Iterative Monte Carlo Approximations for Bayesian Inference

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.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2021

Author dc:creator

• Duffield, Samuel

Advisor dc:contributor.advisor

• Singh, Sumeetpal

• Bayesian inference
• Monte Carlo
• State-space Models
• Statistics

Licence

• https://creativecommons.org/licenses/by-nc/4.0/

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.83098

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/335667