Numerical solutions for patterns statistics on Markov chains. We propose here a review of the methods available to compute pattern statistics on texts generated by a Markov source. Theoretical, but also numerical aspects are detailed for a wide range of techniques (exact, Gaussian, large deviations, binomial and compound Poisson). The SPatt package (Statistics for Pattern, free software available at http://stat.genopole.cnrs.fr/spatt) implementing all these methods is then used to compare all these approaches in terms of computational time and reliability in the most complete pattern statistics benchmark available at the present time.
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References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Nuel, Gregory; Dumas, Jean-Guillaume: Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source (2013)
- Nuel, G.: On the first $k$ moments of the random count of a pattern in a multistate sequence generated by a Markov source (2010)
- Behrens, Sarah; Löwe, Matthias: Moderate deviations for word counts in biological sequences (2009)
- Nuel, Grégory: Cumulative distribution function of a geometric Poisson distribution (2008)
- Nuel, Grégory: Pattern Markov chains: Optimal Markov chain embedding through deterministic finite automata (2008)
- Vergne, Nicolas: Drifting Markov models with polynomial drift and applications to DNA sequences (2008)
- Nuel, Gregory: Numerical solutions for patterns statistics on Markov chains (2006)