Year

2013

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

Mean field variational Bayes (MFVB) is a fast, deterministic inference tool for use in Bayesian hierarchical models. We develop and examine the performance of MFVB algorithms in semiparametric regression applications involving elaborate distributions. We assess the accuracy of MFVB in these settings via comparison with a Markov chain Monte Carlo (MCMC) baseline. MFVB methodology for Generalized Extreme Value additive models performs well, culminating in fast, accurate analysis of the Sydney hinterland maximum rainfall data. Quantile regression based on the Asymmetric Laplace distribution provides another area for successful application of MFVB. Examination of MFVB algorithms for continuous sparseness signal shrinkage in univariate models illustrates the danger of näive application of MFVB. This leads to development of a new tool to add to the MFVB armory: continuous fraction approximation of special functions using Lentz’s Algorithm. MFVB performs well in both simple and more complex penalized wavelet regression models, illustrated by analysis of the radiation pneumonitis data. Overall, MFVB is a viable inference tool for semiparametric regression involving elaborate distributions. Generally, MFVB is good at retrieving trend estimates, but underestimates variability. MFVB is best used in applications where analysis is constrained by computational time and/or storage.

FoR codes (2008)

0103 NUMERICAL AND COMPUTATIONAL MATHEMATICS, 0104 STATISTICS

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Unless otherwise indicated, the views expressed in this thesis are those of the author and do not necessarily represent the views of the University of Wollongong.