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.