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Title: Bayesian methods and machine learning in astrophysics
Author: Higson, Edward John
ISNI:       0000 0004 7651 661X
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2019
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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 $\texttt{nestcheck}$ 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 $\texttt{dyPolyChord}$ and $\texttt{perfectns}$ 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.
Supervisor: Lasenby, Anthony ; Hobson, Mike ; Handley, Will Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
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