Identification of copy number aberrations in the human genome has been an important
area in cancer research. In the first part of my thesis, I propose a new model
for determining genomic copy numbers using high-density single nucleotide polymorphism
genotyping microarrays. The method is based on a Bayesian spatial normal
mixture model with an unknown number of components corresponding to true copy
numbers. A reversible jump Markov chain Monte Carlo algorithm is used to implement
the model and perform posterior inference. The second part of the thesis
describes a new method for the detection of gene-gene interactions using gene expression
data extracted from micro array experiments. The method is based on a two-step
Genetic Algorithm, with the first step detecting main effects and the second step
looking for interacting gene pairs. The performances of both algorithms are examined
on both simulated data and real cancer data and are compared with popular
existing algorithms. Conclusions are given and possible extensions are discussed
