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Simultaneous Occurrences of Runs in Independent Markov Chains |
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| Authors: | S Robin V T Stefanov |
| Institution: | (1) UMR 518 AgroParisTech/INRA Appl. Math. & Comput. Sci., 16, rue Claude Bernard, 75005 Paris, France;(2) School of Mathematics and Statistics, The University of Western Australia, Crawley, Perth, 6009, WA, Australia |
| Abstract: | 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. |
| Keywords: | Comparative genomic hybridization Exact bounds Markov chains Simultaneous occurrences Runs |
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