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Simultaneous Occurrences of Runs in Independent Markov Chains

Author

Listed:
  • S. Robin

    (UMR 518 AgroParisTech/INRA Appl. Math. & Comput. Sci.)

  • V. T. Stefanov

    (The University of Western 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.

Suggested Citation

  • S. Robin & V. T. Stefanov, 2009. "Simultaneous Occurrences of Runs in Independent Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 11(2), pages 267-275, June.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:2:d:10.1007_s11009-008-9093-3
    DOI: 10.1007/s11009-008-9093-3
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    Cited by:

    1. Stéphane Robin & Valeri T. Stefanov, 2015. "Detection of Significant Genomic Alterations via Simultaneous Minimal Sojourns at a State by Independent Continuous-time Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 479-487, June.

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