Genomic alterations have been linked to the development and progression of cancer.The technique of comparative genomic hybridization (CGH) yields data consisting of fluorescence intensity ratios of test and reference DNA samples.The intensity ratios provide information about the number of copies in DNA.Practical issues such as the contamination of tumor ceils in tissue specimens and normalization errors necessitate the use of statistics for learning about the genomic alterations from array CGH data.As increasing amounts of array CGH data become available, there is a growing need for automated algorithms for characterizing genomic profiles.Specifically, there is a need for algorithms that can identify gains and losses in the number of copies based on statistical considerations, rather than merely detect trends in the data.We adopt a Bayesian approach, relying on the hidden Markov model to account for the inherent dependence in the intensity ratios.Posterior inferences are made about gains and losses in copy number.Localized amplifications (associated with oncogene mutations) and deletions (associated with mutations of tumor sup pressors) are identified using posterior probabilities.Global trends such as extended regions of altered copy number are detected.Because the posterior distribution is analytically intractable, we implement a Metropolis-within-Gibbs algorithm for efficient simulation-based inference.Publicly available data on pancreatic adenocar cinoma, glioblastoma multiforme, and breast cancer are analyzed, and comparisons are made with some widely used algorithms to illustrate the reliability and success of the technique.