The conflation of ignorance and knowledge in the inference of clade posteriors

The objective Bayesian approach relies on the construction of prior distributions that reflect ignorance. When topologies are considered equally probable a priori, clades cannot be. Shifting justifications have been offered for the use of uniform topological priors in Bayesian inference. These include: (i) topological priors do not inappropriately influence Bayesian inference when they are uniform; (ii) although clade priors are not uniform, their undesirable influence is negated by the likelihood function, even when data sets are small; and (iii) the influence of nonuniform clade priors is an appropriate reflection of knowledge. The first two justifications have been addressed previously: the first is false, and the second was found to be questionable. The third and most recent justification is inconsistent with the first two, and with the objective Bayesian philosophy itself. Thus, there has been no coherent justification for the use of nonflat clade priors in Bayesian phylogenetics. We discuss several solutions: (i) Bayesian inference can be abandoned in favour of other methods of phylogenetic inference; (ii) the objective Bayesian philosophy can be abandoned in favour of a subjective interpretation; (iii) the topology with the greatest posterior probability, which is also the tree of greatest marginal likelihood, can be accepted as optimal, with clade support estimated using other means; or (iv) a Bayes factor, which accounts for differences in priors among competing hypotheses, can be used to assess the weight of evidence in support of clades.
©The Willi Hennig Society 2009