A Note on Probabilistic Models over Strings: Inference and Representation with Indexed Matrices

Probabilistic models over strings have played a key role in developing methods allowing indels to be treated as phylogenetically informative events. In this work, we show how to derive a closed-form expression for computing the probability of a collection of observed sequences given a tree. This expression is in terms of elementary operations on indexed collections of matrices, and can be derived for a wide range of indel models.