Upper bounds and importance sampling of p-values for DNA and protein sequence alignments

Abstract

We show in general how the substitution matrix and gap penalty function for local sequence alignments can be chosen such that the score statistic grows at a logarithmic rate when the two sequences are unrelated. The method used is the construction of a mixture distribution in which sequences with large scores are generated with uniformly higher likelihood. This distribution is also used for the importance sampling of the $p$-value of the score. An upper bound of this $p$-value is computed and compared against the simulated value.