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University of Cambridge

1. Higson, Edward John. Bayesian methods and machine learning in astrophysics.

Degree: PhD, 2019, University of Cambridge

This thesis is concerned with methods for Bayesian inference and their applications in astrophysics. We principally discuss two related themes: advances in nested sampling (Chapters 3 to 5), and Bayesian sparse reconstruction of signals from noisy data (Chapters 6 and 7). Nested sampling is a popular method for Bayesian computation which is widely used in astrophysics. Following the introduction and background material in Chapters 1 and 2, Chapter 3 analyses the sampling errors in nested sampling parameter estimation and presents a method for estimating them numerically for a single nested sampling calculation. Chapter 4 introduces diagnostic tests for detecting when software has not performed the nested sampling algorithm accurately, for example due to missing a mode in a multimodal posterior. The uncertainty estimates and diagnostics in Chapters 3 and 4 are implemented in the tt{nestcheck} software package, and both chapters describe an astronomical application of the techniques introduced. Chapter 5 describes dynamic nested sampling: a generalisation of the nested sampling algorithm which can produce large improvements in computational efficiency compared to standard nested sampling. We have implemented dynamic nested sampling in the tt{dyPolyChord} and tt{perfectns} software packages. Chapter 6 presents a principled Bayesian framework for signal reconstruction, in which the signal is modelled by basis functions whose number (and form, if required) is determined by the data themselves. This approach is based on a Bayesian interpretation of conventional sparse reconstruction and regularisation techniques, in which sparsity is imposed through priors via Bayesian model selection. We demonstrate our method for noisy 1- and 2-dimensional signals, including examples of processing astronomical images. The numerical implementation uses dynamic nested sampling, and uncertainties are calculated using the methods introduced in Chapters 3 and 4. Chapter 7 applies our Bayesian sparse reconstruction framework to artificial neural networks, where it allows the optimum network architecture to be determined by treating the number of nodes and hidden layers as parameters. We conclude by suggesting possible areas of future research in Chapter 8.

Subjects/Keywords: Machine Learning; Bayesian Inference; Nested sampling; Cosmology; Black Holes; Gravitational Waves; Neural Networks; Regression; Astrophysics; Sparsity; Parameter Estimation; Bayesian Evidence; Bayesian; Statistics; Bayesian Sparse Reconstruction; Computational Methods; Error Analysis; Dynamic Nested Sampling; nestcheck; perfectns; dyPolyChord; dynesty; Image Processing; Sparse Reconstruction; Planck; diagnostic tests; PolyChord; MultiNest; Hubble Space Telescope; Fitting; Nonparametric statistics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Higson, E. J. (2019). Bayesian methods and machine learning in astrophysics. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/289728 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767929

Chicago Manual of Style (16th Edition):

Higson, Edward John. “Bayesian methods and machine learning in astrophysics.” 2019. Doctoral Dissertation, University of Cambridge. Accessed October 15, 2019. https://www.repository.cam.ac.uk/handle/1810/289728 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767929.

MLA Handbook (7th Edition):

Higson, Edward John. “Bayesian methods and machine learning in astrophysics.” 2019. Web. 15 Oct 2019.

Vancouver:

Higson EJ. Bayesian methods and machine learning in astrophysics. [Internet] [Doctoral dissertation]. University of Cambridge; 2019. [cited 2019 Oct 15]. Available from: https://www.repository.cam.ac.uk/handle/1810/289728 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767929.

Council of Science Editors:

Higson EJ. Bayesian methods and machine learning in astrophysics. [Doctoral Dissertation]. University of Cambridge; 2019. Available from: https://www.repository.cam.ac.uk/handle/1810/289728 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767929


University of Cambridge

2. Higson, Edward John. Bayesian Methods and Machine Learning in Astrophysics .

Degree: University of Cambridge

This thesis is concerned with methods for Bayesian inference and their applications in astrophysics. We principally discuss two related themes: advances in nested sampling (Chapters 3 to 5), and Bayesian sparse reconstruction of signals from noisy data (Chapters 6 and 7). Nested sampling is a popular method for Bayesian computation which is widely used in astrophysics. Following the introduction and background material in Chapters 1 and 2, Chapter 3 analyses the sampling errors in nested sampling parameter estimation and presents a method for estimating them numerically for a single nested sampling calculation. Chapter 4 introduces diagnostic tests for detecting when software has not performed the nested sampling algorithm accurately, for example due to missing a mode in a multimodal posterior. The uncertainty estimates and diagnostics in Chapters 3 and 4 are implemented in the tt{nestcheck} software package, and both chapters describe an astronomical application of the techniques introduced. Chapter 5 describes dynamic nested sampling: a generalisation of the nested sampling algorithm which can produce large improvements in computational efficiency compared to standard nested sampling. We have implemented dynamic nested sampling in the tt{dyPolyChord} and tt{perfectns} software packages. Chapter 6 presents a principled Bayesian framework for signal reconstruction, in which the signal is modelled by basis functions whose number (and form, if required) is determined by the data themselves. This approach is based on a Bayesian interpretation of conventional sparse reconstruction and regularisation techniques, in which sparsity is imposed through priors via Bayesian model selection. We demonstrate our method for noisy 1- and 2-dimensional signals, including examples of processing astronomical images. The numerical implementation uses dynamic nested sampling, and uncertainties are calculated using the methods introduced in Chapters 3 and 4. Chapter 7 applies our Bayesian sparse reconstruction framework to artificial neural networks, where it allows the optimum network architecture to be determined by treating the number of nodes and hidden layers as parameters. We conclude by suggesting possible areas of future research in Chapter 8.

Subjects/Keywords: Machine Learning; Bayesian Inference; Nested sampling; Cosmology; Black Holes; Gravitational Waves; Neural Networks; Regression; Astrophysics; Sparsity; Parameter Estimation; Bayesian Evidence; Bayesian; Statistics; Bayesian Sparse Reconstruction; Computational Methods; Error Analysis; Dynamic Nested Sampling; nestcheck; perfectns; dyPolyChord; dynesty; Image Processing; Sparse Reconstruction; Planck; diagnostic tests; error analysis; PolyChord; MultiNest; Hubble Space Telescope; Fitting; Nonparametric statistics

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Higson, E. J. (n.d.). Bayesian Methods and Machine Learning in Astrophysics . (Thesis). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/289728

Note: this citation may be lacking information needed for this citation format:
No year of publication.
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Higson, Edward John. “Bayesian Methods and Machine Learning in Astrophysics .” Thesis, University of Cambridge. Accessed October 15, 2019. https://www.repository.cam.ac.uk/handle/1810/289728.

Note: this citation may be lacking information needed for this citation format:
No year of publication.
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Higson, Edward John. “Bayesian Methods and Machine Learning in Astrophysics .” Web. 15 Oct 2019.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Vancouver:

Higson EJ. Bayesian Methods and Machine Learning in Astrophysics . [Internet] [Thesis]. University of Cambridge; [cited 2019 Oct 15]. Available from: https://www.repository.cam.ac.uk/handle/1810/289728.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
No year of publication.

Council of Science Editors:

Higson EJ. Bayesian Methods and Machine Learning in Astrophysics . [Thesis]. University of Cambridge; Available from: https://www.repository.cam.ac.uk/handle/1810/289728

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
No year of publication.

.