Simultaneous Occurrences of Runs in Independent Markov Chains

S. Robin () and V. T. Stefanov ()
Additional contact information
S. Robin: UMR 518 AgroParisTech/INRA Appl. Math. & Comput. Sci.
V. T. Stefanov: The University of Western Australia

Methodology and Computing in Applied Probability, 2009, vol. 11, issue 2, 267-275

Abstract: 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; Primary 60J05; Secondary 68R15, 92D99 (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-008-9093-3

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