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An Isaac Newton Institute Workshop

Recent Advances in Monte Carlo Based Inference

Nested Sampling

2nd November 2006

Author: David MacKay (Cambridge)

Abstract

Nested sampling is a new Monte Carlo algorithm invented by John Skilling. Whereas most Monte Carlo methods aim to generate samples from a posterior or to estimate posterior expectations, nested sampling's central aim is to evaluate the evidence (the normalizing constant, also known as the marginal likelihood or partition function). This important quantity can be computed by standard Monte Carlo methods (such as Gibbs sampling) only by adding extra computations (such as reversible-jump Monte Carlo or thermodynamic integration) which require careful tuning.

I will review nested sampling and describe tests of the method on graphical models.

(Joint work with Iain Murray and John Skilling)

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