This research develops two model-based clustering methodologies for characterizing marginal properties and dependence structure in cancer genomic aberrations recorded by comparative genomic hybridization (CGH), one of the techniques used to measure changes in DNA copy number in tumor cells. The first model is the instability selection tree-like network model (ISTN) and the second one is the instability selection general network model (ISGN). These models generalize the instability selection network (ISN) model proposed by Newton (2002). The ISN model encodes two biological phenomena: genetic instability, which causes aberrations to appear, and cell-level selection, which characterizes genomic aberrations that are relevant to tumor growth. The ISN model is parameterized by sets of genomic aberrations called ensembles. In a tumor progenitor cell, the co-occurrence of all aberrations in an ensemble is relevant to tumor progression in the sense of increasing the chance of selection into a tumor. In the original ISN model, aberrations residing on one ensemble could not reside on another, to simplify computations. To extend this limitation. Newton et al. (2003) defined tree-like network in which ensembles could be organized in a tree-like structure, however analysis and implementation of this model remains unavailable. Research presented here develops inference methods and implementation the tree-like network model. This research also develops a general network model, which has essentially no restrictions on the set of ensembles, and thus provides more a flexible model than a tree-like network model. The implementation of the general network model is based on sampling properties such that aberrations residing on a sample ensemble have a non-negative covariance and aberrations residing on different ensembles have a negative covariance. A Bayesian approach is developed to extract information from the likelihood. To implement both methods, the research discusses appropriate prior and Markov Chain Monte Carlo methods, and applies each methodology to data on renal cell carcinoma, breast cancer, and melanoma.