving the goal of generating radiation maps using sparse data.
Advisors/Committee Members: Nokleby, Scott, Waller, Ed.
Subjects/Keywords: Radiation mapping; Robotics; Markov Chain Monte Carlo
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APA (6th Edition):
McDougall, R. (2015). Robotic radiation mapping using modelling and probabilistic analysis of sparse data. (Thesis). University of Ontario Institute of Technology. Retrieved from http://hdl.handle.net/10155/552
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
McDougall, Robin. “Robotic radiation mapping using modelling and probabilistic analysis of sparse data.” 2015. Thesis, University of Ontario Institute of Technology. Accessed February 23, 2020.
http://hdl.handle.net/10155/552.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
McDougall, Robin. “Robotic radiation mapping using modelling and probabilistic analysis of sparse data.” 2015. Web. 23 Feb 2020.
Vancouver:
McDougall R. Robotic radiation mapping using modelling and probabilistic analysis of sparse data. [Internet] [Thesis]. University of Ontario Institute of Technology; 2015. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/10155/552.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
McDougall R. Robotic radiation mapping using modelling and probabilistic analysis of sparse data. [Thesis]. University of Ontario Institute of Technology; 2015. Available from: http://hdl.handle.net/10155/552
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Alberta
4.
Habib, Shahnoor.
A Combined Three-Phase Signal Extraction of the Sudbury
Neutrino Observatory Data Using Markov Chain Monte Carlo
Technique.
Degree: PhD, Department of Physics, 2011, University of Alberta
URL: https://era.library.ualberta.ca/files/cvx021f21f
► \begin{Large} \truedoublespacing \begin{center} bf{Abstract} \end{center} Neutrino physics has entered an era of precision, after proving that the Standard Solar Model is a viable theory and…
(more)
▼ \begin{Large} \truedoublespacing \begin{center}
bf{Abstract} \end{center} Neutrino physics has entered an era
of precision, after proving that the Standard Solar Model is a
viable theory and going beyond the current Standard Model of
particle physics by proving that neutrinos possess nonzero masses.
The Sudbury Neutrino Observatory (SNO) experiment, along with other
experiments, has restricted neutrino mixing angle (θ12)
and the mass square difference (Δ m221) to lie within
the large mixing solution area. SNO, located 2~km underground in
Sudbury, Canada, was an ultraclean heavy-water (D2O) imaging
detector for observing neutrinos produced by fusion reactions in
the Sun. Neutrino interactions with heavy water resulted in flashes
of light called \breve{{C}}erenkov radiation which was
detected by an array of photomultiplier tubes. SNO took data from
November 1999 to November 2006, totalling 1082 days of data taking.
This work describes an improved measurement of the mixing
parameters from a combined fit of all the data. For the signal
extraction fit on the data consisting of 4 observable of an event
– radial position, recoil electron energy, direction relative to
the Sun and event isotropy – Markov Chain Monte Carlo (MCMC)
method based on Metropolis algorithm was employed. The nuisance
parameters (systematics), weighted by external constraints, were
allowed to vary in the fit. The goal of the thesis was to extract
the survival probabilities of electron neutrinos and determine the
total flux of active-flavour neutrinos from 8B decay in the
Sun measured through the neutral current interactions of neutrinos
on deuterium. The 8B flux from the fit is (5.24±0.02)
× 106~{cm}-2~ s-1; uncertainty from statistics
and systematics is 3.56%. Along with 8B flux, the fit
extracted energy spectra of charged current interactions of
neutrinos on deuterium and elastic scattering interactions of
neutrinos on electrons. The fit described the energy-dependent day
survival probability of solar neutrinos as a quadratic equation and
asymmetry on the day survival probability as a linear equation.
Four polynomial coefficients of the survival probability were
extracted from the fit: constant coefficient as 0.3206±0.0197,
linear coefficient as 0.005±0.008 and quadratic coefficient as
-0.0014±0.0033. There are two coefficients on the day-night
asymmetry: constant coefficient as 0.0496±0.0347 and the linear
coefficient as -0.018±0.028. The day-night asymmetry (0.0496)
observed is 1.4σ away from zero. Using these findings, the
oscillation space in terms of Δ m221 and θ12
will be further constrained. Compared to the previous published SNO
results, the uncertainty on 8B went down from 3.83% to 3.56%
and average 8B νe survival probability (p0) went down
from 6.57% to 6.14%. If the data were analysed with the same
assumptions, the decrease in uncertainties would have been
approximately twice as big; however,…
Subjects/Keywords: neutrino physics; Markov Chain Monte Carlo
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APA ·
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APA (6th Edition):
Habib, S. (2011). A Combined Three-Phase Signal Extraction of the Sudbury
Neutrino Observatory Data Using Markov Chain Monte Carlo
Technique. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/cvx021f21f
Chicago Manual of Style (16th Edition):
Habib, Shahnoor. “A Combined Three-Phase Signal Extraction of the Sudbury
Neutrino Observatory Data Using Markov Chain Monte Carlo
Technique.” 2011. Doctoral Dissertation, University of Alberta. Accessed February 23, 2020.
https://era.library.ualberta.ca/files/cvx021f21f.
MLA Handbook (7th Edition):
Habib, Shahnoor. “A Combined Three-Phase Signal Extraction of the Sudbury
Neutrino Observatory Data Using Markov Chain Monte Carlo
Technique.” 2011. Web. 23 Feb 2020.
Vancouver:
Habib S. A Combined Three-Phase Signal Extraction of the Sudbury
Neutrino Observatory Data Using Markov Chain Monte Carlo
Technique. [Internet] [Doctoral dissertation]. University of Alberta; 2011. [cited 2020 Feb 23].
Available from: https://era.library.ualberta.ca/files/cvx021f21f.
Council of Science Editors:
Habib S. A Combined Three-Phase Signal Extraction of the Sudbury
Neutrino Observatory Data Using Markov Chain Monte Carlo
Technique. [Doctoral Dissertation]. University of Alberta; 2011. Available from: https://era.library.ualberta.ca/files/cvx021f21f
University of Alberta
5.
Howard, Christopher William.
A search for hep neutrinos with the Sudbury Neutrino
Observatory.
Degree: PhD, Department of Physics, 2010, University of Alberta
URL: https://era.library.ualberta.ca/files/v118rd64z
► This thesis focuses on the search for neutrinos from the solar hep reaction using the combined three phases of the Sudbury Neutrino Observatory (SNO) data.…
(more)
▼ This thesis focuses on the search for neutrinos from
the solar hep reaction using the combined three phases of the
Sudbury Neutrino Observatory (SNO) data. The data were taken over
the years 1999–2006, totalling 1,083 days of live neutrino time.
The previous published SNO hep neutrino search was completed in
2001 and only included the first phase of data taking. That hep
search used an event counting approach in one energy bin with no
energy spectral information included. This thesis will use a
spectral analysis approach. The hep neutrino search will be a
Bayesian analysis using Markov Chain Monte Carlo (MCMC), and a
Metropolis-Hastings algorithm to sample the likelihood space. The
method allows us to determine the best fit values for the
parameters. This signal extraction will measure the 8B flux, the
atmospheric neutrino background rate in the SNO detector, and the
hep flux. This thesis describes the tests used to verify the MCMC
algorithm and signal extraction. It defines the systematic
uncertainties and how they were accounted for in the fit. It also
shows the correlations between all of the parameters and the effect
of each systematic uncertainty on the result. The three phase hep
signal extraction was completed using only 1/3 of the full data
set. With these lowered statistics, this analysis was able to place
an upper limit on the hep flux of 4.2 × 104 cm−2 s−1 with a 90%
confidence limit. It was able to measure a hep flux of
(2.40(+1.19)(-1.60))×104 cm−2 s−1. These numbers can be compared
with the previous SNO upper limit of 2.3×104 cm−2 s−1 with a 90%
confidence limit, and the standard solar model prediction of (7.970
± 1.236) × 103 cm−2 s−1.
Subjects/Keywords: neutrino; solar model; markov chain monte carlo
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APA (6th Edition):
Howard, C. W. (2010). A search for hep neutrinos with the Sudbury Neutrino
Observatory. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/v118rd64z
Chicago Manual of Style (16th Edition):
Howard, Christopher William. “A search for hep neutrinos with the Sudbury Neutrino
Observatory.” 2010. Doctoral Dissertation, University of Alberta. Accessed February 23, 2020.
https://era.library.ualberta.ca/files/v118rd64z.
MLA Handbook (7th Edition):
Howard, Christopher William. “A search for hep neutrinos with the Sudbury Neutrino
Observatory.” 2010. Web. 23 Feb 2020.
Vancouver:
Howard CW. A search for hep neutrinos with the Sudbury Neutrino
Observatory. [Internet] [Doctoral dissertation]. University of Alberta; 2010. [cited 2020 Feb 23].
Available from: https://era.library.ualberta.ca/files/v118rd64z.
Council of Science Editors:
Howard CW. A search for hep neutrinos with the Sudbury Neutrino
Observatory. [Doctoral Dissertation]. University of Alberta; 2010. Available from: https://era.library.ualberta.ca/files/v118rd64z
Rochester Institute of Technology
6.
Dumont, Michael.
Markov chain Monte Carlo on the GPU.
Degree: Computer Science (GCCIS), 2011, Rochester Institute of Technology
URL: https://scholarworks.rit.edu/theses/83
► Markov chains are a useful tool in statistics that allow us to sample and model a large population of individuals. We can extend this idea…
(more)
▼ Markov chains are a useful tool in statistics that allow us to sample and model a large population of individuals. We can extend this idea to the challenge of sampling solutions to problems. Using
Markov chain Monte Carlo (MCMC) techniques we can also attempt to approximate the number of solutions with a certain confidence based on the number of samples we use to compute our estimate. Even though this approximation works very well for getting accurate results for very large problems, it is still computationally intensive. Many of the current algorithms use parallel implementations to improve their performance. Modern day graphics processing units (GPU's) have been increasing in computational power very rapidly over the past few years. Due to their inherently parallel nature and increased flexibility for general purpose computation, they lend themselves very well to building a framework for general purpose
Markov chain simulation and evaluation. In addition, the majority of mid- to high-range workstations have graphics cards capable of supporting modern day general purpose GPU (GPGPU) frameworks such as OpenCL, CUDA, or DirectCompute. This thesis presents work done to create a general purpose framework for
Markov chain simulations and
Markov chain Monte Carlo techniques on the GPU using the OpenCL toolkit. OpenCL is a GPGPU framework that is platform and hardware independent, which will further increase the accessibility of the software. Due to the increasing power, flexibility, and prevalence of GPUs, a wider range of developers and researchers will be able to take advantage of a high performing general purpose framework in their research. A number of experiments are also conducted to demonstrate the benefits and feasibility of using the power of the GPU to solve
Markov chain Monte Carlo problems.
Advisors/Committee Members: Bez´akov´a, Ivona.
Subjects/Keywords: Approximation; GPGPU; GPU; Markov chain; Monte carlo
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APA (6th Edition):
Dumont, M. (2011). Markov chain Monte Carlo on the GPU. (Thesis). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/83
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Dumont, Michael. “Markov chain Monte Carlo on the GPU.” 2011. Thesis, Rochester Institute of Technology. Accessed February 23, 2020.
https://scholarworks.rit.edu/theses/83.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Dumont, Michael. “Markov chain Monte Carlo on the GPU.” 2011. Web. 23 Feb 2020.
Vancouver:
Dumont M. Markov chain Monte Carlo on the GPU. [Internet] [Thesis]. Rochester Institute of Technology; 2011. [cited 2020 Feb 23].
Available from: https://scholarworks.rit.edu/theses/83.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Dumont M. Markov chain Monte Carlo on the GPU. [Thesis]. Rochester Institute of Technology; 2011. Available from: https://scholarworks.rit.edu/theses/83
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
7.
Tibbits, Matthew McLean.
Parallel Multivariate Slice Sampling.
Degree: MS, Statistics, 2009, Penn State University
URL: https://etda.libraries.psu.edu/catalog/9151
► Slice sampling provides an easily implemented method for constructing a Markov chain Monte Carlo (MCMC) algorithm. However, slice sampling has two major drawbacks: (i) it…
(more)
▼ Slice sampling provides an easily implemented method
for constructing a Markov chain Monte Carlo (MCMC) algorithm.
However, slice sampling has two major drawbacks: (i) it requires
repeated evaluation of likelihoods for each update, which can make
it impractical when each evaluation is expensive or as the number
of evaluations grows (geometrically) with the dimension of the
slice sampler, and (ii) since it can be challenging to construct
multivariate updates, the updates are typically univariate, often
resulting in slow mixing samplers. We propose an approach to
multivariate slice sampling that naturally lends itself to a
parallel implementation. Our approach takes advantage of recent
advances in computer architecture, for instance, the newest
generation of graphics cards can execute roughly 30,000 threads
simultaneously. We demonstrate that it is possible to construct a
multivariate slice sampler that has good mixing properties and is
efficient in terms of computing time. The contributions of this
article are therefore twofold. We study approaches for constructing
a multivariate slice sampler, and we show how parallel computing
can be useful for making MCMC algorithms computationally efficient.
We study various implementations of our algorithm in the context of
real and simulated data.
Subjects/Keywords: Bayesian inference; Markov chain Monte Carlo;
Para
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APA (6th Edition):
Tibbits, M. M. (2009). Parallel Multivariate Slice Sampling. (Masters Thesis). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/9151
Chicago Manual of Style (16th Edition):
Tibbits, Matthew McLean. “Parallel Multivariate Slice Sampling.” 2009. Masters Thesis, Penn State University. Accessed February 23, 2020.
https://etda.libraries.psu.edu/catalog/9151.
MLA Handbook (7th Edition):
Tibbits, Matthew McLean. “Parallel Multivariate Slice Sampling.” 2009. Web. 23 Feb 2020.
Vancouver:
Tibbits MM. Parallel Multivariate Slice Sampling. [Internet] [Masters thesis]. Penn State University; 2009. [cited 2020 Feb 23].
Available from: https://etda.libraries.psu.edu/catalog/9151.
Council of Science Editors:
Tibbits MM. Parallel Multivariate Slice Sampling. [Masters Thesis]. Penn State University; 2009. Available from: https://etda.libraries.psu.edu/catalog/9151
University of Waterloo
8.
Mathew, Manoj.
The Application of Markov Chain Monte Carlo Techniques in Non-Linear Parameter Estimation for Chemical Engineering Models.
Degree: 2013, University of Waterloo
URL: http://hdl.handle.net/10012/7906
► Modeling of chemical engineering systems often necessitates using non-linear models. These models can range in complexity, from a simple analytical equation to a system of…
(more)
▼ Modeling of chemical engineering systems often necessitates using non-linear models. These models can range in complexity, from a simple analytical equation to a system of differential equations. Regardless of what type of model is being utilized, determining parameter estimates is essential in everyday chemical engineering practice. One promising approach to non-linear regression is a technique called Markov Chain Monte Carlo (MCMC).This method produces reliable parameter estimates and generates joint confidence regions (JCRs) with correct shape and correct probability content. Despite these advantages, its application in chemical engineering literature has been limited. Therefore, in this project, MCMC methods were applied to a variety of chemical engineering models. The objectives of this research is to (1) illustrate how to implement MCMC methods in complex non-linear models (2) show the advantages of using MCMC techniques over classical regression approaches and (3) provide practical guidelines on how to reduce the computational time.
MCMC methods were first applied to the biological oxygen demand (BOD) problem. In this case study, an implementation procedure was outlined using specific examples from the BOD problem. The results from the study illustrated the importance of estimating the pure error variance as a parameter rather than fixing its value based on the mean square error. In addition, a comparison was carried out between the MCMC results and the results obtained from using classical regression approaches. The findings show that although similar point estimates are obtained, JCRs generated from approximation methods cannot model the parameter uncertainty adequately.
Markov Chain Monte Carlo techniques were then applied in estimating reactivity ratios in the Mayo-Lewis model, Meyer-Lowry model, the direct numerical integration model and the triad fraction multiresponse model. The implementation steps for each of these models were discussed in detail and the results from this research were once again compared to previously used approximation methods. Once again, the conclusion drawn from this work showed that MCMC methods must be employed in order to obtain JCRs with the correct shape and correct probability content.
MCMC methods were also applied in estimating kinetic parameter used in the solid oxide fuel cell study. More specifically, the kinetics of the water-gas shift reaction, which is used in generating hydrogen for the fuel cell, was studied. The results from this case study showed how the MCMC output can be analyzed in order to diagnose parameter observability and correlation. A significant portion of the model needed to be reduced due to these issues of observability and correlation. Point estimates and JCRs were then generated using the reduced model and diagnostic checks were carried out in order to ensure the model was able to capture the data adequately.
A few select parameters in the Waterloo Polymer Simulator were estimated using the MCMC algorithm. Previous studies…
Subjects/Keywords: Markov Chain Monte Carlo; Parameter Estimation
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APA (6th Edition):
Mathew, M. (2013). The Application of Markov Chain Monte Carlo Techniques in Non-Linear Parameter Estimation for Chemical Engineering Models. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/7906
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Mathew, Manoj. “The Application of Markov Chain Monte Carlo Techniques in Non-Linear Parameter Estimation for Chemical Engineering Models.” 2013. Thesis, University of Waterloo. Accessed February 23, 2020.
http://hdl.handle.net/10012/7906.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Mathew, Manoj. “The Application of Markov Chain Monte Carlo Techniques in Non-Linear Parameter Estimation for Chemical Engineering Models.” 2013. Web. 23 Feb 2020.
Vancouver:
Mathew M. The Application of Markov Chain Monte Carlo Techniques in Non-Linear Parameter Estimation for Chemical Engineering Models. [Internet] [Thesis]. University of Waterloo; 2013. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/10012/7906.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Mathew M. The Application of Markov Chain Monte Carlo Techniques in Non-Linear Parameter Estimation for Chemical Engineering Models. [Thesis]. University of Waterloo; 2013. Available from: http://hdl.handle.net/10012/7906
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of New South Wales
9.
Peters, Gareth William.
Advances in approximate Bayesian computation and trans-dimensional sampling methodology.
Degree: Mathematics & Statistics, 2010, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/50086
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9018/SOURCE02?view=true
► Bayesian statistical models continue to grow in complexity, drivenin part by a few key factors: the massive computational resourcesnow available to statisticians; the substantial gains…
(more)
▼ Bayesian statistical models continue to grow in complexity, drivenin part by a few key factors: the massive computational resourcesnow available to statisticians; the substantial gains made insampling methodology and algorithms such as
Markov chainMonte
Carlo (MCMC), trans-dimensional MCMC (TDMCMC), sequentialMonte
Carlo (SMC), adaptive algorithms and stochasticapproximation methods and approximate Bayesian computation (ABC);and development of more realistic models for real world phenomenaas demonstrated in this thesis for financial models andtelecommunications engineering. Sophisticated statistical modelsare increasingly proposed for practical solutions to real world problems in order to better capture salient features ofincreasingly more complex data. With sophistication comes aparallel requirement for more advanced and automated statisticalcomputational methodologies.The key focus of this thesis revolves around innovation related tothe following three significant Bayesian research questions.1. How can one develop practically useful Bayesian models and corresponding computationally efficient sampling methodology, when the likelihood model is intractable?2. How can one develop methodology in order to automate
Markov chain Monte Carlo sampling approaches to efficiently explore the support of a posterior distribution, defined across multiple Bayesian statistical models?3. How can these sophisticated Bayesian modelling frameworks and sampling methodologies be utilized to solve practically relevant and important problems in the research fields of financial risk modeling and telecommunications engineering ?This thesis is split into three bodies of work represented inthree parts. Each part contains journal papers with novelstatistical model and sampling methodological development. Thecoherent link between each part involves the novelsampling methodologies developed in Part I and utilized in Part II and Part III. Papers contained ineach part make progress at addressing the core researchquestions posed.Part I of this thesis presents generally applicable keystatistical sampling methodologies that will be utilized andextended in the subsequent two parts. In particular it presentsnovel developments in statistical methodology pertaining tolikelihood-free or ABC and TDMCMC methodology.The TDMCMC methodology focuses on several aspects of automationin the between model proposal construction, includingapproximation of the optimal between model proposal kernel via aconditional path sampling density estimator. Then this methodologyis explored for several novel Bayesian model selectionapplications including cointegrated vector autoregressions (CVAR)models and mixture models in which there is an unknown number ofmixture components. The second area relates to development ofABC methodology with particular focuson SMC Samplers methodology in an ABC context via PartialRejection Control (PRC). In addition to novel algorithmicdevelopment, key theoretical properties are also studied for theclasses of algorithms developed. Then this…
Advisors/Committee Members: Sisson, Scott, Mathematics & Statistics, Faculty of Science, UNSW, Fan, Yanan, Mathematics & Statistics, Faculty of Science, UNSW, Shevchenko, Pavel, CSIRO.
Subjects/Keywords: Sequential Monte Carlo; Markov Chain Monte Carlo; Approximate Bayesian Computation
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APA (6th Edition):
Peters, G. W. (2010). Advances in approximate Bayesian computation and trans-dimensional sampling methodology. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/50086 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9018/SOURCE02?view=true
Chicago Manual of Style (16th Edition):
Peters, Gareth William. “Advances in approximate Bayesian computation and trans-dimensional sampling methodology.” 2010. Doctoral Dissertation, University of New South Wales. Accessed February 23, 2020.
http://handle.unsw.edu.au/1959.4/50086 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9018/SOURCE02?view=true.
MLA Handbook (7th Edition):
Peters, Gareth William. “Advances in approximate Bayesian computation and trans-dimensional sampling methodology.” 2010. Web. 23 Feb 2020.
Vancouver:
Peters GW. Advances in approximate Bayesian computation and trans-dimensional sampling methodology. [Internet] [Doctoral dissertation]. University of New South Wales; 2010. [cited 2020 Feb 23].
Available from: http://handle.unsw.edu.au/1959.4/50086 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9018/SOURCE02?view=true.
Council of Science Editors:
Peters GW. Advances in approximate Bayesian computation and trans-dimensional sampling methodology. [Doctoral Dissertation]. University of New South Wales; 2010. Available from: http://handle.unsw.edu.au/1959.4/50086 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:9018/SOURCE02?view=true
University of Edinburgh
10.
Matthews, James.
Markov chains for sampling matchings.
Degree: 2008, University of Edinburgh
URL: http://hdl.handle.net/1842/3072
► Markov Chain Monte Carlo algorithms are often used to sample combinatorial structures such as matchings and independent sets in graphs. A Markov chain is defined…
(more)
▼ Markov Chain Monte Carlo algorithms are often used to sample combinatorial structures such as matchings and independent sets in graphs. A Markov chain is defined whose state space includes the desired sample space, and which has an appropriate stationary distribution. By simulating the chain for a sufficiently large number of steps, we can sample from a distribution arbitrarily close to the stationary distribution. The number of steps required to do this is known as the mixing time of the Markov chain. In this thesis, we consider a number of Markov chains for sampling matchings, both in general and more restricted classes of graphs, and also for sampling independent sets in claw-free graphs. We apply techniques for showing rapid mixing based on two main approaches: coupling and conductance. We consider chains using single-site moves, and also chains using large block moves. Perfect matchings of bipartite graphs are of particular interest in our community. We investigate the mixing time of a Markov chain for sampling perfect matchings in a restricted class of bipartite graphs, and show that its mixing time is exponential in some instances. For a further restricted class of graphs, however, we can show subexponential mixing time. One of the techniques for showing rapid mixing is coupling. The bound on the mixing time depends on a contraction ratio b. Ideally, b < 1, but in the case b = 1 it is still possible to obtain a bound on the mixing time, provided there is a sufficiently large probability of contraction for all pairs of states. We develop a lemma which obtains better bounds on the mixing time in this case than existing theorems, in the case where b = 1 and the probability of a change in distance is proportional to the distance between the two states. We apply this lemma to the Dyer-Greenhill chain for sampling independent sets, and to a Markov chain for sampling 2D-colourings.
Subjects/Keywords: 004; Informatics; Computer Science; Markov Chain Monte Carlo algorithm; Markov chain
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APA (6th Edition):
Matthews, J. (2008). Markov chains for sampling matchings. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/3072
Chicago Manual of Style (16th Edition):
Matthews, James. “Markov chains for sampling matchings.” 2008. Doctoral Dissertation, University of Edinburgh. Accessed February 23, 2020.
http://hdl.handle.net/1842/3072.
MLA Handbook (7th Edition):
Matthews, James. “Markov chains for sampling matchings.” 2008. Web. 23 Feb 2020.
Vancouver:
Matthews J. Markov chains for sampling matchings. [Internet] [Doctoral dissertation]. University of Edinburgh; 2008. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1842/3072.
Council of Science Editors:
Matthews J. Markov chains for sampling matchings. [Doctoral Dissertation]. University of Edinburgh; 2008. Available from: http://hdl.handle.net/1842/3072
University of Melbourne
11.
Vu, Tuyet Thi Anh.
A Particle Markov Chain Monte Carlo algorithm for random finite set based multi-target tracking.
Degree: 2011, University of Melbourne
URL: http://hdl.handle.net/11343/36875
► The multi target tracking (MTT) problem is essentially that of estimating the presence and associated time trajectories of moving objects based on measurements from a…
(more)
▼ The multi target tracking (MTT) problem is essentially that of estimating the presence and associated time trajectories of moving objects based on measurements from a variety of sensors. Tracking a large number of unknown targets which move close and cross each other such as biological cells becomes difficult. The targets being tracked may randomly appear and disappear from the field of view, they may be temporarily obscured by other objects, may merge and split, may spawn other targets, and may cross or travel very close to each other for extended periods of time. Sensor measurements also present a number of challenging characteristics, such as noise which introduces location errors and may cause missed detection of targets, false measurements which do not belong to a valid target of interest, ghosting, misidentification etc.
A new approach to this problem is proposed by first formulating the problem in a random set finite framework and then using the Particle Markov Chain Monte Carlo (PMCMC) method for solving the problem. Under the random finite set (RFS) framework originally proposed by Mahler, a multi-target posterior distribution is propagated recursively via a Bayesian framework. The intractability of the posterior distribution is computed by using the PMCMC method that uses the sequential Monte Carlo outputs for the Markov Chain Monte Carlo (MCMC) method.
A RFS is a finite-set valued random variable. Alternatively, RFS can be interpreted as a random variable that is random in number of elements and in the values of these elements themselves and that the order of its elements is irrelevant. As a result, the RFS framework is a mathematically rigorous tool for capturing all uncertainties of its elements and its cardinality. With the uncertain properties of the MTT problem, the RFS framework is naturally used to formulate the MTT problem to capture the essence of MTT problem and then allows the multi-target posterior distribution to be propagated via a Bayesian framework. The first contribution of this dissertation is to derive the posterior distribution for the trajectories of the targets that is the special case for the multi-target posterior distribution. The multi-target posterior distribution is intractable so an approximation method such as PMCMC is required. PMCMC methods proposed by use the Sequential Monte Carlo (SMC) algorithm to design an efficient high dimensional proposal distribution for the Markov Chain Monte Carlo (MCMC) method. The premise of this method is to sample from any distribution which has no closed form solution and which applying the traditional MCMC method or SMC method fails to give a reliable solution or is unfeasible on its own. The second contribution is to derive a RFS based PMCMC algorithm and implement this algorithm for the multi-target tracking problem when targets move close and/or cross each other in a dense environment and the number of targets is unknown.
Subjects/Keywords: multi-target tracking; Particle Markov Chain Monte Carlo; Markov Chain Monte Carlo; random sets; Sequential Monte Carlo
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APA (6th Edition):
Vu, T. T. A. (2011). A Particle Markov Chain Monte Carlo algorithm for random finite set based multi-target tracking. (Doctoral Dissertation). University of Melbourne. Retrieved from http://hdl.handle.net/11343/36875
Chicago Manual of Style (16th Edition):
Vu, Tuyet Thi Anh. “A Particle Markov Chain Monte Carlo algorithm for random finite set based multi-target tracking.” 2011. Doctoral Dissertation, University of Melbourne. Accessed February 23, 2020.
http://hdl.handle.net/11343/36875.
MLA Handbook (7th Edition):
Vu, Tuyet Thi Anh. “A Particle Markov Chain Monte Carlo algorithm for random finite set based multi-target tracking.” 2011. Web. 23 Feb 2020.
Vancouver:
Vu TTA. A Particle Markov Chain Monte Carlo algorithm for random finite set based multi-target tracking. [Internet] [Doctoral dissertation]. University of Melbourne; 2011. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/11343/36875.
Council of Science Editors:
Vu TTA. A Particle Markov Chain Monte Carlo algorithm for random finite set based multi-target tracking. [Doctoral Dissertation]. University of Melbourne; 2011. Available from: http://hdl.handle.net/11343/36875
12.
Santos, Tássio Naia dos.
Grafos aleatórios exponenciais.
Degree: Mestrado, Ciência da Computação, 2013, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/45/45134/tde-19022014-195734/
;
► Estudamos o comportamento da familia aresta-triangulo de grafos aleatorios exponenciais (ERG) usando metodos de Monte Carlo baseados em Cadeias de Markov. Comparamos contagens de subgrafos…
(more)
▼ Estudamos o comportamento da familia aresta-triangulo de grafos aleatorios exponenciais (ERG) usando metodos de Monte Carlo baseados em Cadeias de Markov. Comparamos contagens de subgrafos e correlacoes entre arestas de ergs as de Grafos Aleatorios Binomiais (BRG, tambem chamados de Erdos-Renyi). E um resultado teorico conhecido que para algumas parametrizacoes os limites das contagens de subgrafos de ERGs convergem para os de BRGs, assintoticamente no numero de vertices [BBS11, CD11]. Observamos esse fenomeno em grafos com poucos (20) vertices em nossas simulacoes.
We study the behavior of the edge-triangle family of exponential random graphs (ERG) using the Markov Chain Monte Carlo method. We compare ERG subgraph counts and edge correlations to those of the classic Binomial Random Graph (BRG, also called Erdos-Renyi model). It is a known theoretical result that for some parameterizations the limit ERG subgraph counts converge to those of BRGs, as the number of vertices grows [BBS11, CD11]. We observe this phenomenon on graphs with few (20) vertices in our simulations.
Advisors/Committee Members: Kohayakawa, Yoshiharu.
Subjects/Keywords: Cadeia de Markov; Combinatória; Combinatorics; Grafos Aleatórios; Markov Chain; Monte Carlo; Monte Carlo; Random Graphs
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APA (6th Edition):
Santos, T. N. d. (2013). Grafos aleatórios exponenciais. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45134/tde-19022014-195734/ ;
Chicago Manual of Style (16th Edition):
Santos, Tássio Naia dos. “Grafos aleatórios exponenciais.” 2013. Masters Thesis, University of São Paulo. Accessed February 23, 2020.
http://www.teses.usp.br/teses/disponiveis/45/45134/tde-19022014-195734/ ;.
MLA Handbook (7th Edition):
Santos, Tássio Naia dos. “Grafos aleatórios exponenciais.” 2013. Web. 23 Feb 2020.
Vancouver:
Santos TNd. Grafos aleatórios exponenciais. [Internet] [Masters thesis]. University of São Paulo; 2013. [cited 2020 Feb 23].
Available from: http://www.teses.usp.br/teses/disponiveis/45/45134/tde-19022014-195734/ ;.
Council of Science Editors:
Santos TNd. Grafos aleatórios exponenciais. [Masters Thesis]. University of São Paulo; 2013. Available from: http://www.teses.usp.br/teses/disponiveis/45/45134/tde-19022014-195734/ ;
The Ohio State University
13.
Olsen, Andrew Nolan.
When Infinity is Too Long to Wait: On the Convergence of
Markov Chain Monte Carlo Methods.
Degree: PhD, Statistics, 2015, The Ohio State University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1433770406
► Markov chains are an incredibly powerful tool for statisticians and other practitioners. They allow for random draws, though autocorrelated, to be obtained from a vast…
(more)
▼ Markov chains are an incredibly powerful tool for
statisticians and other practitioners. They allow for random draws,
though autocorrelated, to be obtained from a vast array of target
distributions, even when the distribution is known only up to a
constant. These draws may then be used to answer key questions of
interest.
Markov chains are used in many settings and are the
predominant method for performing inference for Bayesian methods.
The utility of
Markov chains lies largely in the simplicity with
which they are implemented. The most basic algorithms are easily
understood and are not challenging to program. The trade-off with
ease of implementation, however, is that issues with
Markov chains,
particularly with respect to convergence, can occasionally be left
undiagnosed. For example, a
Markov chain may not have been run long
enough to accurately capture the features of the distribution of
interest, or perhaps the error of the resulting estimates is
grossly underrepresented, if it is considered at all.The study of
Markov chain convergence can be summarized by two main
questions:Question 1: Was the simulation run long enough? Question
2: How accurate are the resulting estimates?While simple and clear,
these questions are often left unanswered when
Markov chain Monte
Carlo methods are implemented. This is largely due to the fact that
these answers require theoretical analysis of the convergence of
the
Markov chain, which can be challenging. This dissertation
discusses the theory of
Markov chains and their convergence,
including how to rigorously answer Question 1 and Question 2. A
variety of methods are available, and several are illustrated with
examples.One approach answers Question 1 by obtaining draws that
approximate the target distribution closely.
Markov chains may then
be started from these draws, resulting in immediate closeness to
the target distribution. Several algorithms for accomplishing this
are introduced and developed. Results are provided which quantify
the quality of the approximations. A comparison of the efficiency
of the algorithms is also provided. Another approach is the formal
establishment of convergence rates. Once these are established, one
method to answer Question 1 is to compute the number of iterations
required so that the ultimate distribution obtained is close to the
target distribution. This approach is also illustrated with
examples.A final approach is to compute standard errors of the
resulting estimates, which directly answers Question 2. Question 1,
however, is also answered because when estimates are accurate
enough, the
chain has been run for a sufficient duration. This is
similarly illustrated with examples.Bayesian scale-usage models are
used to analyze surveys where individual respondents differ in
their use of a rating scale. The convergence rate theory for these
models, which guarantees answers to Question 1 and Question 2, is
fully established. The methods are then extended to a setting where
demographics can govern the way in which respondents differ in
their answer…
Advisors/Committee Members: Herbei, Radu (Advisor).
Subjects/Keywords: Statistics; Markov chain Monte Carlo convergence; Markov chain Monte Carlo standard errors; geometric ergodicity; scale-usage heterogeneity
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APA (6th Edition):
Olsen, A. N. (2015). When Infinity is Too Long to Wait: On the Convergence of
Markov Chain Monte Carlo Methods. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1433770406
Chicago Manual of Style (16th Edition):
Olsen, Andrew Nolan. “When Infinity is Too Long to Wait: On the Convergence of
Markov Chain Monte Carlo Methods.” 2015. Doctoral Dissertation, The Ohio State University. Accessed February 23, 2020.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1433770406.
MLA Handbook (7th Edition):
Olsen, Andrew Nolan. “When Infinity is Too Long to Wait: On the Convergence of
Markov Chain Monte Carlo Methods.” 2015. Web. 23 Feb 2020.
Vancouver:
Olsen AN. When Infinity is Too Long to Wait: On the Convergence of
Markov Chain Monte Carlo Methods. [Internet] [Doctoral dissertation]. The Ohio State University; 2015. [cited 2020 Feb 23].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1433770406.
Council of Science Editors:
Olsen AN. When Infinity is Too Long to Wait: On the Convergence of
Markov Chain Monte Carlo Methods. [Doctoral Dissertation]. The Ohio State University; 2015. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1433770406
University of Edinburgh
14.
Graham, Matthew McKenzie.
Auxiliary variable Markov chain Monte Carlo methods.
Degree: PhD, 2018, University of Edinburgh
URL: http://hdl.handle.net/1842/28962
► Markov chain Monte Carlo (MCMC) methods are a widely applicable class of algorithms for estimating integrals in statistical inference problems. A common approach in MCMC…
(more)
▼ Markov chain Monte Carlo (MCMC) methods are a widely applicable class of algorithms for estimating integrals in statistical inference problems. A common approach in MCMC methods is to introduce additional auxiliary variables into the Markov chain state and perform transitions in the joint space of target and auxiliary variables. In this thesis we consider novel methods for using auxiliary variables within MCMC methods to allow approximate inference in otherwise intractable models and to improve sampling performance in models exhibiting challenging properties such as multimodality. We first consider the pseudo-marginal framework. This extends the Metropolis–Hastings algorithm to cases where we only have access to an unbiased estimator of the density of target distribution. The resulting chains can sometimes show ‘sticking’ behaviour where long series of proposed updates are rejected. Further the algorithms can be difficult to tune and it is not immediately clear how to generalise the approach to alternative transition operators. We show that if the auxiliary variables used in the density estimator are included in the chain state it is possible to use new transition operators such as those based on slice-sampling algorithms within a pseudo-marginal setting. This auxiliary pseudo-marginal approach leads to easier to tune methods and is often able to improve sampling efficiency over existing approaches. As a second contribution we consider inference in probabilistic models defined via a generative process with the probability density of the outputs of this process only implicitly defined. The approximate Bayesian computation (ABC) framework allows inference in such models when conditioning on the values of observed model variables by making the approximation that generated observed variables are ‘close’ rather than exactly equal to observed data. Although making the inference problem more tractable, the approximation error introduced in ABC methods can be difficult to quantify and standard algorithms tend to perform poorly when conditioning on high dimensional observations. This often requires further approximation by reducing the observations to lower dimensional summary statistics. We show how including all of the random variables used in generating model outputs as auxiliary variables in a Markov chain state can allow the use of more efficient and robust MCMC methods such as slice sampling and Hamiltonian Monte Carlo (HMC) within an ABC framework. In some cases this can allow inference when conditioning on the full set of observed values when standard ABC methods require reduction to lower dimensional summaries for tractability. Further we introduce a novel constrained HMC method for performing inference in a restricted class of differentiable generative models which allows conditioning the generated observed variables to be arbitrarily close to observed data while maintaining computational tractability. As a final topicwe consider the use of an auxiliary temperature variable in MCMC methods to improve exploration of…
Subjects/Keywords: probability theory; Markov chain Monte Carlo algorithm; Metropolis–Hastings algorithm; algorithms; Hamiltonian Monte Carlo
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APA (6th Edition):
Graham, M. M. (2018). Auxiliary variable Markov chain Monte Carlo methods. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/28962
Chicago Manual of Style (16th Edition):
Graham, Matthew McKenzie. “Auxiliary variable Markov chain Monte Carlo methods.” 2018. Doctoral Dissertation, University of Edinburgh. Accessed February 23, 2020.
http://hdl.handle.net/1842/28962.
MLA Handbook (7th Edition):
Graham, Matthew McKenzie. “Auxiliary variable Markov chain Monte Carlo methods.” 2018. Web. 23 Feb 2020.
Vancouver:
Graham MM. Auxiliary variable Markov chain Monte Carlo methods. [Internet] [Doctoral dissertation]. University of Edinburgh; 2018. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1842/28962.
Council of Science Editors:
Graham MM. Auxiliary variable Markov chain Monte Carlo methods. [Doctoral Dissertation]. University of Edinburgh; 2018. Available from: http://hdl.handle.net/1842/28962
15.
Minvielle-Larrousse, Pierre.
Méthodes de simulation stochastique pour le traitement de l’information : Stochastic simulation methods for information processing.
Degree: Docteur es, Mathématiques, 2019, Pau
URL: http://www.theses.fr/2019PAUU3005
► Lorsqu’une grandeur d’intérêt ne peut être directement mesurée, il est fréquent de procéder à l’observation d’autres quantités qui lui sont liées par des lois physiques.…
(more)
▼ Lorsqu’une grandeur d’intérêt ne peut être directement mesurée, il est fréquent de procéder à l’observation d’autres quantités qui lui sont liées par des lois physiques. Ces quantités peuvent contenir de l’information sur la grandeur d’intérêt si l’on sait résoudre le problème inverse, souvent mal posé, et inférer la valeur. L’inférence bayésienne constitue un outil statistique puissant pour l’inversion, qui requiert le calcul d’intégrales en grande dimension. Les méthodes Monte Carlo séquentielles (SMC), aussi dénommées méthodes particulaires, sont une classe de méthodes Monte Carlo permettant d’échantillonner selon une séquence de densités de probabilité de dimension croissante. Il existe de nombreuses applications, que ce soit en filtrage, en optimisation globale ou en simulation d’évènement rare. Les travaux ont porté notamment sur l’extension des méthodes SMC dans un contexte dynamique où le système, régi par un processus de Markov caché, est aussi déterminé par des paramètres statiques que l’on cherche à estimer. En estimation bayésienne séquentielle, la détermination de paramètres fixes provoque des difficultés particulières : un tel processus est non-ergodique, le système n’oubliant pas ses conditions initiales. Il est montré comment il est possible de surmonter ces difficultés dans une application de poursuite et identification de formes géométriques par caméra numérique CCD. Des étapes d’échantillonnage MCMC (Chaîne de Markov Monte Carlo) sont introduites pour diversifier les échantillons sans altérer la distribution a posteriori. Pour une autre application de contrôle de matériau, qui cette fois « hors ligne » mêle paramètres statiques et dynamiques, on a proposé une approche originale. Elle consiste en un algorithme PMMH (Particle Marginal Metropolis-Hastings) intégrant des traitements SMC Rao-Blackwellisés, basés sur des filtres de Kalman d’ensemble en interaction.D’autres travaux en traitement de l’information ont été menés, que ce soit en filtrage particulaire pour la poursuite d’un véhicule en phase de rentrée atmosphérique, en imagerie radar 3D par régularisation parcimonieuse ou en recalage d’image par information mutuelle.
When a quantity of interest is not directly observed, it is usual to observe other quantities that are linked by physical laws. They can provide information about the quantity of interest if it is able to solve the inverse problem, often ill posed, and infer the value. Bayesian inference is a powerful tool for inversion that requires the computation of high dimensional integrals. Sequential Monte Carlo (SMC) methods, a.k.a. interacting particles methods, are a type of Monte Carlo methods that are able to sample from a sequence of probability densities of growing dimension. They are many applications, for instance in filtering, in global optimization or rare event simulation.The work has focused in particular on the extension of SMC methods in a dynamic context where the system, governed by a hidden Markov process, is also determined by static parameters that we seek to…
Advisors/Committee Members: Tordeux, Sébastien (thesis director).
Subjects/Keywords: Statistiques appliquées; Problème inverse; Monte Carlo séquentiel; Chaîne de Markov Monte Carlo; Applied statistics; Inverse problem; Sequential Monte Carlo; Markov Chain Monte Carlo; 510
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APA (6th Edition):
Minvielle-Larrousse, P. (2019). Méthodes de simulation stochastique pour le traitement de l’information : Stochastic simulation methods for information processing. (Doctoral Dissertation). Pau. Retrieved from http://www.theses.fr/2019PAUU3005
Chicago Manual of Style (16th Edition):
Minvielle-Larrousse, Pierre. “Méthodes de simulation stochastique pour le traitement de l’information : Stochastic simulation methods for information processing.” 2019. Doctoral Dissertation, Pau. Accessed February 23, 2020.
http://www.theses.fr/2019PAUU3005.
MLA Handbook (7th Edition):
Minvielle-Larrousse, Pierre. “Méthodes de simulation stochastique pour le traitement de l’information : Stochastic simulation methods for information processing.” 2019. Web. 23 Feb 2020.
Vancouver:
Minvielle-Larrousse P. Méthodes de simulation stochastique pour le traitement de l’information : Stochastic simulation methods for information processing. [Internet] [Doctoral dissertation]. Pau; 2019. [cited 2020 Feb 23].
Available from: http://www.theses.fr/2019PAUU3005.
Council of Science Editors:
Minvielle-Larrousse P. Méthodes de simulation stochastique pour le traitement de l’information : Stochastic simulation methods for information processing. [Doctoral Dissertation]. Pau; 2019. Available from: http://www.theses.fr/2019PAUU3005
16.
Chernoukhov, Alexander.
Bayesian Spatial Additive Hazard Model.
Degree: MS, Mathematics and
Statistics, 2013, National Library of Canada
URL: http://scholar.uwindsor.ca/etd/4965
► This thesis will be dealing with the problem of Bayesian estimation in additive survival data models accounting for spatial dependencies. We consider the Aalen's…
(more)
▼ This thesis will be dealing with the
problem of Bayesian estimation in additive survival data models
accounting for spatial dependencies. We consider the Aalen's
additive hazards model in which baseline hazard function, the
regression coecients as well as the covariates are all allowed to
be time varying processes. We incorporate in this model an extra
random vector of frailties accounting for spatial variations among
the observations. Consequently, we propose a Bayesian approach to
solving the inference problem for such spatial frailty model by
assuming piece-wise constant structure on all timevarying functions
in the model and hence, imposing appropriately chosen priors on all
model parameters. We then employ some versions of MCMC and Gibbs
sampling approaches to carry out the inference about the model
parameters and apply the resulting algorithm to Prostate cancer
diagnosis data for the state of Louisiana, taken from the
Surveillance, Epidemiology, and End Results (SEER)
databases.
Advisors/Committee Members: Hussein, Abdulkadir, Nkurunziza, Severien.
Subjects/Keywords: Pure sciences; Additive hazard; Bayesian; Markov chain monte carlo; Spatial; Survival
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APA (6th Edition):
Chernoukhov, A. (2013). Bayesian Spatial Additive Hazard Model. (Masters Thesis). National Library of Canada. Retrieved from http://scholar.uwindsor.ca/etd/4965
Chicago Manual of Style (16th Edition):
Chernoukhov, Alexander. “Bayesian Spatial Additive Hazard Model.” 2013. Masters Thesis, National Library of Canada. Accessed February 23, 2020.
http://scholar.uwindsor.ca/etd/4965.
MLA Handbook (7th Edition):
Chernoukhov, Alexander. “Bayesian Spatial Additive Hazard Model.” 2013. Web. 23 Feb 2020.
Vancouver:
Chernoukhov A. Bayesian Spatial Additive Hazard Model. [Internet] [Masters thesis]. National Library of Canada; 2013. [cited 2020 Feb 23].
Available from: http://scholar.uwindsor.ca/etd/4965.
Council of Science Editors:
Chernoukhov A. Bayesian Spatial Additive Hazard Model. [Masters Thesis]. National Library of Canada; 2013. Available from: http://scholar.uwindsor.ca/etd/4965
Texas A&M University
17.
Hwang, Kyubum.
Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method.
Degree: 2010, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-680
► More difficulties are now expected in exploring economically valuable reservoirs because most reservoirs have been already developed since beginning seismic exploration of the subsurface. In…
(more)
▼ More difficulties are now expected in exploring economically valuable reservoirs
because most reservoirs have been already developed since beginning seismic exploration
of the subsurface. In order to efficiently analyze heterogeneous fine-scale properties
in subsurface layers, one ongoing challenge is accurately upscaling fine-scale
(high frequency) logging measurements to coarse-scale data, such as surface seismic
images. In addition, numerically efficient modeling cannot use models defined on the
scale of log data. At this point, we need an upscaling method replaces the small scale
data with simple large scale models. However, numerous unavoidable uncertainties
still exist in the upscaling process, and these problems have been an important emphasis
in geophysics for years. Regarding upscaling problems, there are predictable
or unpredictable uncertainties in upscaling processes; such as, an averaging method,
an upscaling algorithm, analysis of results, and so forth.
To minimize the uncertainties, a Bayesian framework could be a useful tool for
providing the posterior information to give a better estimate for a chosen model
with a conditional probability. In addition, the likelihood of a Bayesian framework
plays an important role in quantifying misfits between the measured data and the
calculated parameters. Therefore, Bayesian methodology can provide a good solution
for quantification of uncertainties in upscaling.
When analyzing many uncertainties in porosities, wave velocities, densities, and
thicknesses of rocks through upscaling well log data, the
Markov Chain Monte Carlo
(MCMC) method is a potentially beneficial tool that uses randomly generated parameters
with a Bayesian framework producing the posterior information. In addition,
the method provides reliable model parameters to estimate economic values of hydrocarbon
reservoirs, even though log data include numerous unknown factors due to
geological heterogeneity. In this thesis, fine layered well log data from the North Sea
were selected with a depth range of 1600m to 1740m for upscaling using an MCMC implementation. The results allow us to automatically identify important depths
where interfaces should be located, along with quantitative estimates of uncertainty
in data. Specifically, interfaces in the example are required near depths of 1,650m,
1,695m, 1,710m, and 1,725m. Therefore, the number and location of blocked layers
can be effectively quantified in spite of uncertainties in upscaling log data.
Advisors/Committee Members: Gibson, Richard L. (advisor), Blasingagme, Tomas A. (committee member), Sun, Yuefeng (committee member).
Subjects/Keywords: Upscaling; Markov Chain Monte Carlo; MCMC; Bayesian Framework
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APA (6th Edition):
Hwang, K. (2010). Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method. (Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-680
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Hwang, Kyubum. “Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method.” 2010. Thesis, Texas A&M University. Accessed February 23, 2020.
http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-680.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Hwang, Kyubum. “Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method.” 2010. Web. 23 Feb 2020.
Vancouver:
Hwang K. Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method. [Internet] [Thesis]. Texas A&M University; 2010. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-680.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Hwang K. Uncertainty Analysis in Upscaling Well Log data By Markov Chain Monte Carlo Method. [Thesis]. Texas A&M University; 2010. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-680
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
The Ohio State University
18.
Yang, Chao.
ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN
COMPLEX SYSTEMS.
Degree: PhD, Mechanical Engineering, 2017, The Ohio State University
URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962
► This dissertation aims to study three crucial problems related to Monte Carlo based particle methods for solving uncertainty quantification problems in complex systems. The first…
(more)
▼ This dissertation aims to study three crucial problems
related to
Monte Carlo based particle methods for solving
uncertainty quantification problems in complex systems. The first
problem concerns the existence of a "benchmark" sampling method
that i.) can generate an ensemble directly drawn from the unknown,
propagated state pdf, and ii.) guarantee the quality of the
aforementioned ensemble with respect to the true evolved state
uncertainty at all future times. In this context, a new particle
uncertainty forecasting framework is proposed that combines
Markov
chain Monte Carlo (MCMC) sampling with the method of
characteristics (MOC). The resulting MCMC-MOC ensemble is by
construction, directly sampled from the true (and unknown)
propagated state probability density function, and thereby
equivalent in measure to the truth. Inspired by the new MCMC-MOC
approach, a second problem on the transient effectiveness of MCS is
posed in the context of
Markov chain Monte Carlo theory. The
propagated ensemble is viewed as the realization of a
Markov chain
at each time instant, generated by an associated instantaneous
transition kernel. An equation governing the time evolution of the
transition kernel is developed. It is shown that for a special
class of nonlinear systems that have zero divergence, the
propagated kernel is in detailed balance with the true state
probability density function. This guarantees statistical
consistency of the MCS ensemble with the truth at all times for
such systems. The third and final problem addressed in this
dissertation is the following: "is it possible to develop
adaptation rules for MCS such that it may perform within prescribed
bounds of accuracy using the "minimum" possible number of
simulations at all future times?" In the context of this problem, a
new adaptive MCS framework is developed. This approach is designed
to control its transient performance as well as the associated
computational load on-the-fly. When the transient performance of
MCS fails to meet the user-defined lower bound on its accuracy,
"optimally" selected particles are sequentially introduced at the
initial time, and then forward propagated to join the current
ensemble until it reaches the required level of accuracy. This is
done by following a two-layer approach targeted at improving its
rate of convergence by satisfying both non-collapsing and
space-filling properties. On the other hand, when MCS exceeds the
prescribed accuracy level, particles are removed from the current
ensemble in the interest of reducing computational load. Particle
removal is based on their relative weightage evaluated via the
associated stochastic Liouville equation. Finally, numerical
simulations are given to illustrate the benefits of the developed
tools for solving uncertainty forecasting problems, including
applications in space situational awareness and wind
forecasting.
Advisors/Committee Members: Kumar, Mrinal (Advisor).
Subjects/Keywords: Mechanical Engineering; Markov chain Monte Carlo theory; Mechanical Engineering
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APA (6th Edition):
Yang, C. (2017). ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN
COMPLEX SYSTEMS. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962
Chicago Manual of Style (16th Edition):
Yang, Chao. “ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN
COMPLEX SYSTEMS.” 2017. Doctoral Dissertation, The Ohio State University. Accessed February 23, 2020.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962.
MLA Handbook (7th Edition):
Yang, Chao. “ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN
COMPLEX SYSTEMS.” 2017. Web. 23 Feb 2020.
Vancouver:
Yang C. ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN
COMPLEX SYSTEMS. [Internet] [Doctoral dissertation]. The Ohio State University; 2017. [cited 2020 Feb 23].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962.
Council of Science Editors:
Yang C. ON PARTICLE METHODS FOR UNCERTAINTY QUANTIFICATION IN
COMPLEX SYSTEMS. [Doctoral Dissertation]. The Ohio State University; 2017. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1511967797285962
University of New Mexico
19.
Gong, Maozhen.
Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models.
Degree: Mathematics & Statistics, 2015, University of New Mexico
URL: http://hdl.handle.net/1928/27788
► Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive…
(more)
▼ Selecting an appropriate prior distribution is a fundamental issue in Bayesian Statistics. In this dissertation, under the framework provided by Berger and Bernardo, I derive the reference priors for several models which include: Analysis of Variance (ANOVA)/Analysis of Covariance (ANCOVA) models with a categorical variable under common ordering constraints, the conditionally autoregressive (CAR) models and the simultaneous autoregressive (SAR) models with a spatial autoregression parameter considered. The performances of reference priors for ANOVA/ANCOVA models are evaluated by simulation studies with comparisons to Jeffreys' prior and Least Squares Estimation (LSE). The priors are then illustrated in a Bayesian model of the "Risk of Type 2 Diabetes in New Mexico" data, where the relationship between the type 2 diabetes risk (through Hemoglobin A1c) and different smoking levels is investigated. In both simulation studies and real data set modeling, the reference priors that incorporate internal order information show good performances and can be used as default priors. The reference priors for the CAR and SAR models are also illustrated in the "1999 SAT State Average Verbal Scores" data with a comparison to a Uniform prior distribution. Due to the complexity of the reference priors for both CAR and SAR models, only a portion (12 states in the Midwest) of the original data set is considered. The reference priors can give a different marginal posterior distribution compared to a Uniform prior, which provides an alternative for prior specifications for areal data in Spatial statistics.
Advisors/Committee Members: Huerta, Gabriel, Erhardt, Erik, Zhang, Guoyi, Luan, Shuang.
Subjects/Keywords: Bayesian Models; Non-informative priors; Markov chain Monte Carlo.
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MLA ·
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CSE |
Export
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APA (6th Edition):
Gong, M. (2015). Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/27788
Chicago Manual of Style (16th Edition):
Gong, Maozhen. “Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models.” 2015. Doctoral Dissertation, University of New Mexico. Accessed February 23, 2020.
http://hdl.handle.net/1928/27788.
MLA Handbook (7th Edition):
Gong, Maozhen. “Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models.” 2015. Web. 23 Feb 2020.
Vancouver:
Gong M. Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models. [Internet] [Doctoral dissertation]. University of New Mexico; 2015. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1928/27788.
Council of Science Editors:
Gong M. Order-Constrained Reference Priors with Implications for Bayesian Isotonic Regression, Analysis of Covariance and Spatial Models. [Doctoral Dissertation]. University of New Mexico; 2015. Available from: http://hdl.handle.net/1928/27788
University of New Mexico
20.
Herskowitz, Lawrence.
Kinetic and Statistical Mechanical Modeling of DNA Unzipping and Kinesin Mechanochemistry.
Degree: Physics & Astronomy, 2011, University of New Mexico
URL: http://hdl.handle.net/1928/12079
► This thesis explores two topics. The first is shotgun DNA mapping (SDM). Ability to map polymerases and nucleosomes on chromatin is important for understanding the…
(more)
▼ This thesis explores two topics. The first is shotgun DNA mapping (SDM). Ability to map polymerases and nucleosomes on chromatin is important for understanding the impact of chromatin remodeling on key cellular processes. Current methods have produced a wealth of information that demonstrates this importance, but key information is elusive in these methods. We are pursuing a new single-molecule chromatin mapping method based on unzipping native chromatin molecules with optical tweezers. The first step we are taking towards this ability is SDM. This is the ability to identify the genomic location of a random DNA fragment based on its naked DNA unzipping forces compared with simulated unzipping forces of a published genome. We show that ~32 separate experimental unzipping curves for pBR322 were correctly matched to their simulated unzipping curves hidden in a background of the ~2700 sequences neighboring XhoI sites in the <i>S. cerevisiae</i> (yeast) genome. We describe this method and characterize its robustness as well as discuss future applications. The second topic is a discrete state model for kinesin-1's processivity. Kinesin-1 is a homodimeric molecular motor protein that uses ATP and a hand-over-hand motion to transport cargo along microtubules. Minimal kinetic models are often developed to both explain kinesin's hand-over-hand forward-stepping behavior and to infer important kinetic rate constants from experimental data. These minimal models are often limited to a handful of two-headed states on a core cycle. However, it is not always clear how to evolve these core-cycle models to explain more complex behavior. We have developed a kinetic model without a predefined core cycle. Our model includes 80 two-headed states and permits transitions between any two states that differ by a single catalytic or binding event. We constrain the rate constants as much as possible by published rates and mechanical strain in the kinesin neck linkers and their docking state. We present a model for neck-linker modulation of head and nucleotide binding and unbinding rates. We show that our model reproduces generally-accepted experimental results. The core cycles that emerge are slightly different than those seen in previous experiments. We also explore how processivity and speed change with neck linker length.
Advisors/Committee Members: Koch, Steven, Atlas, Susan, Dunlap, David, Fields, Douglas, Koch, Steven.
Subjects/Keywords: discrete state model; DNA unzipping; Markov Chain; kinesin; Monte Carlo; tracking
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Herskowitz, L. (2011). Kinetic and Statistical Mechanical Modeling of DNA Unzipping and Kinesin Mechanochemistry. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/12079
Chicago Manual of Style (16th Edition):
Herskowitz, Lawrence. “Kinetic and Statistical Mechanical Modeling of DNA Unzipping and Kinesin Mechanochemistry.” 2011. Doctoral Dissertation, University of New Mexico. Accessed February 23, 2020.
http://hdl.handle.net/1928/12079.
MLA Handbook (7th Edition):
Herskowitz, Lawrence. “Kinetic and Statistical Mechanical Modeling of DNA Unzipping and Kinesin Mechanochemistry.” 2011. Web. 23 Feb 2020.
Vancouver:
Herskowitz L. Kinetic and Statistical Mechanical Modeling of DNA Unzipping and Kinesin Mechanochemistry. [Internet] [Doctoral dissertation]. University of New Mexico; 2011. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1928/12079.
Council of Science Editors:
Herskowitz L. Kinetic and Statistical Mechanical Modeling of DNA Unzipping and Kinesin Mechanochemistry. [Doctoral Dissertation]. University of New Mexico; 2011. Available from: http://hdl.handle.net/1928/12079
University of Newcastle
21.
Henriksen, Soren John.
Computational Bayesian methods for communications and control.
Degree: PhD, 2013, University of Newcastle
URL: http://hdl.handle.net/1959.13/939998
► Research Doctorate - Doctor of Philosophy (PhD)
As available computing power increases, there are now opportunities to use computational numerical methods to solve engineering problems…
(more)
▼ Research Doctorate - Doctor of Philosophy (PhD)
As available computing power increases, there are now opportunities to use computational numerical methods to solve engineering problems that were once intractable. This thesis presents the application of stochastic simulation methods to areas of telecommunications and system identification. While there are many randomised algorithms available for solving problems of optimisation and integration, the focus in this work is on those based on Markov chain Monte-Carlo methods, for which it is possible to prove convergence results. This thesis provides an introduction to the Markov chain theory that is used in this area, through to the point of proving convergence properties of the algorithms developed and showing the conditions required. A method is presented for multi-user detection in code division multiple-access communications systems. The Metropolis algorithm is used to build a soft-input, soft-output detector, which provides the maximum a posteriori estimate of the symbols sent, together with the probability of error. This demonstrates the ability of stochastic algorithms to be used in high speed applications. For the second application of this thesis, the parameter estimation of dynamic systems models is considered. Not only does this provide a means of obtaining maximum a posteriori estimates of parameters in nonlinear and non-Gaussian model structures, but also provides full probability density functions of the parameters given the observed measurements. By additionally incorporating the Particle Filter, a wide class of model structures may be used. The steps required to achieve this in a computationally efficient manner are described, including a parallel implementation using Graphic Processing Units.
Advisors/Committee Members: University of Newcastle. Faculty of Engineering and Built Environment, School of Electrical Engineering and Computer Science.
Subjects/Keywords: Bayesian; metropolis; system identification; Markov chain Monte Carlo; multi-user detection
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APA (6th Edition):
Henriksen, S. J. (2013). Computational Bayesian methods for communications and control. (Doctoral Dissertation). University of Newcastle. Retrieved from http://hdl.handle.net/1959.13/939998
Chicago Manual of Style (16th Edition):
Henriksen, Soren John. “Computational Bayesian methods for communications and control.” 2013. Doctoral Dissertation, University of Newcastle. Accessed February 23, 2020.
http://hdl.handle.net/1959.13/939998.
MLA Handbook (7th Edition):
Henriksen, Soren John. “Computational Bayesian methods for communications and control.” 2013. Web. 23 Feb 2020.
Vancouver:
Henriksen SJ. Computational Bayesian methods for communications and control. [Internet] [Doctoral dissertation]. University of Newcastle; 2013. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1959.13/939998.
Council of Science Editors:
Henriksen SJ. Computational Bayesian methods for communications and control. [Doctoral Dissertation]. University of Newcastle; 2013. Available from: http://hdl.handle.net/1959.13/939998
University of Southern California
22.
Zhang, Beijia.
Geometric bounds for Markov Chain and brief applications in
Monte Carlo methods.
Degree: MS, Statistics, 2010, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027
► Since we have the preliminary fact that the irreducible, aperiodic and reversible Markov Chain can asymptotically converge to a unique stationary distribution, and then the…
(more)
▼ Since we have the preliminary fact that the
irreducible, aperiodic and reversible
Markov Chain can
asymptotically converge to a unique stationary distribution, and
then the rate of convergence have been well studied by many
researchers in the field, this convergence rate depends heavily on
the second largest eigenvalue of the transition matrix for the
chain, so in order to analyze this fact, I developed the
convergence bounds as well as the geometric interpretation, which
has application on simple random walk on a graph and cube.; I also
have a brief introduction beyond the idea of the convergence
bounds, which is the extension of
Markov Chain on the
Monte Carlo
methods, because there seems to be an increasing number of problems
that require the techniques of simulation. One interesting model is
the “Simulated Annealing”, although the process concerns more about
the optimization than the simulation.
Advisors/Committee Members: Fulman, Jason (Committee Chair), Goldstein, Larry M. (Committee Member), Li, Lei M. (Committee Member).
Subjects/Keywords: second largest eigenvalue; Markov chain; Monte Carlo; simulation
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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APA (6th Edition):
Zhang, B. (2010). Geometric bounds for Markov Chain and brief applications in
Monte Carlo methods. (Masters Thesis). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027
Chicago Manual of Style (16th Edition):
Zhang, Beijia. “Geometric bounds for Markov Chain and brief applications in
Monte Carlo methods.” 2010. Masters Thesis, University of Southern California. Accessed February 23, 2020.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027.
MLA Handbook (7th Edition):
Zhang, Beijia. “Geometric bounds for Markov Chain and brief applications in
Monte Carlo methods.” 2010. Web. 23 Feb 2020.
Vancouver:
Zhang B. Geometric bounds for Markov Chain and brief applications in
Monte Carlo methods. [Internet] [Masters thesis]. University of Southern California; 2010. [cited 2020 Feb 23].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027.
Council of Science Editors:
Zhang B. Geometric bounds for Markov Chain and brief applications in
Monte Carlo methods. [Masters Thesis]. University of Southern California; 2010. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/301124/rec/3027
University of Edinburgh
23.
Walker, Matthew James.
Methods for Bayesian inversion of seismic data.
Degree: PhD, 2015, University of Edinburgh
URL: http://hdl.handle.net/1842/10504
► The purpose of Bayesian seismic inversion is to combine information derived from seismic data and prior geological knowledge to determine a posterior probability distribution over…
(more)
▼ The purpose of Bayesian seismic inversion is to combine information derived from seismic data and prior geological knowledge to determine a posterior probability distribution over parameters describing the elastic and geological properties of the subsurface. Typically the subsurface is modelled by a cellular grid model containing thousands or millions of cells within which these parameters are to be determined. Thus such inversions are computationally expensive due to the size of the parameter space (being proportional to the number of grid cells) over which the posterior is to be determined. Therefore, in practice approximations to Bayesian seismic inversion must be considered. A particular, existing approximate workflow is described in this thesis: the so-called two-stage inversion method explicitly splits the inversion problem into elastic and geological inversion stages. These two stages sequentially estimate the elastic parameters given the seismic data, and then the geological parameters given the elastic parameter estimates, respectively. In this thesis a number of methodologies are developed which enhance the accuracy of this approximate workflow. To reduce computational cost, existing elastic inversion methods often incorporate only simplified prior information about the elastic parameters. Thus a method is introduced which transforms such results, obtained using prior information specified using only two-point geostatistics, into new estimates containing sophisticated multi-point geostatistical prior information. The method uses a so-called deep neural network, trained using only synthetic instances (or `examples') of these two estimates, to apply this transformation. The method is shown to improve the resolution and accuracy (by comparison to well measurements) of elastic parameter estimates determined for a real hydrocarbon reservoir. It has been shown previously that so-called mixture density network (MDN) inversion can be used to solve geological inversion analytically (and thus very rapidly and efficiently) but only under certain assumptions about the geological prior distribution. A so-called prior replacement operation is developed here, which can be used to relax these requirements. It permits the efficient MDN method to be incorporated into general stochastic geological inversion methods which are free from the restrictive assumptions. Such methods rely on the use of Markov-chain Monte-Carlo (MCMC) sampling, which estimate the posterior (over the geological parameters) by producing a correlated chain of samples from it. It is shown that this approach can yield biased estimates of the posterior. Thus an alternative method which obtains a set of non-correlated samples from the posterior is developed, avoiding the possibility of bias in the estimate. The new method was tested on a synthetic geological inversion problem; its results compared favourably to those of Gibbs sampling (a MCMC method) on the same problem, which exhibited very significant bias. The geological prior information used in seismic…
Subjects/Keywords: 551.22; Bayes; seismic inversion; geostatistics; MCMC; Markov-chain Monte-Carlo
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APA (6th Edition):
Walker, M. J. (2015). Methods for Bayesian inversion of seismic data. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/10504
Chicago Manual of Style (16th Edition):
Walker, Matthew James. “Methods for Bayesian inversion of seismic data.” 2015. Doctoral Dissertation, University of Edinburgh. Accessed February 23, 2020.
http://hdl.handle.net/1842/10504.
MLA Handbook (7th Edition):
Walker, Matthew James. “Methods for Bayesian inversion of seismic data.” 2015. Web. 23 Feb 2020.
Vancouver:
Walker MJ. Methods for Bayesian inversion of seismic data. [Internet] [Doctoral dissertation]. University of Edinburgh; 2015. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/1842/10504.
Council of Science Editors:
Walker MJ. Methods for Bayesian inversion of seismic data. [Doctoral Dissertation]. University of Edinburgh; 2015. Available from: http://hdl.handle.net/1842/10504
University of Otago
24.
Ma, Erfang.
Application of Markov Chain Monte Carlo Methods in Electrical Impedance Tomography
.
Degree: 2013, University of Otago
URL: http://hdl.handle.net/10523/4045
► This thesis discusses the application of Markov chain Monte Carlo (MCMC) methods in electrical impedance tomography (EIT). This topic arises in the Bayesian approach to…
(more)
▼ This thesis discusses the application of
Markov chain Monte Carlo (MCMC) methods in electrical impedance tomography (EIT). This topic arises in the Bayesian approach to the reconstruction problem of EIT. This study is a derivative of the work of Higdon et al. (2011).
First, the computation of a forward map in EIT is discussed, since this computation is very important for the application of MCMC methods in EIT. The computation involves solving a boundary value problem using the finite element method (FEM). The convergence of the FEM approximation is studied numerically, and compelling evidence is provided for the validity of this approximation. Numerical experiments have shown that updating the Cholesky factor of stiffness matrix in FEM, can make the forward map computation much more efficient. The approximate computation of forward map is also discussed. This approximation uses a local linearisation of forward map, and is useful in making efficient MCMC proposals. The accuracy of this approximation is improved dramatically after a log-transformation on the variable of conductivity is introduced into this approximation. The improvement on the accuracy is later on shown to be crucial for this approximation to be employed in making an efficient proposal.
Second, this thesis extends the work of Higdon et al. (2011). The same EIT model as in Higdon et al. (2011) is considered here. As in Higdon et al. (2011), a Bayesian approach is employed to reconstruct the conductivity distribution. The resulting posterior distribution is sampled by single site Metropolis, Random walk Metropolis (RWM), differential evolution MCMC (DE-MCMC), and Directional Random Walk Metropolis (DRWM). Our results on the performance of these MCMC algorithms are generally consistent with those of Higdon et al. (2011). Single site Metropolis, RWM and DRWM have also been analysed on sampling a high-dimensional Gaussian distribution. For their performance, elegant formulae for the acceptance rate for these MCMC samplers are obtained. These formulae indicate these algorithms perform similarly in this case as well, thus provide valuable insights into these MCMC algorithms.
Finally and most importantly, this study comes up with some novel MCMC algorithms that dramatically outperform the standard single site Metropolis as in Higdon et al. (2011), for sampling the posterior distribution in EIT. According to Higdon et al. (2011), the performance of standard single site Metropolis was hard to surpass for this application. However, some of the novel MCMC algorithms in this thesis, when equipped with efficient computation of forward map, can be as many as 100 times more efficient than the standard single site Metropolis. These novel algorithms could be employed to explore posterior distribution of similar kind in other applications, e.g., electrical capacitance tomography. The success of these algorithms in this thesis indicates that they would also achieve equal success there.
Advisors/Committee Members: Fox, Colin (advisor).
Subjects/Keywords: Markov chain Monte Carlo;
electrical impedance tomography;
inverse problems;
Bayesian inference
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APA (6th Edition):
Ma, E. (2013). Application of Markov Chain Monte Carlo Methods in Electrical Impedance Tomography
. (Doctoral Dissertation). University of Otago. Retrieved from http://hdl.handle.net/10523/4045
Chicago Manual of Style (16th Edition):
Ma, Erfang. “Application of Markov Chain Monte Carlo Methods in Electrical Impedance Tomography
.” 2013. Doctoral Dissertation, University of Otago. Accessed February 23, 2020.
http://hdl.handle.net/10523/4045.
MLA Handbook (7th Edition):
Ma, Erfang. “Application of Markov Chain Monte Carlo Methods in Electrical Impedance Tomography
.” 2013. Web. 23 Feb 2020.
Vancouver:
Ma E. Application of Markov Chain Monte Carlo Methods in Electrical Impedance Tomography
. [Internet] [Doctoral dissertation]. University of Otago; 2013. [cited 2020 Feb 23].
Available from: http://hdl.handle.net/10523/4045.
Council of Science Editors:
Ma E. Application of Markov Chain Monte Carlo Methods in Electrical Impedance Tomography
. [Doctoral Dissertation]. University of Otago; 2013. Available from: http://hdl.handle.net/10523/4045
25.
Araki, Takamitsu.
Adaptive Markov chain Monte Carlo for auxiliary variable method and its applications : 補助変数法に対する適応的マルコフ連鎖モンテカルロ法とその応用; ホジョ ヘンスウホウ ニ タイスル テキオウテキ マルコフ レンサ モンテカルロホウ ト ソノ オウヨウ.
Degree: 博士(工学), Nara Institute of Science and Technology / 奈良先端科学技術大学院大学
URL: http://hdl.handle.net/10061/9190
Subjects/Keywords: Markov chain Monte Carlo methods
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APA (6th Edition):
Araki, T. (n.d.). Adaptive Markov chain Monte Carlo for auxiliary variable method and its applications : 補助変数法に対する適応的マルコフ連鎖モンテカルロ法とその応用; ホジョ ヘンスウホウ ニ タイスル テキオウテキ マルコフ レンサ モンテカルロホウ ト ソノ オウヨウ. (Thesis). Nara Institute of Science and Technology / 奈良先端科学技術大学院大学. Retrieved from http://hdl.handle.net/10061/9190
Note: this citation may be lacking information needed for this citation format:
No year of publication.
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Araki, Takamitsu. “Adaptive Markov chain Monte Carlo for auxiliary variable method and its applications : 補助変数法に対する適応的マルコフ連鎖モンテカルロ法とその応用; ホジョ ヘンスウホウ ニ タイスル テキオウテキ マルコフ レンサ モンテカルロホウ ト ソノ オウヨウ.” Thesis, Nara Institute of Science and Technology / 奈良先端科学技術大学院大学. Accessed February 23, 2020.
http://hdl.handle.net/10061/9190.
Note: this citation may be lacking information needed for this citation format:
No year of publication.
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Araki, Takamitsu. “Adaptive Markov chain Monte Carlo for auxiliary variable method and its applications : 補助変数法に対する適応的マルコフ連鎖モンテカルロ法とその応用; ホジョ ヘンスウホウ ニ タイスル テキオウテキ マルコフ レンサ モンテカルロホウ ト ソノ オウヨウ.” Web. 23 Feb 2020.
Note: this citation may be lacking information needed for this citation format:
No year of publication.
Vancouver:
Araki T. Adaptive Markov chain Monte Carlo for auxiliary variable method and its applications : 補助変数法に対する適応的マルコフ連鎖モンテカルロ法とその応用; ホジョ ヘンスウホウ ニ タイスル テキオウテキ マルコフ レンサ モンテカルロホウ ト ソノ オウヨウ. [Internet] [Thesis]. Nara Institute of Science and Technology / 奈良先端科学技術大学院大学; [cited 2020 Feb 23].
Available from: http://hdl.handle.net/10061/9190.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
No year of publication.
Council of Science Editors:
Araki T. Adaptive Markov chain Monte Carlo for auxiliary variable method and its applications : 補助変数法に対する適応的マルコフ連鎖モンテカルロ法とその応用; ホジョ ヘンスウホウ ニ タイスル テキオウテキ マルコフ レンサ モンテカルロホウ ト ソノ オウヨウ. [Thesis]. Nara Institute of Science and Technology / 奈良先端科学技術大学院大学; Available from: http://hdl.handle.net/10061/9190
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
No year of publication.
Penn State University
26.
Warner, Ashley Elizabeth.
Statistical Skill in the Emulation of Climate Models.
Degree: MS, Meteorology, 2014, Penn State University
URL: https://etda.libraries.psu.edu/catalog/22840
► A climate model of low complexity can be used to emulate the performance of one with higher complexity by identifying the parameters for each model…
(more)
▼ A climate model of low complexity can be used to
emulate the performance of one with higher complexity by
identifying the parameters for each model that yield similar model
responses. In this thesis, an energy balance model, the Diffusive
Ocean Energy balance CLIMate model (DOECLIM) was calibrated to
match the output from 639 simulations of the MIT Integrated Global
System Model (IGSM), where each IGSM simulation has a different set
of values for three key climate parameters: climate sensitivity,
vertical ocean diffusivity and aerosol forcing. The energy balance
model estimates the globally averaged climate state based on
simplified model physics. The IGSM estimates the zonal mean state
of the atmosphere and ocean based on physics in higher complexity
climate models, and estimates climate changes that include
significant internal variability. The DOECLIM parameters were
estimated for each IGSM run to find the parameter settings for the
simpler model that would best match results from the more complex
model. This allows for the simpler model to be used as an emulator
over a range of parameter settings. Two model calibration
techniques were used and compared. These techniques are
Differential Evolution (DE), a genetic algorithm that produces a
single set of parameters providing best fit values, and Markov
Chain Monte Carlo (MCMC), which produces a joint probability
distribution for the parameters. The study analyzed the statistical
skill, including potential biases, that exist when calibrating the
energy balance model to IGSM output. In particular, the estimated
DOECLIM climate sensitivity values tended to be lower than their
corresponding IGSM values, particularly for runs with low ocean
diffusivity. The parameter estimates also vary depending on the
choice of noise model, AR(1) or AR(0) for the atmosphere and ocean
temperatures.
Subjects/Keywords: climate models; climate sensitivity; differential
evolution; markov chain monte carlo
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APA (6th Edition):
Warner, A. E. (2014). Statistical Skill in the Emulation of Climate Models. (Masters Thesis). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/22840
Chicago Manual of Style (16th Edition):
Warner, Ashley Elizabeth. “Statistical Skill in the Emulation of Climate Models.” 2014. Masters Thesis, Penn State University. Accessed February 23, 2020.
https://etda.libraries.psu.edu/catalog/22840.
MLA Handbook (7th Edition):
Warner, Ashley Elizabeth. “Statistical Skill in the Emulation of Climate Models.” 2014. Web. 23 Feb 2020.
Vancouver:
Warner AE. Statistical Skill in the Emulation of Climate Models. [Internet] [Masters thesis]. Penn State University; 2014. [cited 2020 Feb 23].
Available from: https://etda.libraries.psu.edu/catalog/22840.
Council of Science Editors:
Warner AE. Statistical Skill in the Emulation of Climate Models. [Masters Thesis]. Penn State University; 2014. Available from: https://etda.libraries.psu.edu/catalog/22840
Penn State University
27.
Liu, Rong.
MULTIPLE IMPUTATION FOR MISSING ITEMS IN MULTI-THEMED
QUESTIONNAIRES.
Degree: PhD, Statistics, 2010, Penn State University
URL: https://etda.libraries.psu.edu/catalog/10552
► Questionnaires used in survey-based research are often arranged in multiple sections. Each section contains items that are closely interrelated, serving one or more themes. Even…
(more)
▼ Questionnaires used in survey-based research are often
arranged in multiple sections. Each section contains items that are
closely interrelated, serving one or more themes. Even with a
modest number of sections, the resulting dataset may have a large
number of variables, which poses special analytic challenges for
dealing with missing values. Current procedures for multiple
imputation may fail because the underlying models do not take into
account the thematic nature of the questionnaire and are
over-parameterized. Attempts to simplify the model – for example, by
assuming that the items within a theme are conditionally
independent given a small number of latent factors – may fail to
capture special features of the data if the specified model does
not fit. In this dissertation, I develop new multiple-imputation
procedures for multi-themed questionnaire data based on a fexible
class of confirmatory factor models. I present PX-EM algorithms for
maximum-likelihood estimation in exploratory and cofirmatory factor
analysis with incomplete data. The factor model is then relaxed by
adding an additional random component which allows the covariance
structure to deviate from the assumed model. I present an MCMC
algorithm for generating Bayesian multiple imputations under this
extended model. These techniques are illustrated using data on
emotional distress from a large adolescent health
survey.
Subjects/Keywords: factor model; EM algorithm; Markov chain Monte Carlo;
incomplete data
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APA ·
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MLA ·
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Export
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Manager
APA (6th Edition):
Liu, R. (2010). MULTIPLE IMPUTATION FOR MISSING ITEMS IN MULTI-THEMED
QUESTIONNAIRES. (Doctoral Dissertation). Penn State University. Retrieved from https://etda.libraries.psu.edu/catalog/10552
Chicago Manual of Style (16th Edition):
Liu, Rong. “MULTIPLE IMPUTATION FOR MISSING ITEMS IN MULTI-THEMED
QUESTIONNAIRES.” 2010. Doctoral Dissertation, Penn State University. Accessed February 23, 2020.
https://etda.libraries.psu.edu/catalog/10552.
MLA Handbook (7th Edition):
Liu, Rong. “MULTIPLE IMPUTATION FOR MISSING ITEMS IN MULTI-THEMED
QUESTIONNAIRES.” 2010. Web. 23 Feb 2020.
Vancouver:
Liu R. MULTIPLE IMPUTATION FOR MISSING ITEMS IN MULTI-THEMED
QUESTIONNAIRES. [Internet] [Doctoral dissertation]. Penn State University; 2010. [cited 2020 Feb 23].
Available from: https://etda.libraries.psu.edu/catalog/10552.
Council of Science Editors:
Liu R. MULTIPLE IMPUTATION FOR MISSING ITEMS IN MULTI-THEMED
QUESTIONNAIRES. [Doctoral Dissertation]. Penn State University; 2010. Available from: https://etda.libraries.psu.edu/catalog/10552
Carnegie Mellon University
28.
Potter, Christopher C. J.
Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carol.
Degree: 2013, Carnegie Mellon University
URL: http://repository.cmu.edu/dissertations/249
► Markov Chain Monte Carlo (MCMC) is a technique for sampling from a target probability distribution, and has risen in importance as faster computing hardware has…
(more)
▼ Markov Chain Monte Carlo (MCMC) is a technique for sampling from a target probability distribution, and has risen in importance as faster computing hardware has made possible the exploration of hitherto difficult distributions. Unfortunately, this powerful technique is often misapplied by poor selection of transition kernel for the Markov chain that is generated by the simulation.
Some kernels are used without being checked against the convergence requirements for MCMC (total balance and ergodicity), but in this work we prove the existence of a simple proxy for total balance that is not as demanding as detailed balance, the most widely used standard. We show that, for discrete-state MCMC, that if a transition kernel is equivalent when it is “reversed” and applied to data which is also “reversed”, then it satisfies total balance. We go on to prove that the sequential single-variable update Metropolis kernel, where variables are simply updated in order, does indeed satisfy total balance for many discrete target distributions, such as the Ising model with uniform exchange constant.
Also, two well-known papers by Gelman, Roberts, and Gilks (GRG)[1, 2] have proposed the application of the results of an interesting mathematical proof to the realistic optimization of Markov Chain Monte Carlo computer simulations. In particular, they advocated tuning the simulation parameters to select an acceptance ratio of 0.234 .
In this paper, we point out that although the proof is valid, its result’s application to practical computations is not advisable, as the simulation algorithm considered in the proof is so inefficient that it produces very poor results under all circumstances. The algorithm used by Gelman, Roberts, and Gilks is also shown to introduce subtle time-dependent correlations into the simulation of intrinsically independent variables. These correlations are of particular interest since they will be present in all simulations that use multi-dimensional MCMC moves.
Subjects/Keywords: Markov Chain Monte Carlo; detailed balance; acceptance ratio; Metropolis algorithm; Mathematics
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APA (6th Edition):
Potter, C. C. J. (2013). Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carol. (Thesis). Carnegie Mellon University. Retrieved from http://repository.cmu.edu/dissertations/249
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Potter, Christopher C J. “Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carol.” 2013. Thesis, Carnegie Mellon University. Accessed February 23, 2020.
http://repository.cmu.edu/dissertations/249.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Potter, Christopher C J. “Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carol.” 2013. Web. 23 Feb 2020.
Vancouver:
Potter CCJ. Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carol. [Internet] [Thesis]. Carnegie Mellon University; 2013. [cited 2020 Feb 23].
Available from: http://repository.cmu.edu/dissertations/249.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Potter CCJ. Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carol. [Thesis]. Carnegie Mellon University; 2013. Available from: http://repository.cmu.edu/dissertations/249
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Berkeley
29.
Kitchen, Nathan.
Markov Chain Monte Carlo Stimulus Generation for Constrained Random Simulation.
Degree: Electrical Engineering & Computer Sciences, 2010, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/6gp3z1t0
► As integrated circuits have grown in size and complexity, the time required for functional verification has become the largest part of total design time. The…
(more)
▼ As integrated circuits have grown in size and complexity, the time required for functional verification has become the largest part of total design time. The main workhorse in state-of-the-art practical verification is constrained random simulation. In this approach, a randomized solver generates solutions to declaratively specified input constraints, and the solutions are applied as stimuli to a logic simulator. The efficiency of the overall verification process depends critically on the speed of the solver and the distribution of the generated solutions. Previous methods for stimulus generation achieve speed at the expense of quality of distribution or rely on techniques that do not scale well to large designs.In this dissertation, we propose a new method for stimulus generation based on Markov chain Monte Carlo (MCMC) methods. We describe the basic principles of MCMC methods and one of the most common of these methods, Metropolis-Hastings sampling. We present our approach, which combines the Metropolis-Hastings algorithm with stochastic local search. We show with experimental results that it surpasses existing stimulus-generation methods in speed, robustness, and quality of distribution. After presenting our basic algorithm, we describe several refinements and variations of it. These refinements include the addition of control variables to handle dependencies on external data and elimination of variables to increase efficiency and distribution. In addition, we present a parallel version of our algorithm and give theoretical analysis and experimental evidence of the speedup achieved by parallelization.
Subjects/Keywords: Electrical Engineering; Markov chain Monte Carlo; Metropolis algorithm; simulation; verification
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APA (6th Edition):
Kitchen, N. (2010). Markov Chain Monte Carlo Stimulus Generation for Constrained Random Simulation. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/6gp3z1t0
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Kitchen, Nathan. “Markov Chain Monte Carlo Stimulus Generation for Constrained Random Simulation.” 2010. Thesis, University of California – Berkeley. Accessed February 23, 2020.
http://www.escholarship.org/uc/item/6gp3z1t0.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Kitchen, Nathan. “Markov Chain Monte Carlo Stimulus Generation for Constrained Random Simulation.” 2010. Web. 23 Feb 2020.
Vancouver:
Kitchen N. Markov Chain Monte Carlo Stimulus Generation for Constrained Random Simulation. [Internet] [Thesis]. University of California – Berkeley; 2010. [cited 2020 Feb 23].
Available from: http://www.escholarship.org/uc/item/6gp3z1t0.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Kitchen N. Markov Chain Monte Carlo Stimulus Generation for Constrained Random Simulation. [Thesis]. University of California – Berkeley; 2010. Available from: http://www.escholarship.org/uc/item/6gp3z1t0
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Berkeley
30.
Kominiarczuk, Jakub.
Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization.
Degree: Mathematics, 2013, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/99d0g6x0
► We present a method for sampling high-dimensional probability spaces, applicable to Markov fields with both discrete and continuous variables, based on an approximate acyclic representation…
(more)
▼ We present a method for sampling high-dimensional probability spaces, applicable to Markov fields with both discrete and continuous variables, based on an approximate acyclic representation of the probability density. Our method generalizes and places in a common framework some recent work on computing renormalized Hamiltonians and stochastic multigrid sampling.An acyclic representation of a probability distribution function (PDF) is obtained when one chooses an ordering of the variables and writes the PDF as a product of conditional probabilities, so that the probability of any variable is conditional only on the variables that precede it in the ordering. An acyclic representation makes the sampling efficient, because it uses the sparsity present in the model. We derive an approximate acyclic representation for general graphs by finding marginals through a fast marginalization scheme. The partial derivatives of the logarithm of the marginal probability are computed approximately through stochastic linear projection onto a polynomial basis, followed by reconstruction of the marginal through integration. The projection is based on an optimized inner product, making possible the use of Gaussian quadrature. Probability distributions involving discrete variables are handled by embedding the PDFs in differentiable extensions. Our algorithm can be extended to the evaluation of renormalized Hamiltonians formed using general renormalization schemes.The approximate acyclic representation of the PDF is then used for sampling. The variables are sampled in a fixed order, producing independent samples together with their sampling weights. We present an optimized sampling strategy that uses a maximum amount of information to choose individual variable values. The samples are further improved using techniques from particle filtering. We also introduce a block Markov chain Monte Carlo scheme based on the sampling weights. Finally, we present applications of our methodology to the Ising model.
Subjects/Keywords: Applied mathematics; Markov Chain Monte Carlo; Sampling; Simulation
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APA (6th Edition):
Kominiarczuk, J. (2013). Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/99d0g6x0
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Kominiarczuk, Jakub. “Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization.” 2013. Thesis, University of California – Berkeley. Accessed February 23, 2020.
http://www.escholarship.org/uc/item/99d0g6x0.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Kominiarczuk, Jakub. “Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization.” 2013. Web. 23 Feb 2020.
Vancouver:
Kominiarczuk J. Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization. [Internet] [Thesis]. University of California – Berkeley; 2013. [cited 2020 Feb 23].
Available from: http://www.escholarship.org/uc/item/99d0g6x0.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Kominiarczuk J. Acyclic Monte Carlo: Efficient multi-level sampling of undirected graphical models through fast marginalization. [Thesis]. University of California – Berkeley; 2013. Available from: http://www.escholarship.org/uc/item/99d0g6x0
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
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Open Access Theses and Dissertations