Iterative Monte Carlo Approximations for Bayesian Inference


Type
Thesis
Change log
Authors
Duffield, Samuel 
Abstract

The common theme of this thesis is the concept of using Monte Carlo techniques to approximate a sequence of probability distributions. Novel methodological contributions are found in Chapter 3 through to Chapter 6. In Chapter 3 we derive a method for the complete characterisation of online statistical models where Monte Carlo approximations are defined sequentially as new data arrive. We then demonstrate the utility of this method in Chapter 4 for the compelling application of de-noising sequential GPS coordinates to be restricted to a road network. In Chapter 5 and Chapter 6, the sequence of probability distributions are defined artificially in order to gradually (and more effectively) approach a single offline target probability distribution. Chapter 5 adopts ideas from high-dimensional time series to efficiently tackle the difficult setting where we cannot evaluate the density of the target distribution and instead can only generate synthetic data. Chapter 6 explores the use of a scalable Hessian approximation in the more common scenario where the target density can be evaluated and even differentiated. Finally, Chapter 7 describes a general purpose software package that can be used to implement and customise all of the discussed algorithms at competitive speeds.

Description
Date
2021-09-06
Advisors
Singh, Sumeetpal
Keywords
Bayesian inference, Monte Carlo, State-space Models, Statistics
Qualification
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge
Sponsorship
EPSRC (1890282)
Engineering and Physical Sciences Research Council (1890282)
EPSRC
Relationships
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