We review and discuss some recent progress on the theory of Markov chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.

There are two conceptually distinct tasks in Markov chain Monte Carlo (MCMC): a sampler is designed for simulating a Markov chain and then an estimator is constructed on the Markov chain for computing integrals and expectations. In this article, we aim to address the second task by extending the likelihood approach of Kong et al. for Monte Carlo integration. We consider a general Markov chain s...

Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. Aft...

In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach more practical in general, higher-dimensional spaces. We first introduce a new target distribution which is able to incorporate more reward information from sa...

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Abstract: We examine the prospects of detecting the light Higgs scalar h of the Constrained MSSM at the Tevatron. To this end we explore large ranges of the CMSSM parameter space with μ > 0 using a Markov Chain Monte Carlo technique, and apply all relevant collider and cosmological constraints including their uncertainties, as well as those of the Standard Model parameters. Using the formalism ...

This paper deals with the prediction of the amount of outstanding claims that an insurance company will pay in the near future. We consider various competing models using Bayesian theory and Markov chain Monte Carlo methods. Claim counts are used in order to add a further hierarchical stage in the usual log-normaland state-space models. By this way, we incorporate information from both the outs...