Article,
Nested sampling for general Bayesian computation
Bayesian Analysis, 1 (4): 833--859 (2006)
Abstract
Nested sampling estimates directly how the likelihood function relates
to prior mass. The evidence (alternatively the marginal likelihood,
marginal density of the data, or the prior predictive) is immediately
obtained by summation. It is the prime result of the computation,
and is accompanied by an estimate of numerical uncertainty. Samples
from the posterior distribution are an optional by-product, obtainable
for any temperature. The method relies on sampling within a hard
constraint on likelihood value, as opposed to the softened likelihood
of annealing methods. Progress depends only on the shape of the nested
contours of likelihood, and not on the likelihood values. This invariance
(over monotonic relabelling) allows the method to deal with a class
of phase-change problems which effectively defeat thermal annealing.
Tags
- algorithm,
- annealing,
- bayesian
- change,
- computation,
- evidence,
- likelihood,
- marginal
- model
- nest,
- phase
- selection
