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Cornell University
1.
Bessonov, Mariya.
Probabilistic Models For Population Dynamics.
Degree: PhD, Mathematics, 2013, Cornell University
URL: http://hdl.handle.net/1813/34311 
► Two interacting particle systems that serve as probabilistic models for population dynamics are studied in this work. The quadratic contact process is a stochastic spatial…
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▼ Two interacting particle systems that serve as probabilistic models for population dynamics are studied in this work. The quadratic contact process is a stochastic spatial model for a population in which each individual has two parents and the dynamics are governed by random birth and death rates and an offspring distribution kernel. Another population model, due to Bolker and Pacala, models competition of different species in a forest. In both cases, we are interested in proving the existence of nontrivial stationary distributions.
Advisors/Committee Members: Durrett, Richard Timothy (chair), Saloff-Coste, Laurent Pascal (committee member), Gross, Leonard (committee member), Molchanov, Stanislav A (committee member).
Subjects/Keywords: probability
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APA (6th Edition):
Bessonov, M. (2013). Probabilistic Models For Population Dynamics. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/34311
Chicago Manual of Style (16th Edition):
Bessonov, Mariya. “Probabilistic Models For Population Dynamics.” 2013. Doctoral Dissertation, Cornell University. Accessed March 01, 2021.
http://hdl.handle.net/1813/34311.
MLA Handbook (7th Edition):
Bessonov, Mariya. “Probabilistic Models For Population Dynamics.” 2013. Web. 01 Mar 2021.
Vancouver:
Bessonov M. Probabilistic Models For Population Dynamics. [Internet] [Doctoral dissertation]. Cornell University; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1813/34311.
Council of Science Editors:
Bessonov M. Probabilistic Models For Population Dynamics. [Doctoral Dissertation]. Cornell University; 2013. Available from: http://hdl.handle.net/1813/34311
University of Limerick
2.
Murphy, Conor.
An investigation into the teaching and learning of probability at senior cycle.
Degree: 2011, University of Limerick
URL: http://hdl.handle.net/10344/2025
► peer-reviewed
In Ireland at present, the National Council for Curriculum and Assessment is comprehensively overhauling the Second Level Mathematics curriculum. This reformed curriculum is known…
(more)
▼ peer-reviewed
In Ireland at present, the National Council for Curriculum and Assessment is comprehensively overhauling the Second Level Mathematics curriculum. This reformed curriculum is known as Project Maths and is a response to concerns about how Irish students are taught and learn mathematics. These concerns are based around the achievement of Irish student’s in international studies (Close and Oldham 2005; Cosgrove, Shiel, Sofroniou, Zastrutzki and Shortt 2005; Perkins, Moran, Cosgrove and Shiel 2010; Oldham 2002, 2006) as well as domestic and international literature which, highlights the problems associated with the behaviourist methodology favoured by Irish teachers (Conway and Sloane 2006; English, O’Donoghue and Bajpai 1992; Lyons, Lynch, Close, Sheerin and Boland 2003; NCCA 2005). The aim of the study was to improve the teaching and learning of Probability through the development of a resource pack. probability was chosen as the focus of the intervention due to the author’s experiences in the classroom, international literature highlighting its pedagogical difficulties (Shaughnessy 1992; Fischbein, Nello and Marino 1991; Ahlgren and Garfield 1988; Hawkins and Kapadia 1984) and its lack of popularity among Irish Leaving Certificate students (Chief Examiner 2000, 2005). The study was designed to examine the benefits of the active learning methodologies and contextualised questions promoted by the Project Maths curriculum, specifically with regards to students’ attitudes and understanding through the implementation and evaluation of a resource pack designed by the author.
The evaluation process produced data, which was inconclusive in establishing a link between the promoted methodologies and students’ attitudes and understanding. The
only significant shift in students’ attitude was a negative one in response to the statement “I know I can do well in Maths”. A dip in students’ confidence however is not unusual in studies involving changes in pedagogical style (Carpenter, Franke, Jacobs, Fennema and Epsom 1998; Cobb, Wood, Yackel, Nicholls, Wheatley, Trigatti and Perlwitz, 1991; Vershaffel and De Corte 1997; Fauzan et al. 2002; Van Reeuwijk 1992) and though not significant, student scores did improve in the three sub-categories of ‘Perception of Usefulness’, ‘Anxiety’ and ‘Effective Motivation’. There were also indications that these methodologies had a positive effect on understanding. The data also suggested that the resource pack, designed and developed by the author to support the teaching and learning of probability, will be of use to teachers who embrace Project Maths and what it is trying to achieve in Irish classrooms.
Advisors/Committee Members: O'Donoghue, John, Ní Ríordáin, Máire.
Subjects/Keywords: probability; probability and statistics
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APA (6th Edition):
Murphy, C. (2011). An investigation into the teaching and learning of probability at senior cycle. (Thesis). University of Limerick. Retrieved from http://hdl.handle.net/10344/2025
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):
Murphy, Conor. “An investigation into the teaching and learning of probability at senior cycle.” 2011. Thesis, University of Limerick. Accessed March 01, 2021.
http://hdl.handle.net/10344/2025.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Murphy, Conor. “An investigation into the teaching and learning of probability at senior cycle.” 2011. Web. 01 Mar 2021.
Vancouver:
Murphy C. An investigation into the teaching and learning of probability at senior cycle. [Internet] [Thesis]. University of Limerick; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10344/2025.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Murphy C. An investigation into the teaching and learning of probability at senior cycle. [Thesis]. University of Limerick; 2011. Available from: http://hdl.handle.net/10344/2025
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Texas A&M University
3.
Na, Wonhee.
Some Results on Bi-Free Probability.
Degree: PhD, Mathematics, 2018, Texas A&M University
URL: http://hdl.handle.net/1969.1/174489
► This study consists of two projects on bi-free probability. In the first project, a bi-free central limit distribution is investigated. We find the principal function…
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▼ This study consists of two projects on bi-free
probability. In the first project, a bi-free central limit distribution is investigated. We find the principal function of the completely non-normal operator l(vv1) + l(vv1)∗ + i(r(vv2) ∗ + r(v2) ∗ ) on a subspace of the full Fock space F(H) which arises from a bi-free central limit distribution. By the fact that the principal function of a pure hyponormal operator with trace class self-commutator is an extension of the Fredholm index of the operator, we find the essential spectrum of this operator. In the second part, we examine the reduced bi-free product C*-algebra generated by two pairs of commuting self-adjoint projections. In particular, we partially describe how to find the bi-free product states and the corresponding C*-algebra given by the GNS construction for a generic distribution of the projections. We prove some general results analogous to Voiculescu’s partial R- and S-transforms by using combinatorial techniques on bi-free setting.
Advisors/Committee Members: Dykema, Kenneth (advisor), Kerr, David (committee member), Long, James (committee member), Smith, Roger (committee member).
Subjects/Keywords: Free Probability; Bi-free probability
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APA (6th Edition):
Na, W. (2018). Some Results on Bi-Free Probability. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/174489
Chicago Manual of Style (16th Edition):
Na, Wonhee. “Some Results on Bi-Free Probability.” 2018. Doctoral Dissertation, Texas A&M University. Accessed March 01, 2021.
http://hdl.handle.net/1969.1/174489.
MLA Handbook (7th Edition):
Na, Wonhee. “Some Results on Bi-Free Probability.” 2018. Web. 01 Mar 2021.
Vancouver:
Na W. Some Results on Bi-Free Probability. [Internet] [Doctoral dissertation]. Texas A&M University; 2018. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1969.1/174489.
Council of Science Editors:
Na W. Some Results on Bi-Free Probability. [Doctoral Dissertation]. Texas A&M University; 2018. Available from: http://hdl.handle.net/1969.1/174489
McMaster University
4.
Abdulkarimova, Ulviya.
Frailty Models for Modelling Heterogeneity.
Degree: MSc, 2013, McMaster University
URL: http://hdl.handle.net/11375/12911
► In the analysis of lifetime data, heterogeneity may be present in many situations. This heterogeneity is also referred to as frailty. Analysis that ignore…
(more)
▼ In the analysis of lifetime data, heterogeneity may be present in many situations. This heterogeneity is also referred to as frailty. Analysis that ignore frailty when it is present leads to incorrect inferences. In lifetime analysis, Cox proportional hazards model is commonly used to measure the effects of covariates. The covariates may fail to fully account for the true differences in risk. This may be due to an existence of another variable that is ignored in the model but can be explained by random frailty. Including frailty in the model can avoid underestimation and overestimation of parameters and also correctly measure the effects of the covariates on the response variable. This thesis presents an extension of Cox model to parametric frailty model in which the exponential and Weibull distributions are used as the distributions of baseline hazard, and the gamma and Weibull distributions are used as frailty distributions. We examine the maximum likelihood estimation procedures and propose the use of Monte Carlo integration method or quadrature method in complicated cases where explicit solutions to the likelihood functions can not be obtained. The gamma distribution is one of the most commonly used distributions for frailty. It has a closed form likelihood function that can be readily maximized. In this thesis, we study the performance of the Weibull distribution as a frailty distribution and compare with the gamma frailty model. Through simulation studies, the performance of the parameter estimates are evaluated. The effects of increasing the sample size and cluster size separately are also studied through Monte Carlo simulations. The Akaike Information Criteria (AIC) is used to compare the performance of the gamma and Weibull frailty models. The developed methods are then illustrated with numerical examples.
Master of Science (MSc)
Advisors/Committee Members: Balakrishnan, Narayanaswamy, R. Viveros-Aguilera, A. Childs, Statistics.
Subjects/Keywords: Statistics and Probability; Statistics and Probability
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APA (6th Edition):
Abdulkarimova, U. (2013). Frailty Models for Modelling Heterogeneity. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/12911
Chicago Manual of Style (16th Edition):
Abdulkarimova, Ulviya. “Frailty Models for Modelling Heterogeneity.” 2013. Masters Thesis, McMaster University. Accessed March 01, 2021.
http://hdl.handle.net/11375/12911.
MLA Handbook (7th Edition):
Abdulkarimova, Ulviya. “Frailty Models for Modelling Heterogeneity.” 2013. Web. 01 Mar 2021.
Vancouver:
Abdulkarimova U. Frailty Models for Modelling Heterogeneity. [Internet] [Masters thesis]. McMaster University; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/11375/12911.
Council of Science Editors:
Abdulkarimova U. Frailty Models for Modelling Heterogeneity. [Masters Thesis]. McMaster University; 2013. Available from: http://hdl.handle.net/11375/12911
McMaster University
5.
Ahsan, Zahra.
A Simulation Study to Examine a New Method of Sampling When Information on the Target Population Is Very Limited.
Degree: MSc, 2011, McMaster University
URL: http://hdl.handle.net/11375/9915
► A new sampling method was developed for use in areas where standard methods for sampling from a population may be difficult or impossible to…
(more)
▼ A new sampling method was developed for use in areas where standard methods for sampling from a population may be difficult or impossible to use. The new method uses Global Positioning System (GPS) points and satellite photos to identify datapoints (locations) within selected towns. A circle (of a specified radius) is drawn around each datapoint, which may include several buildings or sometimes none. A single household is sampled from each circle and then one adult (aged 18 years or older) is interviewed from the household, based on who had the most recent birthday. Two issues arise with this new sampling method: first, the probability of sampling any household may vary, depending on the datapoint its chosen from; and second, circles surrounding the chosen datapoints may overlap. The thesis used simulations to see whether the first issue affected the point estimates of two population parameters. The second issue was too complex to investigate so it was ignored when sampling households. Simulations were run to test the sampling method on two different hypothetical towns, one with denser population than the other. Results from the simulations showed that estimates did not always match what was expected, but the observed differences were not substantial. It was presumed that the reason for differences was due to the issue of multiple probabilities for selection as well as overlapping circles (which had been ignored during sampling), since both issues were inherent in this sampling method. Although some differences were observed from true values, they appeared not to be very different from the population values, so I conclude that this sampling method is a useful one. Future work may look more closely at understanding the issue of overlapping circles and how it affects the point estimates.
Master of Science (MSc)
Advisors/Committee Members: Shannon, H., Statistics.
Subjects/Keywords: Statistics and Probability; Statistics and Probability
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APA ·
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Manager
APA (6th Edition):
Ahsan, Z. (2011). A Simulation Study to Examine a New Method of Sampling When Information on the Target Population Is Very Limited. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/9915
Chicago Manual of Style (16th Edition):
Ahsan, Zahra. “A Simulation Study to Examine a New Method of Sampling When Information on the Target Population Is Very Limited.” 2011. Masters Thesis, McMaster University. Accessed March 01, 2021.
http://hdl.handle.net/11375/9915.
MLA Handbook (7th Edition):
Ahsan, Zahra. “A Simulation Study to Examine a New Method of Sampling When Information on the Target Population Is Very Limited.” 2011. Web. 01 Mar 2021.
Vancouver:
Ahsan Z. A Simulation Study to Examine a New Method of Sampling When Information on the Target Population Is Very Limited. [Internet] [Masters thesis]. McMaster University; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/11375/9915.
Council of Science Editors:
Ahsan Z. A Simulation Study to Examine a New Method of Sampling When Information on the Target Population Is Very Limited. [Masters Thesis]. McMaster University; 2011. Available from: http://hdl.handle.net/11375/9915
McMaster University
6.
Wong, Hoi Suen.
Analyzing Health Utility Data with Generalized Additive Models.
Degree: MSc, 2011, McMaster University
URL: http://hdl.handle.net/11375/9916
► The money put into health care has been increasing dramatically. Comparison of different programs is important in helping government to make decision as to…
(more)
▼ The money put into health care has been increasing dramatically. Comparison of different programs is important in helping government to make decision as to what health care services to be provided. The cost-effectiveness of different health care programs can be compared based on the improvement of a person's health states and the cost it incurred. To measure the health states of a person, health utility scores can be used. But health utility data exhibit features such as non-normality, heteroscedasticity of variances, and the majority of observations attaining values close to or at the maximum of the measurement scale. This brings challenges to analyzing health utility data. For example, linear regression with the assumption of normality might not be valid since non-normality is present in health utility data. To address these problems, other methods are used. In this study, we investigate the performance of generalized additive models (GAMs) in handling health utility data. In GAMs, the relationship between the response and the predictor variables can be non-linearly defined. So GAM methods give more options in the assumption of the relationship between the response and the predictors. For comparison, we also use ordinary least squares. To evaluate the performance of generalized additive models, simulation is used. Data are generated from the simulation model, and GAMs will be used to fit the simulated data. Bias and coverage probability will be used to assess the performance of the GAM method. A comparison between OLS and GAM will be also be done in the study. And, as an illustration, GAM will be applied to a real data set called Diabetes Hamilton which "vas collected from some diabetic patients who participated in a community program based in Hamilton, Ontario. When GAM is applied to the real data set, similar results to the OLS method in terms of the estimates of the parameters is observed. Both methods give similar coefficient values for each parameter. From the simulation results, the estimate given by the GAM method is closer to the true value than the OLS method in general. The bias produced by the GAM is smaller than the OLS method. So overall, GAM method seems to be valid in analyzing the data set such as those used in this study and also the general health utility data.
Master of Science (MSc)
Advisors/Committee Members: Childs, Aaron, Pullenayegum, Eleanor, Statistics.
Subjects/Keywords: Statistics and Probability; Statistics and Probability
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APA (6th Edition):
Wong, H. S. (2011). Analyzing Health Utility Data with Generalized Additive Models. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/9916
Chicago Manual of Style (16th Edition):
Wong, Hoi Suen. “Analyzing Health Utility Data with Generalized Additive Models.” 2011. Masters Thesis, McMaster University. Accessed March 01, 2021.
http://hdl.handle.net/11375/9916.
MLA Handbook (7th Edition):
Wong, Hoi Suen. “Analyzing Health Utility Data with Generalized Additive Models.” 2011. Web. 01 Mar 2021.
Vancouver:
Wong HS. Analyzing Health Utility Data with Generalized Additive Models. [Internet] [Masters thesis]. McMaster University; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/11375/9916.
Council of Science Editors:
Wong HS. Analyzing Health Utility Data with Generalized Additive Models. [Masters Thesis]. McMaster University; 2011. Available from: http://hdl.handle.net/11375/9916
McMaster University
7.
Liu, Jennifer.
Statistical Issues in a Meta-analysis of Studies of Integrated Treatment Programs for Women with Substance Use Problems and Their Children.
Degree: MS, 2011, McMaster University
URL: http://hdl.handle.net/11375/8959
► Meta-analysis is a statistical technique for combining findings from independent studies. A meta-analysis was performed to evaluate the effectiveness of integrated treatment programs for…
(more)
▼ Meta-analysis is a statistical technique for combining findings from independent studies. A meta-analysis was performed to evaluate the effectiveness of integrated treatment programs for women with substance use issues and their children. Primary outcomes included substance use, maternal and child well-being, length of treatment, and parenting. A total of 9 randomized controlled trials (RCTs) and 84 observational studies were included in the final analysis. The
p-value and capture re-capture method, were used to combine studies using different measures of treatment effect and evaluate the completeness of the literature search, respectively. Modified weights incorporating study quality were used to assess the impact of study quality on treatment effects. We also conducted a sensitivity analysis of correlation coefficients on combined estimates as a method for handling missing data. Study quality adjusted weighting and traditional inverse variance weights provided different results for combined estimates of birth weight outcomes measured by standardized mean difference. The results from weighting by study quality provided a statistically significant result with a combined estimate of 0.2644 (95% CI: 0.0860, 0.4428), while the traditional method gave a non-significant combined estimate of 0.3032 with (95% CI: -0.0725,0.6788). The sensitivity analysis of correlation coefficients (r) on combined estimates of maternal depression effects were similar, with confidence intervals that narrowed as r increased. Values ofr = 0.2, 0.5, 0.65, 0.75, and 0.85 gave corresponding results (with 95% CI) of 0.67 (-0.10, 1.45), 0.67 (0.04, 1.3), 0.67 (0.12, 1.2),0.67 (0.18, 1.15), and 0.66 (0.25, 1.07). Robustness of the sensitivity analysis for study quality weighting and choice of correlation coefficient on combined estimates revealed benefits of integrated treatment programs for birth weight outcomes and maternal depression. Evidence of benefit for at least some of the clients was apparent for parenting attitude measured by the Adult-Adolescent Parenting Inventory (AAPI). Results for each subscale of the AAPI were reported by timing of assessments (=< 4,5-8, => 9 months). Combined
p-values were 0.0006, <0.0001, <<0.0001 for Inappropriate Expectations, 0.1938, 0.1656, <<0.0001 for Lack of Empathy, 0.0007, <0.0001 <<0.0001 for Corporal Punishment, 0.0352, 0.0002, <<0.0001 for Role Reversal, and 0.5178 (5-8 months) for Power Independence. There was insufficient evidence for concluding a significant effect of treatment on neonatal behavioural assessments measured by Apgar scores. Combined
p-values of 0.6980 and 0.3294 were obtained for the 1-minute and 5-minute Apgar, respectively. The number of missing articles estimated by the capture recapture method was 8 (95% CI: 2,24), which suggests a 90% capture rate of all relevant world literature. This result indicates that a sufficient amount of studies were retrieved to avoid bias in the results of the meta-analysis. Conclusions…
Advisors/Committee Members: Thabane, Lehana, Statistics.
Subjects/Keywords: Statistics and Probability; Statistics and Probability
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APA ·
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APA (6th Edition):
Liu, J. (2011). Statistical Issues in a Meta-analysis of Studies of Integrated Treatment Programs for Women with Substance Use Problems and Their Children. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/8959
Chicago Manual of Style (16th Edition):
Liu, Jennifer. “Statistical Issues in a Meta-analysis of Studies of Integrated Treatment Programs for Women with Substance Use Problems and Their Children.” 2011. Masters Thesis, McMaster University. Accessed March 01, 2021.
http://hdl.handle.net/11375/8959.
MLA Handbook (7th Edition):
Liu, Jennifer. “Statistical Issues in a Meta-analysis of Studies of Integrated Treatment Programs for Women with Substance Use Problems and Their Children.” 2011. Web. 01 Mar 2021.
Vancouver:
Liu J. Statistical Issues in a Meta-analysis of Studies of Integrated Treatment Programs for Women with Substance Use Problems and Their Children. [Internet] [Masters thesis]. McMaster University; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/11375/8959.
Council of Science Editors:
Liu J. Statistical Issues in a Meta-analysis of Studies of Integrated Treatment Programs for Women with Substance Use Problems and Their Children. [Masters Thesis]. McMaster University; 2011. Available from: http://hdl.handle.net/11375/8959
McMaster University
8.
Qin, Maochang.
Variable Selection Methods for Population-based Genetic Association Studies: SPLS and HSIC.
Degree: MS, 2011, McMaster University
URL: http://hdl.handle.net/11375/9165
► This project aims to identify the single nucleotide polymorphisms(SNPs), which are associated with the muscle size and strength in Caucasian. Two methods sparse partial…
(more)
▼ This project aims to identify the single nucleotide polymorphisms(SNPs), which are associated with the muscle size and strength in Caucasian. Two methods sparse partial least squares (SPLS) and sparse Hilbert-Schmidt independence criterion (HSIC) were applied for dimension reduction and variables selection in the Functional SNPs Associated with Muscle Size and Strength(FAMuss) Study. The selection ability of two methods was compared by simulations. The genetic determinants of skeletal muscle size and strength before and after exercise training in Caucasian were selected by using these two methods.
Master of Science (MS)
Advisors/Committee Members: Balakrishnan, Narayanaswamy, Xie, Changchun, Statistics.
Subjects/Keywords: Statistics and Probability; Statistics and Probability
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APA ·
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APA (6th Edition):
Qin, M. (2011). Variable Selection Methods for Population-based Genetic Association Studies: SPLS and HSIC. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/9165
Chicago Manual of Style (16th Edition):
Qin, Maochang. “Variable Selection Methods for Population-based Genetic Association Studies: SPLS and HSIC.” 2011. Masters Thesis, McMaster University. Accessed March 01, 2021.
http://hdl.handle.net/11375/9165.
MLA Handbook (7th Edition):
Qin, Maochang. “Variable Selection Methods for Population-based Genetic Association Studies: SPLS and HSIC.” 2011. Web. 01 Mar 2021.
Vancouver:
Qin M. Variable Selection Methods for Population-based Genetic Association Studies: SPLS and HSIC. [Internet] [Masters thesis]. McMaster University; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/11375/9165.
Council of Science Editors:
Qin M. Variable Selection Methods for Population-based Genetic Association Studies: SPLS and HSIC. [Masters Thesis]. McMaster University; 2011. Available from: http://hdl.handle.net/11375/9165
Carnegie Mellon University
9.
Galyardt, April.
Mixed Membership Distributions with Applications to Modeling Multiple Strategy Usage.
Degree: 2012, Carnegie Mellon University
URL: http://repository.cmu.edu/dissertations/219
► This dissertation examines two related questions. How do mixed membership models work? and Can mixed membership be used to model how students use multiple strategies…
(more)
▼ This dissertation examines two related questions. How do mixed membership models work? and Can mixed membership be used to model how students use multiple strategies to solve problems?
Mixed membership models have been used in thousands of applications from text and image processing to genetic microarray analysis. Yet these models are crafted on a case-by-case basis because we do not yet understand the larger class of mixed membership models.
The work presented here addresses this gap and examines two different aspects of the general class of models. First I establish that categorical data is a special case, and allows for a different interpretation of mixed membership than in the general case. Second, I present a new identifiability result that characterizes equivalence classes of mixed membership models which produce the same distribution of data. These results provide a strong foundation for building a model that captures how students use multiple strategies.
How to assess which strategies students use, is an open question. Most psychometric models either do not model strategies at all, or they assume that each student uses a single strategy on all problems, even if they allow different students to use different strategies. The problem is, that’s not what students do. Students switch strategies. Even on the very simplest of arithmetic problems, students use different strategies on different problems, and experts use a different mixture of strategies than novices do.
Assessing which strategies students use is an important part of assessing student knowledge, yet the concept of ‘strategy’ can be ill-defined. I use the Knowledge- Learning-Instruction framework to define a strategy as a particular type of integrative knowledge component. I then look at two different ways to model how students use multiple strategies.
I combine cognitive diagnosis models with mixed membership models to create a multiple strategies model. This new model allows for students to switch strategies from problem to problem, and allows us to estimate both the strategies that students are using and how often each student uses each strategy. I demonstrate this model on a modestly sized assessment of least common multiples.
Lastly, I present an analysis of the different strategies that students use to estimate numerical magnitude. Three smaller results come out of this analysis. First, this illustrates the limits of the general mixed membership model. The properties of mixed membership models developed in this dissertation show that without serious changes to the model, it cannot describe the variation between students that is present in this data set. Second, I develop a exploratory data analysis method for summarizing functional data. Finally, this analysis demonstrates that existing psychological theory for how children estimate numerical magnitude is incomplete. There is more variation between students than is captured by current theoretical models.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Galyardt, A. (2012). Mixed Membership Distributions with Applications to Modeling Multiple Strategy Usage. (Thesis). Carnegie Mellon University. Retrieved from http://repository.cmu.edu/dissertations/219
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):
Galyardt, April. “Mixed Membership Distributions with Applications to Modeling Multiple Strategy Usage.” 2012. Thesis, Carnegie Mellon University. Accessed March 01, 2021.
http://repository.cmu.edu/dissertations/219.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Galyardt, April. “Mixed Membership Distributions with Applications to Modeling Multiple Strategy Usage.” 2012. Web. 01 Mar 2021.
Vancouver:
Galyardt A. Mixed Membership Distributions with Applications to Modeling Multiple Strategy Usage. [Internet] [Thesis]. Carnegie Mellon University; 2012. [cited 2021 Mar 01].
Available from: http://repository.cmu.edu/dissertations/219.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Galyardt A. Mixed Membership Distributions with Applications to Modeling Multiple Strategy Usage. [Thesis]. Carnegie Mellon University; 2012. Available from: http://repository.cmu.edu/dissertations/219
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Carnegie Mellon University
10.
Weaver, Rhiannon.
Behavioral Modeling of Botnet Populations Viewed through Internet Protocol Address Space.
Degree: 2012, Carnegie Mellon University
URL: http://repository.cmu.edu/dissertations/152
► A botnet is a collection of computers infected by a shared set of malicious software, that maintain communications to a single human administrator or small…
(more)
▼ A botnet is a collection of computers infected by a shared set of malicious software, that maintain communications to a single human administrator or small organized group. Botnets are indirectly observable populations; cyber-analysts often measure a botnet’s threat in terms of its size, but size is derived from a count of the observable network touchpoints through which infected machines communicate. Activity is often a count of packets or connection attempts, representing logins to command and control servers, spam messages sent, peer-to-peer communications, or other discrete network behavior. Front line analysts use sandbox testing of a botnet’s malicious software to discover signatures for detecting an infected computer and shutting it down, but there is less focus on modeling the botnet population as a collection of machines obscured by the kaleidoscope view of Internet Protocol (IP) address space. This research presents a Bayesian model for generic modeling of a botnet due to its observable activity across a network. A generation-allocation model is proposed, that separates observable network activity at time t into the counts yt generated by the malicious software, and the network’s allocation of these counts among available IP addresses. As a first step, the framework outlines how to develop a directly observable behavioral model informed by sandbox tests and day-to-day user activity, and then how to use this model as a basis for population estimation in settings using proxies or Network Address Translation (NAT) in which only the aggregate sum of all machine activity is observed. The model is explored via a case study using the Conficker-C botnet that emerged in March of 2009.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Weaver, R. (2012). Behavioral Modeling of Botnet Populations Viewed through Internet Protocol Address Space. (Thesis). Carnegie Mellon University. Retrieved from http://repository.cmu.edu/dissertations/152
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):
Weaver, Rhiannon. “Behavioral Modeling of Botnet Populations Viewed through Internet Protocol Address Space.” 2012. Thesis, Carnegie Mellon University. Accessed March 01, 2021.
http://repository.cmu.edu/dissertations/152.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Weaver, Rhiannon. “Behavioral Modeling of Botnet Populations Viewed through Internet Protocol Address Space.” 2012. Web. 01 Mar 2021.
Vancouver:
Weaver R. Behavioral Modeling of Botnet Populations Viewed through Internet Protocol Address Space. [Internet] [Thesis]. Carnegie Mellon University; 2012. [cited 2021 Mar 01].
Available from: http://repository.cmu.edu/dissertations/152.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Weaver R. Behavioral Modeling of Botnet Populations Viewed through Internet Protocol Address Space. [Thesis]. Carnegie Mellon University; 2012. Available from: http://repository.cmu.edu/dissertations/152
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Carnegie Mellon University
11.
Okamura, Shuhei.
The Short Time Fourier Transform and Local Signals.
Degree: 2011, Carnegie Mellon University
URL: http://repository.cmu.edu/dissertations/58
► In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform…
(more)
▼ In this thesis, I examine the theoretical properties of the short time discrete Fourier transform (STFT). The STFT is obtained by applying the Fourier transform by a fixed-sized, moving window to input series. We move the window by one time point at a time, so we have overlapping windows. I present several theoretical properties of the STFT, applied to various types of complex-valued, univariate time series inputs, and their outputs in closed forms. In particular, just like the discrete Fourier transform, the STFT’s modulus time series takes large positive values when the input is a periodic signal. One main point is that a white noise time series input results in the STFT output being a complex-valued stationary time series and we can derive the time and time-frequency dependency structure such as the cross- covariance functions. Our primary focus is the detection of local periodic signals. I present a method to detect local signals by computing the probability that the squared modulus STFT time series has consecutive large values exceeding some threshold after one exceeding observation following one observation less than the threshold. We discuss a method to reduce the computation of such probabilities by the Box-Cox transformation and the delta method, and show that it works well in comparison to the Monte Carlo simulation method.
Subjects/Keywords: Statistics and Probability
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APA ·
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APA (6th Edition):
Okamura, S. (2011). The Short Time Fourier Transform and Local Signals. (Thesis). Carnegie Mellon University. Retrieved from http://repository.cmu.edu/dissertations/58
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):
Okamura, Shuhei. “The Short Time Fourier Transform and Local Signals.” 2011. Thesis, Carnegie Mellon University. Accessed March 01, 2021.
http://repository.cmu.edu/dissertations/58.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Okamura, Shuhei. “The Short Time Fourier Transform and Local Signals.” 2011. Web. 01 Mar 2021.
Vancouver:
Okamura S. The Short Time Fourier Transform and Local Signals. [Internet] [Thesis]. Carnegie Mellon University; 2011. [cited 2021 Mar 01].
Available from: http://repository.cmu.edu/dissertations/58.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Okamura S. The Short Time Fourier Transform and Local Signals. [Thesis]. Carnegie Mellon University; 2011. Available from: http://repository.cmu.edu/dissertations/58
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Carnegie Mellon University
12.
Buchman, Susan.
High-Dimensional Adaptive Basis Density Estimation.
Degree: 2011, Carnegie Mellon University
URL: http://repository.cmu.edu/dissertations/169
► In the realm of high-dimensional statistics, regression and classification have received much attention, while density estimation has lagged behind. Yet there are compelling scientific questions…
(more)
▼ In the realm of high-dimensional statistics, regression and classification have received much attention, while density estimation has lagged behind. Yet there are compelling scientific questions which can only be addressed via density estimation using high-dimensional data, such as the paths of North Atlantic tropical cyclones. If we cast each track as a single high-dimensional data point, density estimation allows us to answer such questions via integration or Monte Carlo methods. In this dissertation, I present three new methods for estimating densities and intensities for high-dimensional data, all of which rely on a technique called diffusion maps. This technique constructs a mapping for high-dimensional, complex data into a low-dimensional space, providing a new basis that can be used in conjunction with traditional density estimation methods. Furthermore, I propose a reordering of importance sampling in the high-dimensional setting. Traditional importance sampling estimates high-dimensional integrals with the aid of an instrumental distribution chosen specifically to minimize the variance of the estimator. In many applications, the integral of interest is with respect to an estimated density. I argue that in the high-dimensional realm, performance can be improved by reversing the procedure: instead of estimating a density and then selecting an appropriate instrumental distribution, begin with the instrumental distribution and estimate the density with respect to it directly. The variance reduction follows from the improved density estimate. Lastly, I present some initial results in using climatic predictors such as sea surface temperature as spatial covariates in point process estimation.
Subjects/Keywords: Statistics and Probability
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APA ·
Chicago ·
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CSE |
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APA (6th Edition):
Buchman, S. (2011). High-Dimensional Adaptive Basis Density Estimation. (Thesis). Carnegie Mellon University. Retrieved from http://repository.cmu.edu/dissertations/169
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):
Buchman, Susan. “High-Dimensional Adaptive Basis Density Estimation.” 2011. Thesis, Carnegie Mellon University. Accessed March 01, 2021.
http://repository.cmu.edu/dissertations/169.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Buchman, Susan. “High-Dimensional Adaptive Basis Density Estimation.” 2011. Web. 01 Mar 2021.
Vancouver:
Buchman S. High-Dimensional Adaptive Basis Density Estimation. [Internet] [Thesis]. Carnegie Mellon University; 2011. [cited 2021 Mar 01].
Available from: http://repository.cmu.edu/dissertations/169.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Buchman S. High-Dimensional Adaptive Basis Density Estimation. [Thesis]. Carnegie Mellon University; 2011. Available from: http://repository.cmu.edu/dissertations/169
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Carnegie Mellon University
13.
Goerg, Georg Matthias.
Learning Spatio-Temporal Dynamics: Nonparametric Methods for Optimal Forecasting and Automated Pattern Discovery.
Degree: 2012, Carnegie Mellon University
URL: http://repository.cmu.edu/dissertations/218
► Many important scientific and data-driven problems involve quantities that vary over space and time. Examples include functional magnetic resonance imaging (fMRI), climate data, or experimental…
(more)
▼ Many important scientific and data-driven problems involve quantities that vary over space and time. Examples include functional magnetic resonance imaging (fMRI), climate data, or experimental studies in physics, chemistry, and biology.
Principal goals of many methods in statistics, machine learning, and signal processing are to use this data and i) extract informative structures and remove noisy, uninformative parts; ii) understand and reconstruct underlying spatio-temporal dynamics that govern these systems; and iii) forecast the data, i.e., describe the system in the future.
Being data-driven problems, it is important to have methods and algorithms that work well in practice for a wide range of spatio-temporal processes as well as various data types. In this thesis I present such generally applicable statistical methods that address all three problems in a unifying manner.
I introduce two new techniques for optimal nonparametric forecasting of spatiotemporal data: hard and mixed LICORS (Light Cone Reconstruction of States). Hard LICORS is a consistent predictive state estimator and extends previous work from Shalizi (2003); Shalizi, Haslinger, Rouquier, Klinkner, and Moore (2006); Shalizi, Klinkner, and Haslinger (2004) to continuous-valued spatio-temporal fields. Mixed LICORS builds on a new, fully probabilistic model of light cones and predictive states mappings, and is an EM-like version of hard LICORS. Simulations show that it has much better finite sample properties than hard LICORS. I also propose a sparse variant of mixed LICORS, which improves out-of-sample forecasts even further.
Both methods can then be used to estimate local statistical complexity (LSC) (Shalizi, 2003), a fully automatic technique for pattern discovery in dynamical systems. Simulations and applications to fMRI data demonstrate that the proposed methods work well and give useful results in very general scientific settings.
Lastly, I made most methods publicly available as R (R Development Core Team, 2010) or Python (Van Rossum, 2003) packages, so researchers can use these methods and better understand, forecast, and discover patterns in the data they study.
Subjects/Keywords: Statistics and Probability
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APA ·
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CSE |
Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Goerg, G. M. (2012). Learning Spatio-Temporal Dynamics: Nonparametric Methods for Optimal Forecasting and Automated Pattern Discovery. (Thesis). Carnegie Mellon University. Retrieved from http://repository.cmu.edu/dissertations/218
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):
Goerg, Georg Matthias. “Learning Spatio-Temporal Dynamics: Nonparametric Methods for Optimal Forecasting and Automated Pattern Discovery.” 2012. Thesis, Carnegie Mellon University. Accessed March 01, 2021.
http://repository.cmu.edu/dissertations/218.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Goerg, Georg Matthias. “Learning Spatio-Temporal Dynamics: Nonparametric Methods for Optimal Forecasting and Automated Pattern Discovery.” 2012. Web. 01 Mar 2021.
Vancouver:
Goerg GM. Learning Spatio-Temporal Dynamics: Nonparametric Methods for Optimal Forecasting and Automated Pattern Discovery. [Internet] [Thesis]. Carnegie Mellon University; 2012. [cited 2021 Mar 01].
Available from: http://repository.cmu.edu/dissertations/218.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Goerg GM. Learning Spatio-Temporal Dynamics: Nonparametric Methods for Optimal Forecasting and Automated Pattern Discovery. [Thesis]. Carnegie Mellon University; 2012. Available from: http://repository.cmu.edu/dissertations/218
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of California – Berkeley
14.
Lanoue, Daniel Parmet.
The Metric Coalescent.
Degree: Mathematics, 2015, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/8c01d983
► The Metric Coalescent (MC) is a measure-valued Markov Process generalizing the classical Kingman Coalescent. We show how the MC arises naturally from a discrete agent…
(more)
▼ The Metric Coalescent (MC) is a measure-valued Markov Process generalizing the classical Kingman Coalescent. We show how the MC arises naturally from a discrete agent based model (Compulsive Gambler) of social dynamics and prove an existence and uniqueness theorem extending the MC to the space of all Borel probability measures on any locally compact Polish space.
Subjects/Keywords: Mathematics; Coalescent; Probability
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APA (6th Edition):
Lanoue, D. P. (2015). The Metric Coalescent. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/8c01d983
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):
Lanoue, Daniel Parmet. “The Metric Coalescent.” 2015. Thesis, University of California – Berkeley. Accessed March 01, 2021.
http://www.escholarship.org/uc/item/8c01d983.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Lanoue, Daniel Parmet. “The Metric Coalescent.” 2015. Web. 01 Mar 2021.
Vancouver:
Lanoue DP. The Metric Coalescent. [Internet] [Thesis]. University of California – Berkeley; 2015. [cited 2021 Mar 01].
Available from: http://www.escholarship.org/uc/item/8c01d983.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Lanoue DP. The Metric Coalescent. [Thesis]. University of California – Berkeley; 2015. Available from: http://www.escholarship.org/uc/item/8c01d983
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Oregon State University
15.
Loke, Sooie-Hoe.
Ruin Problems with Risky Investments.
Degree: PhD, Mathematics, 2015, Oregon State University
URL: http://hdl.handle.net/1957/57263
► In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses…
(more)
▼ In this dissertation, we study two risk models. First, we consider the dual risk process which models the surplus of a company that incurs expenses at a constant rate and earns random positive gains at random times. When the surplus is invested in a risky asset following a geometric Brownian motion, we show that the ruin
probability decays algebraically for small volatility and that ruin is certain for large volatility. We use numerical methods to approximate the ruin
probability when the surplus is invested in a risk-free asset. When there are no investments, we recover the exact expression for the ruin
probability via Wiener-Hopf factorization. Second, we are concerned with incurred but not reported (IBNR) claims, modeled by delaying the settlement of each claim by a random time. When the investments follow a geometric Brownian motion, we derive a parabolic integro-partial-differential equation (IPDE) for the ultimate ruin
probability with final value condition given by the ruin
probability under risky investments with no delay. Assuming that the delay times are bounded by a constant, we obtain an existence theorem of the final value IPDE in the space of bounded functions, and a uniqueness theorem in the space of square integrable functions. When the delay times are deterministic, we show that delaying the settlement of claims does not reduce the
probability of ruin when the volatility is large.
Advisors/Committee Members: Thomann, Enrique A. (advisor), Waymire, Edward C. (committee member).
Subjects/Keywords: ruin probability; Investments
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APA ·
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Export
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APA (6th Edition):
Loke, S. (2015). Ruin Problems with Risky Investments. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/57263
Chicago Manual of Style (16th Edition):
Loke, Sooie-Hoe. “Ruin Problems with Risky Investments.” 2015. Doctoral Dissertation, Oregon State University. Accessed March 01, 2021.
http://hdl.handle.net/1957/57263.
MLA Handbook (7th Edition):
Loke, Sooie-Hoe. “Ruin Problems with Risky Investments.” 2015. Web. 01 Mar 2021.
Vancouver:
Loke S. Ruin Problems with Risky Investments. [Internet] [Doctoral dissertation]. Oregon State University; 2015. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1957/57263.
Council of Science Editors:
Loke S. Ruin Problems with Risky Investments. [Doctoral Dissertation]. Oregon State University; 2015. Available from: http://hdl.handle.net/1957/57263
University of Bristol
16.
Lutsko, Chris E. H.
Statistical properties of dynamical systems : from statistical mechanics to hyperbolic geometry.
Degree: PhD, 2020, University of Bristol
URL: http://hdl.handle.net/1983/d8773f13-fca7-478e-812c-8f279ff4ff10
► Broadly, this thesis treats the statistical properties of dynamical systems in two different contexts. That is, we characterise asymptotic behaviour, independence, and randomness in two…
(more)
▼ Broadly, this thesis treats the statistical properties of dynamical systems in two different contexts. That is, we characterise asymptotic behaviour, independence, and randomness in two distinct settings. First we consider two models for diffusion of gasses: the random Lorentz gas and the random wind-tree model. Understanding how typical particles diffuse outwards is one of the central aims of the field. In both these contexts our main results state that (in a particular scaling limit), when considered over long times, the typical particle trajectory converges in distribution to a Brownian motion. We use novel coupling methods to approximate these trajectories by Markovian walks and thus prove these invariance principles. For the second half, we consider a general discrete hyperbolic subgroup. Therefore these groups may be 'thin'. Then we consider the orbit of a point in hyperbolic half-space by this group. The main results concern characterising the limiting local statistics of these orbits in a number of different contexts. We extend methods from homogeneous dynamics to the thin group setting and use Patterson-Sullivan theory and equidistribution of expanding horospheres to characterise the limiting behaviour of these group orbits. This work has applications to sphere packings, Diophantine approximation, continued fractions, and more.
Subjects/Keywords: Dynamical systems; Probability
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APA ·
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APA (6th Edition):
Lutsko, C. E. H. (2020). Statistical properties of dynamical systems : from statistical mechanics to hyperbolic geometry. (Doctoral Dissertation). University of Bristol. Retrieved from http://hdl.handle.net/1983/d8773f13-fca7-478e-812c-8f279ff4ff10
Chicago Manual of Style (16th Edition):
Lutsko, Chris E H. “Statistical properties of dynamical systems : from statistical mechanics to hyperbolic geometry.” 2020. Doctoral Dissertation, University of Bristol. Accessed March 01, 2021.
http://hdl.handle.net/1983/d8773f13-fca7-478e-812c-8f279ff4ff10.
MLA Handbook (7th Edition):
Lutsko, Chris E H. “Statistical properties of dynamical systems : from statistical mechanics to hyperbolic geometry.” 2020. Web. 01 Mar 2021.
Vancouver:
Lutsko CEH. Statistical properties of dynamical systems : from statistical mechanics to hyperbolic geometry. [Internet] [Doctoral dissertation]. University of Bristol; 2020. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1983/d8773f13-fca7-478e-812c-8f279ff4ff10.
Council of Science Editors:
Lutsko CEH. Statistical properties of dynamical systems : from statistical mechanics to hyperbolic geometry. [Doctoral Dissertation]. University of Bristol; 2020. Available from: http://hdl.handle.net/1983/d8773f13-fca7-478e-812c-8f279ff4ff10
University of Waterloo
17.
Kim, Sung Soo.
Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends.
Degree: 2013, University of Waterloo
URL: http://hdl.handle.net/10012/7757
► In this thesis, we consider a risk model which incorporates multiple threshold levels characterizing an insurer's minimal capital requirement, dividend paying situations, and external financial…
(more)
▼ In this thesis, we consider a risk model which incorporates multiple threshold levels characterizing an insurer's minimal capital requirement, dividend paying situations, and external financial activities. Our model is based on discrete monetary and time units, and the main quantities of interest are the finite-time ruin probabilities and the expected total discounted dividends paid prior to ruin. We mainly focus on the development of computational methods to attain these quantities of interest. One of the popular methods in the current literature used for studying such problems involves a recursive approach which incorporates appropriate conditioning arguments on the claim times and sizes, and we implement this procedure as well. Furthermore, ruin can occur due to both a claim as well as interest expense accumulation as our model allows the insurer to borrow money from an external fund. In this thesis, we consider only non-stochastic interest rates for both lending and borrowing activities. After constructing appropriate recursive formulae for the finite-time ruin probabilities and the expected total discounted dividends paid prior to ruin, we investigate various numerical examples and make some observations concerning the impact our threshold levels have on finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.
Subjects/Keywords: Ruin; Applied probability
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APA (6th Edition):
Kim, S. S. (2013). Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/7757
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):
Kim, Sung Soo. “Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends.” 2013. Thesis, University of Waterloo. Accessed March 01, 2021.
http://hdl.handle.net/10012/7757.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Kim, Sung Soo. “Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends.” 2013. Web. 01 Mar 2021.
Vancouver:
Kim SS. Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends. [Internet] [Thesis]. University of Waterloo; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10012/7757.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Kim SS. Ruin Analysis in a Discrete-time Sparre Andersen Model with External Financial Activities and Random Dividends. [Thesis]. University of Waterloo; 2013. Available from: http://hdl.handle.net/10012/7757
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Toronto
18.
Li, Xiang.
On the Logarithimic Calculus and Sidorenko's Conjecture.
Degree: 2011, University of Toronto
URL: http://hdl.handle.net/1807/31311
► We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration…
(more)
▼ We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erdos-Simonovits and Sidorenko for new families of graphs. In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.
MAST
Advisors/Committee Members: Szegedy, Balazs, Mathematics.
Subjects/Keywords: Combinatorics; Probability; 0280
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APA ·
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APA (6th Edition):
Li, X. (2011). On the Logarithimic Calculus and Sidorenko's Conjecture. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/31311
Chicago Manual of Style (16th Edition):
Li, Xiang. “On the Logarithimic Calculus and Sidorenko's Conjecture.” 2011. Masters Thesis, University of Toronto. Accessed March 01, 2021.
http://hdl.handle.net/1807/31311.
MLA Handbook (7th Edition):
Li, Xiang. “On the Logarithimic Calculus and Sidorenko's Conjecture.” 2011. Web. 01 Mar 2021.
Vancouver:
Li X. On the Logarithimic Calculus and Sidorenko's Conjecture. [Internet] [Masters thesis]. University of Toronto; 2011. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1807/31311.
Council of Science Editors:
Li X. On the Logarithimic Calculus and Sidorenko's Conjecture. [Masters Thesis]. University of Toronto; 2011. Available from: http://hdl.handle.net/1807/31311
University of Wisconsin – Milwaukee
19.
Samanthi, Ranadeera Gamage Madhuka.
Comparing the Riskiness of Dependent Portfolios.
Degree: PhD, Mathematics, 2016, University of Wisconsin – Milwaukee
URL: https://dc.uwm.edu/etd/1195
► A nonparametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas, Jones, Puri, and Zitikis (2007).…
(more)
▼ A nonparametric test based on nested L-statistics and designed to compare the riskiness of portfolios was introduced by Brazauskas, Jones, Puri, and Zitikis (2007). Its asymptotic and small-sample properties were primarily explored for independent portfolios, though independence is not a required condition for the test to work. In this dissertation, we investigate how the performance of the test changes when insurance portfolios are dependent. To achieve that goal, we perform a simulation study where we consider three different risk measures: conditional tail expectation, proportional hazards transform, and mean. Further, three portfolios are generated from exponential, Pareto, and lognormal distributions, and their interdependence is modeled with the three-dimensional t and Gaussian copulas. It is found that the presence of comonotonicity makes the test very liberal for all the risk measures under consideration. For various other types of dependence, the results are mixed, i.e., they depend on the chosen risk measure, sample size, and even on the test’s significance level. We illustrate how to incorporate such findings into sensitivity analysis of the decisions. The risks we analyze represent tornado damages in different regions of the United States from 1890 to 1999. In addition, we provide a theoretical explanation to the behavior of the power function of the test by considering the usual stochastic orders of the Gini indexes of multivariate normal risks with the same marginals but different dependence structures. Finally, we generalize the comparison for the Gini indexes of multivariate elliptical risks.
Advisors/Committee Members: Vytaras Brazauskas, Wei Wei.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Samanthi, R. G. M. (2016). Comparing the Riskiness of Dependent Portfolios. (Doctoral Dissertation). University of Wisconsin – Milwaukee. Retrieved from https://dc.uwm.edu/etd/1195
Chicago Manual of Style (16th Edition):
Samanthi, Ranadeera Gamage Madhuka. “Comparing the Riskiness of Dependent Portfolios.” 2016. Doctoral Dissertation, University of Wisconsin – Milwaukee. Accessed March 01, 2021.
https://dc.uwm.edu/etd/1195.
MLA Handbook (7th Edition):
Samanthi, Ranadeera Gamage Madhuka. “Comparing the Riskiness of Dependent Portfolios.” 2016. Web. 01 Mar 2021.
Vancouver:
Samanthi RGM. Comparing the Riskiness of Dependent Portfolios. [Internet] [Doctoral dissertation]. University of Wisconsin – Milwaukee; 2016. [cited 2021 Mar 01].
Available from: https://dc.uwm.edu/etd/1195.
Council of Science Editors:
Samanthi RGM. Comparing the Riskiness of Dependent Portfolios. [Doctoral Dissertation]. University of Wisconsin – Milwaukee; 2016. Available from: https://dc.uwm.edu/etd/1195
Western Michigan University
20.
Wisadrattanapong, Therawat.
Robust Nonparametric Methods for Regression to the Mean Model.
Degree: PhD, Statistics, 2011, Western Michigan University
URL: https://scholarworks.wmich.edu/dissertations/483
► Regression to the mean is a statistical phenomenon that often confounds treatment effects in experiments. Consider an experiment involving a treatment, in which a…
(more)
▼ Regression to the mean is a statistical phenomenon that often confounds treatment effects in experiments. Consider an experiment involving a treatment, in which a response is measured (baseline) on a
subject then a treatment is applied and a second measurement is taken. Then under many bivariate models for the pair of responses (including the bivariate normal), the predicted response of the second measurement will regress to the mean. In experiments where the second response is only taken for a select sample, say above a cutoff value, then this regression to the mean effect may mistakenly be thought of as a treatment effect.
In this investigation, we consider a model of the treatment effect which also takes into account this regression to the mean effect. In particular, we consider the multiplicative model of Naranjo and McKean (2001). Naranjo and McKean developed a bootstrap test for treatment effect based on least squares methods for bivariate normal distributions. We developed robust procedures to assess treatment effects for this multiplicative model. Our procedures are based on rank-based methods, for general score functions. Our preliminary Monte Carlo investigations show that our procedures are robust. We extend this robust and traditional development to models other than the bivariate normal, including the multivariate t distributions. We investigate the finite sample properties of these methods and compare their empirical behavior over a variety of models and situations.
Advisors/Committee Members: Dr. Joseph W. McKean, Dr. Joshua D. Naranjo, Dr. Bradley E. Huitema.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Wisadrattanapong, T. (2011). Robust Nonparametric Methods for Regression to the Mean Model. (Doctoral Dissertation). Western Michigan University. Retrieved from https://scholarworks.wmich.edu/dissertations/483
Chicago Manual of Style (16th Edition):
Wisadrattanapong, Therawat. “Robust Nonparametric Methods for Regression to the Mean Model.” 2011. Doctoral Dissertation, Western Michigan University. Accessed March 01, 2021.
https://scholarworks.wmich.edu/dissertations/483.
MLA Handbook (7th Edition):
Wisadrattanapong, Therawat. “Robust Nonparametric Methods for Regression to the Mean Model.” 2011. Web. 01 Mar 2021.
Vancouver:
Wisadrattanapong T. Robust Nonparametric Methods for Regression to the Mean Model. [Internet] [Doctoral dissertation]. Western Michigan University; 2011. [cited 2021 Mar 01].
Available from: https://scholarworks.wmich.edu/dissertations/483.
Council of Science Editors:
Wisadrattanapong T. Robust Nonparametric Methods for Regression to the Mean Model. [Doctoral Dissertation]. Western Michigan University; 2011. Available from: https://scholarworks.wmich.edu/dissertations/483
Western Michigan University
21.
Villarente Rosales, Karen Grace.
Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions.
Degree: PhD, Statistics, 2010, Western Michigan University
URL: https://scholarworks.wmich.edu/dissertations/622
► Various research fields produce data that are lognormally distributed and inflated with zero values. This type of data follows a delta distribution. In this…
(more)
▼ Various research fields produce data that are lognormally distributed and inflated with zero values. This type of data follows a delta distribution. In this study, we want to extensively investigate different interval and hypothesis testing methods for comparing the means of two delta populations to see which methods are optimal under different conditions of the populations.
For confidence intervals, existing MVUE methods are extended to two sample cases and compared to classical and two proposed robust methods. We investigated the performance of the classical Student's t, Welch t, and Wilcoxon-based interval to see if these methods really perform badly on zero-inflated data. A simulation study is done to assess coverage accuracy of all the methods. Hypothesis testing on the equality of means of two delta distributions is done using confidence intervals. The previous interval methods are compared with two-part models by Lachenbruch (2001), MLEbased intervals, and two proposed robust intervals. The performance of the tests are assessed through a simulation study where the Type I error rates and power rates are computed. A robustness study is conducted by comparing the performance of estimators and tests under various distributions like gamma and Weibull.
Additionally, the Wilcoxon-based interval is assessed on three parameters that measure the difference of the two delta distributions namely, difference of means, difference of medians and median of differences. A simulation study is conducted to evaluate the performance of the three parameters of differences. The Wilcoxon-based interval was found to measure the median of differences best.
Advisors/Committee Members: Dr. Joshua D. Naranjo, Dr. Magdalena Niewiadomska-Bugaj, Dr. Jung Chao Wang.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Villarente Rosales, K. G. (2010). Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions. (Doctoral Dissertation). Western Michigan University. Retrieved from https://scholarworks.wmich.edu/dissertations/622
Chicago Manual of Style (16th Edition):
Villarente Rosales, Karen Grace. “Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions.” 2010. Doctoral Dissertation, Western Michigan University. Accessed March 01, 2021.
https://scholarworks.wmich.edu/dissertations/622.
MLA Handbook (7th Edition):
Villarente Rosales, Karen Grace. “Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions.” 2010. Web. 01 Mar 2021.
Vancouver:
Villarente Rosales KG. Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions. [Internet] [Doctoral dissertation]. Western Michigan University; 2010. [cited 2021 Mar 01].
Available from: https://scholarworks.wmich.edu/dissertations/622.
Council of Science Editors:
Villarente Rosales KG. Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions. [Doctoral Dissertation]. Western Michigan University; 2010. Available from: https://scholarworks.wmich.edu/dissertations/622
Western Michigan University
22.
Okyere, Gabriel Asare.
Robust Adaptive Scheme for Linear Mixed Models.
Degree: PhD, Statistics, 2011, Western Michigan University
URL: https://scholarworks.wmich.edu/dissertations/445
► If the underlying distribution of a statistical model is known then a procedure which maximizes power and efficiency can be selected. For example, if…
(more)
▼ If the underlying distribution of a statistical model is known then a procedure which maximizes power and efficiency can be selected. For example, if the distribution of errors is known to be normal in a linear model then inference based on least squares maximizes power and efficiency. More generally, if this distribution is known then a ranked based inference based on the appropriate rank score function has maximum efficiency. In practice, though, this distribution is not known. Adaptive schemes are procedures which hopefully select appropriate methods to optimize the analysis.
Hogg (1974) presented an adaptive rank-based scheme for testing in the simple two-sample location model. It consists of a family of distribution free tests, each associated with a rank score function, and a selection procedure which chooses a test from this family. For continuous error distributions, Hogg's scheme is valid for testing; that is, it retains the level. This, however, is not true for estimation and fitting. Little has been done to extend Hogg's scheme beyond simple location problems. In this research we extend Hogg's adaptive scheme for testing to mixed models consisting of m clusters of observations.
This is an important practical family of models, including, for example, repeated measure designs, multi-center clinical designs, and randomized block designs. Under the assumption of exchangeable errors, we establish that our testing scheme is valid. In practice, though, for these models fitting is crucial. Based on the fitting of a model a residual analysis can be performed to check, say, quality of fit and to determine outliers. Further, standard errors of the estimates can then be obtained so that confidence intervals for contrasts of interests can readily be formed. With this in mind, we have also developed several adaptive fitting schemes for these models. These are based on several types of rank-based estimation procedures, including joint ranking and multiple ranking types of fitting.
Our schemes are robust and highly efficient. A large Monte Carlo study over error distributions ranging from heavy-tailed to light-tailed distributions and from symmetric distributions to skewed distributions gives empirical credence to our adaptive procedures. We illustrate our procedures with several real clinical examples.
Advisors/Committee Members: Dr. JosephW. McKean, Dr. Joshua D. Naranjo, Dr. Thomas J. Vidmar.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Okyere, G. A. (2011). Robust Adaptive Scheme for Linear Mixed Models. (Doctoral Dissertation). Western Michigan University. Retrieved from https://scholarworks.wmich.edu/dissertations/445
Chicago Manual of Style (16th Edition):
Okyere, Gabriel Asare. “Robust Adaptive Scheme for Linear Mixed Models.” 2011. Doctoral Dissertation, Western Michigan University. Accessed March 01, 2021.
https://scholarworks.wmich.edu/dissertations/445.
MLA Handbook (7th Edition):
Okyere, Gabriel Asare. “Robust Adaptive Scheme for Linear Mixed Models.” 2011. Web. 01 Mar 2021.
Vancouver:
Okyere GA. Robust Adaptive Scheme for Linear Mixed Models. [Internet] [Doctoral dissertation]. Western Michigan University; 2011. [cited 2021 Mar 01].
Available from: https://scholarworks.wmich.edu/dissertations/445.
Council of Science Editors:
Okyere GA. Robust Adaptive Scheme for Linear Mixed Models. [Doctoral Dissertation]. Western Michigan University; 2011. Available from: https://scholarworks.wmich.edu/dissertations/445
23.
Narayanan, Bhargav.
Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.
Degree: PhD, 2015, University of Cambridge
URL: https://www.repository.cam.ac.uk/handle/1810/252850https://www.repository.cam.ac.uk/bitstream/1810/252850/2/license.txt
;
https://www.repository.cam.ac.uk/bitstream/1810/252850/3/license_rdf
;
https://www.repository.cam.ac.uk/bitstream/1810/252850/4/thesis.pdf.txt
;
https://www.repository.cam.ac.uk/bitstream/1810/252850/5/thesis.pdf.jpg
In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.
Subjects/Keywords: Combinatorics; Probability theory
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APA (6th Edition):
Narayanan, B. (2015). Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/252850https://www.repository.cam.ac.uk/bitstream/1810/252850/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/3/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/252850/4/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/5/thesis.pdf.jpg
Chicago Manual of Style (16th Edition):
Narayanan, Bhargav. “Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.” 2015. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://www.repository.cam.ac.uk/handle/1810/252850https://www.repository.cam.ac.uk/bitstream/1810/252850/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/3/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/252850/4/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/5/thesis.pdf.jpg.
MLA Handbook (7th Edition):
Narayanan, Bhargav. “Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.” 2015. Web. 01 Mar 2021.
Vancouver:
Narayanan B. Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory. [Internet] [Doctoral dissertation]. University of Cambridge; 2015. [cited 2021 Mar 01].
Available from: https://www.repository.cam.ac.uk/handle/1810/252850https://www.repository.cam.ac.uk/bitstream/1810/252850/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/3/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/252850/4/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/5/thesis.pdf.jpg.
Council of Science Editors:
Narayanan B. Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory. [Doctoral Dissertation]. University of Cambridge; 2015. Available from: https://www.repository.cam.ac.uk/handle/1810/252850https://www.repository.cam.ac.uk/bitstream/1810/252850/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/3/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/252850/4/thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/252850/5/thesis.pdf.jpg
Iowa State University
24.
Zhou, Ming.
Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data.
Degree: 2011, Iowa State University
URL: https://lib.dr.iastate.edu/etd/11207
► In statistical analysis, distribution assumptions are often subject to be tested. In this dissertation, the problem of testing two important distribution assumptions, the normal distribution…
(more)
▼ In statistical analysis, distribution assumptions are often subject to be tested. In this dissertation, the problem of testing two important distribution assumptions, the normal distribution and uniform distribution, is considered. Specifically, a new characterization of multivariate normality based on univariate projections is developed. On the other hand, a powerful affine invariant test of multivariate normality is proposed. Moreover, this dissertation also presents an asymptotic distribution free test of multivariate uniformity based on m-nearest neighbors. Both tests have demonstrated good power performance by numerical studies.
Incomplete data is another commonly encountered issue in practice. This dissertation also reports an efficient estimation method for population mean in longitudinal surveys under monotone missing pattern. The proposed method is developed using the generalized method of moments technique by incorporating all the available information at each time point. Efficiency of the method over the direct propensity score type estimator is also demonstrated by limited numerical studies.
Subjects/Keywords: Statistics and Probability
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APA ·
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Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Zhou, M. (2011). Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/11207
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):
Zhou, Ming. “Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data.” 2011. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/11207.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Zhou, Ming. “Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data.” 2011. Web. 01 Mar 2021.
Vancouver:
Zhou M. Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data. [Internet] [Thesis]. Iowa State University; 2011. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/11207.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Zhou M. Some goodness-of-fit tests and efficient estimation in longitudinal surveys under missing data. [Thesis]. Iowa State University; 2011. Available from: https://lib.dr.iastate.edu/etd/11207
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
25.
Peng, Liuhua.
Topics in statistical inference for massive data and high-dimensional data.
Degree: 2017, Iowa State University
URL: https://lib.dr.iastate.edu/etd/15601
► This dissertation consists of three research papers that deal with three different problems in statistics concerning high-volume datasets. The first paper studies the distributed statistical…
(more)
▼ This dissertation consists of three research papers that deal with three different problems in statistics concerning high-volume datasets. The first paper studies the distributed statistical inference for massive data. With the increasing size of the data, computational complexity and feasibility should be taken into consideration for statistical analyses. We investigate the statistical efficiency of the distributed version of a general class of statistics. Distributed bootstrap algorithms are proposed to approximate the distribution of the distributed statistics. These approaches relief the computational burdens of conventional methods while preserving adequate statistical efficiency. The second paper deals with testing the identity and sphericity hypotheses problem regarding high-dimensional covariance matrices, with a focus on improving the power of existing methods. By taking advantage of the sparsity in the underlying covariance matrices, the power improvement is accomplished by utilizing the banding estimator for the covariance matrices, which leads to a significant reduction in the variance of the test statistics. The last paper considers variable selection for high-dimensional data. Distance-based variable importance measures are proposed to rank and select variables with dependence structures being taken into consideration. The importance measures are inspired by the multi-response permutation procedure (MRPP) and the energy distance. A backward selection algorithm is developed to discover important variables and to improve the power of the original MRPP for high-dimensional data.
Subjects/Keywords: Statistics and Probability
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Export
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APA (6th Edition):
Peng, L. (2017). Topics in statistical inference for massive data and high-dimensional data. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/15601
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):
Peng, Liuhua. “Topics in statistical inference for massive data and high-dimensional data.” 2017. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/15601.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Peng, Liuhua. “Topics in statistical inference for massive data and high-dimensional data.” 2017. Web. 01 Mar 2021.
Vancouver:
Peng L. Topics in statistical inference for massive data and high-dimensional data. [Internet] [Thesis]. Iowa State University; 2017. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/15601.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Peng L. Topics in statistical inference for massive data and high-dimensional data. [Thesis]. Iowa State University; 2017. Available from: https://lib.dr.iastate.edu/etd/15601
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
26.
Sage, Andrew.
Random forest robustness, variable importance, and tree aggregation.
Degree: 2018, Iowa State University
URL: https://lib.dr.iastate.edu/etd/16453
► Random forest methodology is a nonparametric, machine learning approach capable of strong performance in regression and classification problems involving complex datasets. In addition to making…
(more)
▼ Random forest methodology is a nonparametric, machine learning approach capable of strong performance in regression and classification problems involving complex datasets. In addition to making predictions, random forests can be used to assess the relative importance of explanatory variables. In this dissertation, we explore three topics related to random forests: tree aggregation, variable importance, and robustness. In Chapter 2, we show that the method of tree aggregation used in one popular random forest implementation can lead to biased class probability estimates and that it is often beneficial to combine the tree partitioning algorithm used in one implementation with the aggregation scheme used in another. In Chapter 3, we show that imputing missing values proir to assessing variable importance often leads to inaccurate variable importance measures. Using simulation studies, we investigate the impact on variable importance of six random-forest-based imputation techniques and find that some techniques are prone to overestimating the importance of variables whose values have been imputed, while other techniques tend to underestimate the importance of such variables. In Chapter 4, we propose a new robust approach for random forest regression. Adapted from a popular approach used in polynomial regression, our method uses residual analysis to modify the weights associated with training cases in random forest predictions, so that outlying training cases have less impact. We show, using simulation studies, that this approach outperforms existing robust techniques on noisy, contaminated datasets.
Subjects/Keywords: Statistics and Probability
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APA ·
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MLA ·
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Export
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Manager
APA (6th Edition):
Sage, A. (2018). Random forest robustness, variable importance, and tree aggregation. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/16453
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):
Sage, Andrew. “Random forest robustness, variable importance, and tree aggregation.” 2018. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/16453.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Sage, Andrew. “Random forest robustness, variable importance, and tree aggregation.” 2018. Web. 01 Mar 2021.
Vancouver:
Sage A. Random forest robustness, variable importance, and tree aggregation. [Internet] [Thesis]. Iowa State University; 2018. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/16453.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Sage A. Random forest robustness, variable importance, and tree aggregation. [Thesis]. Iowa State University; 2018. Available from: https://lib.dr.iastate.edu/etd/16453
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
27.
Lin, Hui.
Statistical methods in disease risk analysis, disease testing and nutrition epidemiology.
Degree: 2012, Iowa State University
URL: https://lib.dr.iastate.edu/etd/13380
► The thesis is composed of three separated projects: disease risk scoring systems (chapter 2), statistical tests for proportion difference in one-to-two matched binary data (chapter…
(more)
▼ The thesis is composed of three separated projects: disease risk scoring systems (chapter 2), statistical tests for proportion difference in one-to-two matched binary data (chapter 3) and bivariate measurement error model for nutrition epidemiology (chapter 4). In the first project, we propose to use group lasso algorithm for logistic regression to construct a risk scoring system for predicting disease in swine. We choose the penalty parameter for the group lasso through leave-one-out cross validation and use the area under the receiver operating characteristic curve as criterion. We show our proposed scoring system is superior to existing methods. The second project was originally motivated by the pooling of diagnostic tests. We proposed exact and asymptotic tests for one-to-two matched binary data. Unlike other existing methods, our procedure doesn't rely on a mutual independence assumption. The emphasis on dependence among observations from the same matched set is natural and appealing, as much in human health as it is in veterinary medicine. It can be applied to many kinds of diagnostic studies with a one-to-two matched data structure. Our method can also be generalized to one-to-N matched case in a straightforward manner. In the third paper we consider the problem of estimating the joint distribution of two correlated random variables where one of the variables is observed with error. DKM is first used to adjust the univariate measurement error. A Gaussian copula is then used to model the correlation structure between the two variables after error adjustment.
Subjects/Keywords: Statistics and Probability
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APA ·
Chicago ·
MLA ·
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Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Lin, H. (2012). Statistical methods in disease risk analysis, disease testing and nutrition epidemiology. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/13380
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):
Lin, Hui. “Statistical methods in disease risk analysis, disease testing and nutrition epidemiology.” 2012. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/13380.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Lin, Hui. “Statistical methods in disease risk analysis, disease testing and nutrition epidemiology.” 2012. Web. 01 Mar 2021.
Vancouver:
Lin H. Statistical methods in disease risk analysis, disease testing and nutrition epidemiology. [Internet] [Thesis]. Iowa State University; 2012. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/13380.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Lin H. Statistical methods in disease risk analysis, disease testing and nutrition epidemiology. [Thesis]. Iowa State University; 2012. Available from: https://lib.dr.iastate.edu/etd/13380
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
28.
Zhang, Wei.
Inference based on data from superpositions of identical renewal processes.
Degree: 2016, Iowa State University
URL: https://lib.dr.iastate.edu/etd/16701
► Maintenance data can be used to make inferences about the reliability of system components. In industrial reliability applications, it is common that a fleet contains…
(more)
▼ Maintenance data can be used to make inferences about the reliability of system components. In industrial reliability applications, it is common that a fleet contains multiple systems. Within each system, there are multiple copies of a component installed in multiple locations (sockets). Examples are two automobile headlights, eight DIMM modules in a computing server, sixteen cylinders in a locomotive engine, etc. For each component replacement event, there is system-level information that a component was replaced. The socket-level information (which particular component was replaced), however, is usually unknown. The aggregated data for a system form a collection of superpositions of renewal processes (SRP). The reliability of the system component is of particular interest for future system design and maintenance planning. In this dissertation, statistical models and methods were developed for estimating the lifetime distribution of system components for the SRP data, which is motivated by some real applications.
In Chapter 2, we propose a parametric likelihood-based procedure for estimating the lifetime distribution of a component from the aggregated recurrence data for a fleet with multiple SRPs. We show how to formulate the likelihood function of the SRP data and compute the maximum likelihood (ML) estimator. The performance of the ML estimator is investigated by simulation studies, as well as real applications on two different data sets. Chapter 3 provides more extensive results of simulation studies on the performance of the ML estimator and two confidence interval methods for estimating quantiles of the component lifetime distribution.
Chapter 4 presents two graphical distributional assessment methods to evaluate how well the parametric models proposed in Chapter 2 fit the observed SRP data. The first method provides a flexible semi-parametric estimate of the lifetime distribution of the component, which is based on a piecewise exponential (PEX) model. The nonparametric simultaneous confidence bands (NPSCBs) based on a bootstrap procedure, are given to assess the amount of statistical uncertainty of the semi-parametric estimate. The second method is based on the use of the mean cumulative function (MCF) plot for the SRP data. The amount of sampling error can be evaluated by using NPSCBs, which show the departures from the fitted model.
Chapter 5 describes how the maximum likelihood estimation procedure (proposed in Chapter 2) for the SRP data is implemented in the SRPML R package. Given the required input, which includes the observed SRP data, the specified log-location-scale distribution and certain parameter specifications, the functions in the SRPML package return the parameter ML estimates, the maximized log likelihood, and confidence intervals based on Wald and/or likelihood-based procedures. A real application of the R package is illustrated, and the required computation time for this estimation procedure are summarized.
Subjects/Keywords: Statistics and Probability
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APA (6th Edition):
Zhang, W. (2016). Inference based on data from superpositions of identical renewal processes. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/16701
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):
Zhang, Wei. “Inference based on data from superpositions of identical renewal processes.” 2016. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/16701.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Zhang, Wei. “Inference based on data from superpositions of identical renewal processes.” 2016. Web. 01 Mar 2021.
Vancouver:
Zhang W. Inference based on data from superpositions of identical renewal processes. [Internet] [Thesis]. Iowa State University; 2016. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/16701.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Zhang W. Inference based on data from superpositions of identical renewal processes. [Thesis]. Iowa State University; 2016. Available from: https://lib.dr.iastate.edu/etd/16701
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
29.
Li, Xinyi.
Non/Semi-parametric learning from data with complex features.
Degree: 2018, Iowa State University
URL: https://lib.dr.iastate.edu/etd/17250
► This thesis is mainly focused on developing novel and flexible non/semi-parametric statistical methods dealing with data with complex features. In recent years, advancement of high…
(more)
▼ This thesis is mainly focused on developing novel and flexible non/semi-parametric statistical methods dealing with data with complex features. In recent years, advancement of high throughput technologies has made it possible to collect sophisticated high-dimensional datasets, such as microarray data, genome-wide single nucleotide polymorphism (SNP) data, and RNA sequencing (RNA-seq) data. These advances have caused an escalating demand for innovative dimension reduction tools to extract useful information from the huge amount of data, to visualize the underlying structure, and to facilitate the understanding and analysis of the data. The research undertaken in my thesis are described below.
In Chapter 1, we consider a semiparametric additive partially linear regression model (APLM) for analyzing ultra-high-dimensional data where both the number of linear components and the number of nonlinear components can be much larger than the sample size. We propose a two-step approach for estimation, selection and simultaneous inference of the components in the APLM. In the first step, the nonlinear additive components are approximated using polynomial spline basis functions, and a doubly penalized procedure is proposed to select nonzero linear and nonlinear components based on adaptive LASSO. In the second step, local linear smoothing is then applied to the data with the selected variables to obtain the asymptotic distribution of the estimators of the nonparametric functions of interest. The proposed method selects the correct model with probability approaching one under regularity conditions. The estimators of both the linear part and nonlinear part are consistent and asymptotically normal, which enables us to construct confidence intervals and make inferences about the regression coefficients and the component functions. The performance of the method is evaluated by simulation studies. The proposed method is also applied to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes.
In Chapter 2, we further consider the model identification problem, as long with variable selection, estimation and inference simultaneously for the additive partially linear model (APLM). APLM combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the "curse of dimensionality". A natural question raised in practice is the choice of structure in the nonparametric part, that is, whether the continuous covariates enter into the model in linear or nonparametric form. In this paper we present a comprehensive framework for simultaneous sparse model identification and learning for ultra-high-dimensional APLMs where both the linear and nonparametric components are possibly larger than the sample size. We propose a fast and efficient two-stage procedure. In the first stage, we decompose the nonparametric functions into a linear part and a nonlinear part. The nonlinear functions are approximated by constant spline…
Subjects/Keywords: Statistics and Probability
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Li, X. (2018). Non/Semi-parametric learning from data with complex features. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/17250
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):
Li, Xinyi. “Non/Semi-parametric learning from data with complex features.” 2018. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/17250.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Li, Xinyi. “Non/Semi-parametric learning from data with complex features.” 2018. Web. 01 Mar 2021.
Vancouver:
Li X. Non/Semi-parametric learning from data with complex features. [Internet] [Thesis]. Iowa State University; 2018. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/17250.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Li X. Non/Semi-parametric learning from data with complex features. [Thesis]. Iowa State University; 2018. Available from: https://lib.dr.iastate.edu/etd/17250
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
30.
Wang, Xin.
Topics in generalized linear mixed models and spatial subgroup analysis.
Degree: 2018, Iowa State University
URL: https://lib.dr.iastate.edu/etd/17348
► In this thesis, two topics are studied, generalized linear mixed models and spatial subgroup analysis. Within the topic of generalized linear mixed models, this thesis…
(more)
▼ In this thesis, two topics are studied, generalized linear mixed models and spatial subgroup analysis.
Within the topic of generalized linear mixed models, this thesis focuses on three aspects. First, estimation of link function in generalized linear models is studied. We propose a new algorithm that uses P-spline for nonparametrically estimating the link function which is guaranteed to be mono- tone. We also conduct extensive simulation studies to compare our nonparametric approach with various parametric approaches. Second, a spatial hierarchical model based on generalized Dirichlet distribution is developed to construct small area estimators of compositional proportions in the National Resources Inventory survey. At the observation level, the standard design based estima- tors of the proportions are assumed to follow the generalized Dirichlet distribution. After proper transformation of the design based estimators, beta regression is applicable. We consider a logit mixed model for the expectation of the beta distribution, which incorporates covariates through fixed effects and spatial effect through a conditionally autoregressive process. Finally, convergence rates of Markov chain Monte Carlo algorithms for Bayesian generalized linear mixed models are studied. For Bayesian probit linear mixed models, we construct two-block Gibbs samplers using the data augmentation (DA) techniques and prove the geometric ergodicity of the Gibbs samplers under both proper priors and improper priors. We also provide conditions for posterior propriety when the design matrices take commonly observed forms. For Bayesian logistic regression models, we establish that the Markov chain underlying Polson et al.’s (2013) DA algorithm is geometri- cally ergodic under a flat prior. For Bayesian logistic linear mixed models, we construct a two-block Gibbs sampler using Polson et al.’s (2013) DA technique under proper priors and prove the uniform ergodicity of this Gibbs sampler.
The other topic is spatial subgroup analysis with repeated measures. We use pairwise concave penalties for the differences among group regression coefficients based on smoothly clipped absolute deviation penalty. We also consider pairwise weights associated with each paired penalty based on spatial information. We show that the oracle estimator based on weighted least square is a local minimizer of the objective function with probability approaching 1 under some conditions. In the simulation study, we compare the performances of different weights as well as equal weights, which shows that the spatial information will help when the minimal group difference is small or the number of repeated measures is small.
Subjects/Keywords: Statistics and Probability
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wang, X. (2018). Topics in generalized linear mixed models and spatial subgroup analysis. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/17348
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):
Wang, Xin. “Topics in generalized linear mixed models and spatial subgroup analysis.” 2018. Thesis, Iowa State University. Accessed March 01, 2021.
https://lib.dr.iastate.edu/etd/17348.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Wang, Xin. “Topics in generalized linear mixed models and spatial subgroup analysis.” 2018. Web. 01 Mar 2021.
Vancouver:
Wang X. Topics in generalized linear mixed models and spatial subgroup analysis. [Internet] [Thesis]. Iowa State University; 2018. [cited 2021 Mar 01].
Available from: https://lib.dr.iastate.edu/etd/17348.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Wang X. Topics in generalized linear mixed models and spatial subgroup analysis. [Thesis]. Iowa State University; 2018. Available from: https://lib.dr.iastate.edu/etd/17348
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
