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