IDR for marginal likelihood in Bayesian phylogenetics

It is widely accepted that species diversified in a tree like pattern from a common descendant and that the diversification is mainly due to changes in the genetic codes of the species accumulating during the centuries. The main aim of phylogenetics is to investigate the evolutionary relationships among species, studying similarities and diFFerences of aligned genomic sequences. From a statistical point of view, the problem of analyzing phylogenetic sequences is often formalized as follows: given a set of DNA sequences of different species, we aim at inferring the tree that better represents the evolutionary relationships using the variations occurred in the genetic codes. Since genes evolve accumulating changes, the larger the number of differences in the genetic code of two species, the larger the evolutionary distance between them is likely to be. Alternative tree estimation methods such as parsimony methods (Felsenstein (2004), chapter 7) and distance methods (Fitch and Margoliash, 1967; Cavalli-Sforza and Edwards, 1967) have been proposed. We consider stochastic models for substitution rates in a fully Bayesian framework. We focus on model selection issues and several estimation procedures of the Bayesian model evidence will be rewived. We address within a fully Bayesian framework proposing alternative model evidence estimation procedures.