Bayesian Latent Variable Models for Biostatistical Applications

Ridall, Peter Gareth (2004) Bayesian Latent Variable Models for Biostatistical Applications. PhD thesis, Queensland University of Technology.

Abstract

In this thesis we develop several kinds of latent variable models in order to address

three types of bio-statistical problem. The three problems are the treatment

effect of carcinogens on tumour development, spatial interactions between plant

species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting

of measurements of compound muscle action potential (CMAP) area and amplitude.

Chapter 1 sets out the structure and the development of ideas presented

in this thesis from the point of view of: model structure, model selection, and

efficiency of estimation. Chapter 2 is an introduction to the relevant literature

that has in influenced the development of this thesis. In Chapter 3 we use the EM

algorithm for an application of an autoregressive hidden Markov model to describe

longitudinal counts. The data is collected from experiments to test the

effect of carcinogens on tumour growth in mice. Here we develop forward and

backward recursions for calculating the likelihood and for estimation. Chapter 4

is the analysis of a similar kind of data using a more sophisticated model, incorporating

random effects, but estimation this time is conducted from the Bayesian

perspective. Bayesian model selection is also explored. In Chapter 5 we move

to the two dimensional lattice and construct a model for describing the spatial

interaction of tree types. We also compare the merits of directed and undirected

graphical models for describing the hidden lattice. Chapter 6 is the application

of a Bayesian hierarchical model (MUNE), where the latent variable this time is

multivariate Gaussian and dependent on a covariate, the stimulus. Model selection

is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we

approach the same problem by using the reversible jump methodology (Green,

1995) where this time we use a dual Gaussian-Binary representation of the latent

data. We conclude in Chapter 8 with suggestions for the direction of new

work. In this thesis, all of the estimation carried out on real data has only been

performed once we have been satisfied that estimation is able to retrieve the parameters

from simulated data.

Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov

models (HMM), latent variable models, longitudinal data analysis, motor unit

disease (MND), partially ordered Markov models (POMMs), the pseudo auto-

logistic model, reversible jump, spatial interactions.

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ID Code: 16164
Item Type: QUT Thesis (PhD)
Supervisor: Pettitt, Anthony, McVinish, Ross, & Reeves, Robert
Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov models (HMM), latent variable models, longitudinal data analysis, motor unit disease (MND), partially ordered Markov models (POMMs), the pseudo auto-logistic model, reversible jump, spatial interactions
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Department: Faculty of Science
Institution: Queensland University of Technology
Copyright Owner: Copyright Peter Gareth Ridall
Deposited On: 03 Dec 2008 03:57
Last Modified: 28 Oct 2011 19:44

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