Simultaneous Occurrences of Runs in Independent Markov Chains

S. Robin; Valeri Stefanov

doi:10.1007/s11009-008-9093-3

Simultaneous Occurrences of Runs in Independent Markov Chains

S. Robin
, Valeri Stefanov

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	n/a
Journal	Methodology and Computing in Applied Probability
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s11009-008-9093-3
Publication status	Published - 2009

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10.1007/s11009-008-9093-3

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AB - 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.

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DO - 10.1007/s11009-008-9093-3

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JO - Methodology and Computing in Applied Probability

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Simultaneous Occurrences of Runs in Independent Markov Chains

Abstract

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