Approximate statistical alignment by iterative sampling of substitution matrices

We outline a procedure for jointly sampling substitution matrices and multiple sequence alignments, according to an approximate posterior distribution, using an MCMC-based algorithm. This procedure provides an efficient and simple method by which to generate alternative alignments according to their expected accuracy, and allows appropriate parameters for substitution matrices to be selected in an automated fashion. In the cases considered here, the sampled alignments with the highest likelihood have an accuracy consistently higher than alignments generated using the standard BLOSUM62 matrix.