A versatile MCMC strategy for sampling posterior distributions of analytically intractable models (original) (raw)
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2009
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Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for ra...
2001
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Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doublyintractable distributions in which there are additional parameter-dependent normalization terms; for example, the posterior over parameters of an undirected graphical model. An ingenious auxiliary-variable scheme ) offers a solution: exact sampling (Propp and Wilson, 1996) is used to sample from a Metropolis-Hastings proposal for which the acceptance probability is tractable. Unfortunately the acceptance probability of these expensive updates can be low. This paper provides a generalization of and a new MCMC algorithm, which obtains better acceptance probabilities for the same amount of exact sampling, and removes the need to estimate model parameters before sampling begins.
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Water Resources Research, 2009
In recent years, interest in the Bayesian approach for the calibration of hydrological and environmental simulation (HES) models has been growing. To extract useful information on unknown parameters produced in a Bayesian calibration, it is often necessary to rely on samples drawn from the posterior distribution. Sampling a posterior distribution requires a large number of evaluations of the simulation model, and the total computational costs could be prohibitively high when the simulation model is computationally expensive. A new computing strategy is proposed in this paper to alleviate this computational difficulty by making better use of the information generated in a costly run of the HES model by using multiple evaluations of the posterior density in the less computationally expensive subspace of error model parameters. A multiple-try Markov chain Monte Carlo (MCMC) algorithm is designed to implement this idea and is benchmarked with the Metropolis-Hastings algorithm, a basic recipe for MCMC sampling. The results show that the proposed strategy has potential for improving the computational efficiency of posterior sampling and easing its implementation in the Bayesian calibration of computationally expensive HES models.