Iterative Monte Carlo Approximations for Bayesian Inference
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Authors
Duffield, Samuel
Advisors
Singh, Sumeetpal
Date
2021-09-06Awarding Institution
University of Cambridge
Qualification
Doctor of Philosophy (PhD)
Type
Thesis
Metadata
Show full item recordCitation
Duffield, S. (2021). Iterative Monte Carlo Approximations for Bayesian Inference (Doctoral thesis). https://doi.org/10.17863/CAM.83098
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.
Keywords
Bayesian inference, Monte Carlo, State-space Models, Statistics
Relationships
Is supplemented by: Predicting Taxi Passenger Demand Using Streaming DataPhilatelic Mixtures and Multimodal Densities
Sponsorship
EPSRC
Funder references
EPSRC (1890282)
Engineering and Physical Sciences Research Council (1890282)
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.83098
Rights
Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
Licence URL: https://creativecommons.org/licenses/by-nc/4.0/
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