Grégory Nuel (MAP5, Université Paris Descartes et CNRS)

On the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source

vendredi 15 octobre 2010, 9h15 - 10h30

Salle de réunion, espace Turing


In this talk, we develop an explicit formula allowing to compute the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source.

We derive efficient algorithms allowing to deal both with low or high complexity patterns and either homogeneous or heterogenous Markov models. We then apply these results to the distribution of DNA patterns in genomic sequences where we show that moment-based developments (namely: Edgeworth’s expansion and Gram-Charlier type B series) allow to improve the reliability of common asymptotic approximations like Gaussian or Poisson approximations.