Computational methods in Bayesian statistics

Abstract

This undergraduate research project investigates the utility of the Bayesian framework for dealing with a number of problems in data analysis. A review of the Bayesian modus operandi is given in Chapter 1. In Chapter 2 this is supplemented with a description of the various computational methods available to the Bayesian, ranging from traditional techniques to more modem procedures. In particular we describe in some detail the Variational Bayesian method as well as Nested Sampling. In Chapter 3 we implement these methods in a variety of simple toy problems in order to familiarize ourselves with the framework. In Chapter 4 we tackle harder, yet still engineered, problems and compare Nested Sampling and Variational Bayes in terms of speed and accuracy. We conclude that the two methods give similar results and that Variational Bayes is the faster algorithm. Finally, in Chapter 5, we implement some of these methods in physical situations. We obtain encouraging results when fitting pulsar intensity profiles using Variational Bayes. We also show that Nested Sampling can be used as an optimization method and we test this in the design of microphone arrays.