Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling

Gelfand, Alan E.; Hills, Susan E.; Racine-Poon, Amy; Smith, A. F. M.

doi:10.21236/ada212630

Cited by 78 publications

(94 citation statements)

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“…Lakshmanan and Derin (1989), for example, maximized the pseudo-likelihood using a second level of annealing. Alternatively, by putting hyperpriors on/3 and/or ~r, at least in principle, estimates may be obtained by sampling from the appropriate full conditional P(/31X , Y, ~r) or P(cr[X, Y,/3) as part of the Gibbs sampler update (see, for example, Gelfand et al, 1990, in another context).…”

Section: Overly Clustered and Lacks Sufficient Small Isolated Black Cmentioning

confidence: 99%

Simulating posterior Gibbs distributions: a comparison of the Swendsen-Wang and Gibbs sampler methods

Gray

1994

Stat Comput

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We show in detail how the Swendsen-Wang algorithm, for simulating Potts models, may be used to simulate certain types of posterior Gibbs distribution, as a special case of Edwards and Sokal (1988), and we empirically compare the behaviour of the algorithm with that of the Gibbs sampler. Some marginal posterior mode and simulated annealing image restorations are also examined. Our results demonstrate the importance of the starting configuration. If this is inappropriate, the Swendsen-Wang method can suffer from critical slowing in moderately noise-free situations where the Gibbs sampler convergence is very fast, whereas the reverse is true when noise level is high.

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Section: Overly Clustered and Lacks Sufficient Small Isolated Black Cmentioning

confidence: 99%

Simulating posterior Gibbs distributions: a comparison of the Swendsen-Wang and Gibbs sampler methods

Gray

1994

Stat Comput

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“…This fact has been realised by statisticians for many years and explains the popularity of Gibbs Sampling (cf [8], [9], [10]). The reason is that often one is interested in some low dimensional marginal distribution and not the measure itself.…”

Section: Problems With High-dimensional ®Lteringmentioning

confidence: 94%

Nonlinear filtering and measure-valued processes

Crisan

Lyons

1997

Probab Theory Relat Fields

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“…Although the Metropolis-Hastings sampler is very well suited for most of those applications (only the unnormalized value of the posterior PDF is needed), some other sampling strategies have been proposed. In the case of Gibbs sampler [78,79] it is necessary to know any conditional probability density of the original PDF, in order to be sampled. This requirement is easy to fulfill in closed form expressions for the prior densities, but it can be very computationally expensive for the likelihood term.…”

Section: Markov Chain Monte Carlo Sampling Methodsmentioning

confidence: 99%

“…Several methods have been developed to evaluate the degree of convergence, ranging from graphical methods [79] to more complex statistical methods [87][88][89]. However, despite the solid foundations of all of these methods, it has been demonstrated that any method when applied individually may lead to poor performance.…”

Section: Markov Chain Monte Carlo Sampling Methodsmentioning

confidence: 99%

A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

et al. 2011

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Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task. Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering. In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational cost significantly, us-

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Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling

Cited by 78 publications

References 0 publications

Simulating posterior Gibbs distributions: a comparison of the Swendsen-Wang and Gibbs sampler methods

Simulating posterior Gibbs distributions: a comparison of the Swendsen-Wang and Gibbs sampler methods

Nonlinear filtering and measure-valued processes

A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

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