Thesis presented June 1^st, 2018
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Abstract:
In this thesis we present four applications in bioinformatics with Markov models. That is, we extend the use of such models in the mathematical and statistical analysis of biological data. The data we consider are drawn from a broad range of areas. We consider applications at the genomic level with time series and network data as well as applications at the cellular level with microscopy image data of both cell culture and in vivo tissue.
Collections of objects such as genes, cells or pixels are of particular interest as a whole. We make use of associations within these collections, spatial, temporal or functional, and assume that closer objects are more strongly associated than those further apart. This allows for efficient inference within a Markov model framework and is encoded in terms of conditional independences between variables as represented by vertices and edges in an undirected graph.
Chapter 1 presents an overview of undirected graphical models in general and Markov models in particular. Chapter 2 presents inference for variables in hidden Markov random fields (MRFs) while Chapter 3 presents inference for the parameters of Gaussian MRFs. Chapter 4 outlines the four applications and how the Markov model framework is utilised in each case. For each application, the associated publication is also provided.
In Publication 1, hidden Markov models (HMMs) are used to achieve an alignment and classification of time series data. Publications 2 and 3 concern inference with hidden MRFs to obtain a segmentation of both digital image data and network data respectively. Spatial analysis with Gaussian MRFs is presented in Publication 4. We show that our particular use of Markov models in each of our applications enables us to achieve our aims.

Keywords:
Markov models, cellular biology, statistical analysis

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