Finite Markov Chain Embedding for the Exact Distribution of Patterns in a Set of Random Sequences
Juliette Martin, Leslie Regad, Anne‐Claude Camproux, Grégory Nuel · Birkhäuser Boston eBooks · 2009
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.