Nested sampling for general Bayesian computation

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Nested Sampling for General Bayesian Computation

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 byprod...

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The ingredients to a Bayesian analysis comprise the sampling model {Pθ : θ ∈ Ω} for the response X, the prior Π for the parameter θ, and the observed value X = x. This is equivalent to specifying the joint model Pθ ×Π for (X, θ) and the observed value X = x. In many situations we may also have a loss function but we ignore this here as it is not material to our discussion. We refer to Pθ ×Π as ...

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ژورنال

عنوان ژورنال: Bayesian Analysis

سال: 2006

ISSN: 1936-0975

DOI: 10.1214/06-ba127