Motivation: To illustrate an intuitive and statistically valid method for combining independent sources of evidence that yields a p-value for the complete evidence, and to apply it to the problem of detecting simultaneous matches to multiple patterns in sequence homology searches.
Results: In sequence analysis, two or more (approximately) independent measures of the membership of a sequence (or sequence region) in some class are often available. We would like to estimate the likelihood of the sequence being a member of the class in view of all the available evidence. An example is estimating the significance of the observed match of a macromolecular sequence (DNA or protein) to a set of patterns (motifs) that characterize a biological sequence family. An intuitive way to do this is to express each piece of evidence as a p-value, and then use the product of these p-values as the measure of membership in the family. We derive a formula and algorithm (QFAST) for calculating the statistical distribution of the product of n independent p-values. We demonstrate that sorting sequences by this p-value effectively combines the information present in multiple motifs, leading to highly accurate and sensitive sequence homology searches.