Graphical tools for the examination of high-dimensional functions obtained as the result of Bayesian analysis

Bayesian statistics has a tendency to produce objects that are of many more than three dimensions, typically of the same dimensionality as the parameter set of the problem. This thesis takes the idea of visual, exploratory data analysis and attempts to apply it to those objects. In order to do this it examines several areas, Monte Carlo Markov Chains (MCMC), display graphics and methods – especially Projection Pursuit methods – and Kernel Density Estimation (KDE). During the course of this work acceptable prior technology was found for MCMC and, once the decision for it had been made, Projection Pursuit. However, the current state of KDE gave rise to several objections. Not least among these came from the Bayesian background of the researcher, KDE had not been put in a suitable Bayesian framework and so clashed with the other technology. In addition it was felt that KDE needed too much user input and that is was somewhat ad hoc. This led to reformulating KDE in a Bayesian framework which had the added advantage of removing the need for a user to provide a bandwidth for each application. Chapter 6 of this thesis considers Bayesian theory and how it can be applied to KDE to produce a form more usable and satisfying in terms of Bayesian mathematics. This is shown to provide a powerful and flexible statistical tool without the need for the ad hoc choices often associated with these methods. This formulation of the KDE as a Bayesian problem is believed to be unique. As part of this work, software was produced in R to provide a usable visualisation of BKDE. A large number of examples is provided to demonstrate how this software can allow easy visualisation of a variety of types of dataset both with and without Kernel Density Estimation.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Nottingham Trent University

Year dc:date.issued

2009

Author dc:creator

• Kaye, WK

Language dc:language

en