Nested sampling for general Bayesian computation
نویسندگان
چکیده
منابع مشابه
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...
متن کاملDiscussion of Nested Sampling for Bayesian Computations
We comment on several aspects of Skilling's paper presented at Valencia 8. In particular we prove the convergence in probability of the algorithm for a wide class of situations, comment on its potential utility and discuss aspects where further work is needed to assess the approach.
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Some real problems are more naturally modeled by hybrid Bayesian networks that consist of mixtures of continuous and discrete variables with their interactions described by equations and continuous probability distributions. However, inference in such general hybrid models is hard. Therefore, existing approaches either only deal with special instances, such as Conditional Linear Gaussians (CLGs...
متن کاملDiscussion of Nested Sampling for Bayesian Computations by John Skilling
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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Bayesian model selection provides the cosmologist with an exacting tool to distinguish between competing models based purely on the data, via the Bayesian evidence. Previous methods to calculate this quantity either lacked general applicability or were computationally demanding. However, nested sampling (Skilling 2004), which was recently applied successfully to cosmology by Muhkerjee et al. 20...
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ژورنال
عنوان ژورنال: Bayesian Analysis
سال: 2006
ISSN: 1936-0975
DOI: 10.1214/06-ba127