Nested Sampling: a new Monte Carlo method for Bayesian computation

Iain Murray

Abstract

The evidence or marginal likelihood of a probabilistic model is a key quantity in Bayesian statistics, allowing model comparison. Computing the evidence often involves an intractable integral over model parameters. I review existing Monte Carlo approximations and introduce nested sampling, a new method by John Skilling. We illustrate advantages of nested sampling on the Potts model, an undirected graphical model. This is joint work with John Skilling, David MacKay and Zoubin Ghahramani.

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