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Monte Carlo methods can provide accurate p-value estimates of word countingtest statistics and are easy to implement. They are especially attractive whenan asymptotic theory is absent or when either the search sequence or the wordpattern is too short for the application of asymptotic formulae. Naive directMonte Carlo is undesirable for the estimation of small probabilities becausethe associated rare events of interest are seldom generated. We propose insteadefficient importance sampling algorithms that use controlled insertion of thedesired word patterns on randomly generated sequences. The implementation isillustrated on word patterns of biological interest: Palindromes and invertedrepeats, patterns arising from position specific weight matrices andco-occurrences of pairs of motifs.

Importance Sampling of Word Patterns in DNA and Protein Sequences