Finite Markov Chain Embedding for the Exact Distribution of Patterns in a Set of Random Sequences

Juliette Martin (1) , Leslie Regad (2) , Anne-Claude Camproux (2) , Grégory Nuel (3)

1 IBCP - Institut de biologie et chimie des protéines [Lyon]
2 MTI - Molécules Thérapeutiques in silico
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Patterns with “unusual” frequencies are new functional candidate patterns. Their identification is usually achieved by considering an homogeneous m-order Markov model (m≥ 1) of the sequence, allowing the computation of p-values. For practical reasons, stationarity of the model is often assumed. This approximation can result in some artifacts especially when a large set of small sequences is considered. In this work, an exact method, able to take into account both nonstationarity and fragmentary structure of sequences, is applied on a simulated and a real set of sequences. This illustrates that pattern statistics can be very sensitive to the stationary assumption. Keywords and phrases: stationary distribution - pattern Markov chain - biological patterns - finite Markov chain embedding

Domaines: Probabilités [math.PR]

Juliette Martin, Leslie Regad, Anne-Claude Camproux, Grégory Nuel. Finite Markov Chain Embedding for the Exact Distribution of Patterns in a Set of Random Sequences. Advances in data analysis, Birkhäuser Boston, pp.171-180, 2010, ⟨10.1007/978-0-8176-4799-5_16⟩. ⟨hal-00539547⟩