Hierarchical inference of evidence using posterior samples

The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a hierarchical method that leverages on a multivariate normalised approximant for the posterior probability density to infer the evidence for a model in a hierarchical fashion using a set of posterior samples drawn using an arbitrary sampling scheme.