Exact Distribution 

for the Local Score of a Markov Chain

Claudie HASSENFORDER & Sabine MERCIER

C. R. Acad. Sci. Paris, Volume 336, Issue 10, p: 863-868.

Abstract

Given a sequence X of random variables taking values in {-v,...,0,...,+u}, let's define the local score of the sequence  by 

Hn=max {1£ i £ j £ n}( Sk=i..j Xk ). 

The local score is used to analyze biological sequences pointing out regions of the sequences with interesting biological properties.
 In order to separate randomly events from really interesting segments, we establish here the distribution of the local score of Hn when the sequence X is a Markov chain of order 1.

Key words and phrases: Biological sequence analysis, local score, Markov chain, significativity.