Iain Murray, David MacKay, Zoubin Ghahramani, John Skilling
Nested sampling is a new Monte Carlo method by Skilling  intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior sub ject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.