Simultaneous occurrences of runs in independent markov chains

Stephane Robin (1) , V.T. Stefanov (2)

1 MIA-Paris - Mathématiques et Informatique Appliquées
2 School of Mathematics and Statistics

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.

Mots clés: comparative genomic hybridization; exact bounds; markov chains; simultaneous occurrences; runs

Domaines: Sciences du Vivant [q-bio]

Stephane Robin, V.T. Stefanov. Simultaneous occurrences of runs in independent markov chains. Methodology and Computing in Applied Probability, 2009, 11 (2), pp.267-275. ⟨10.1007/s11009-008-9093-3⟩. ⟨hal-01197597⟩