Ewan Cameron, Anthony Pettitt
We investigate the utility to contemporary Bayesian studies of recursive, Gauss-Seidel-type pathways to marginal likelihood estimation characterized by reverse logistic regression and the density of states. Through a pair of illustrative, numerical examples (including mixture modeling of the well-known 'galaxy dataset') we highlight both the remarkable diversity of bridging schemes amenable to recursive normalization and the notable efficiency of the resulting pseudo-mixture densities for gauging prior-sensitivity in the model selection context. Our key theoretical contributions show the connection between the nested sampling identity and the density of states. Further, we introduce a novel heuristic ('thermodynamic integration via importance sampling') for qualifying the role of the bridging sequence in marginal likelihood estimation. An efficient pseudo-mixture density scheme for harnessing the information content of otherwise discarded draws in ellipse-based nested sampling is also introduced.
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http://arxiv.org/abs/1301.6450
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