Recursive Pathways to Marginal Likelihood Estimation with Prior-Sensitivity Analysis

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as \biased sampling" or \reverse lo- gistic regression" in the statistics literature and \the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable eciency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theo- retical contributions are to introduce a novel heuristic (\thermodynamic integration via importance sampling") for qualifying the role of the bridg- ing sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.