Simultaneous Occurrences of Runs in Independent Markov Chains
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We observe m independent and identically distributed binary Markov chains and look for simultaneous occurrences of runs in several of them. We are interested in the distribution of the maximum number of simultaneous runs on finite time intervals. First we introduce a natural exact approach and also explain why it fails to calculate the required probabilities. Then we find exact upper and lower bounds for the probability of interest. We apply these results to detect genomic deletions in cancer patients.
KeywordsComparative genomic hybridization Exact bounds Markov chains Simultaneous occurrences Runs
AMS 2000 Subject ClassificationPrimary 60J05; Secondary 68R15 92D99
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- Robin S, Rodolphe F, Schbath S (2005) DNA, words and models. Cambridge Univ. PressGoogle Scholar