Spatial whole-brain Bayesian modeling of task-related functional magnetic resonance imaging (fMRI) is a great computational challenge. Most of the currently proposed methods therefore do inference in subregions of the brain separately or do approximate inference without comparison to the true posterior distribution. A popular such method, which is now the standard method for Bayesian single sub...

Markov chain Monte Carlo (MCMC) methods make possible the use of flexible Bayesian models that would otherwise be computationally infeasible. In recent years, a great variety of such applications have been described in the literature. Applied statisticians who are new to these methods may have several questions and concerns, however: How much effort and expertise are needed to design and use a ...

A model describing chemical reactions in the stratosphere ([1]) is studied with MCMC methods. The model is a large ODE system consisting of 33 components, roughly 150 reactions and 150 reaction rate parameters. Thus, it is a good case study for adaptive MCMC methods designed for high-dimensional problems. In this case, the Delayed Rejection Adaptive Metropolis (DRAM, [2]) is succesfully applied...

Increasingly, large data sets pose a challenge for computationally intensive phylogenetic methods such as Bayesian Markov chain Monte Carlo (MCMC). Here, we investigate the performance of common MCMC proposal distributions in terms of median and variance of run time to convergence on 11 data sets. We introduce two new Metropolized Gibbs Samplers for moving through "tree space." MCMC simulation ...

This article presents an efficient method for improving the behavior of the MCMC sampling algorithm involved in the resolution of bilinear inverse problems. Blind deconvolution and source separation are among the applications that benefit from this improvement. The proposed method addresses the scale ambiguity inherent to bilinear inverse problems. Solving this type of problem within a Bayesian...

A search for Markov chain Monte Carlo (or MCMC) articles on Google Scholar yields over 100,000 hits, and a general web search on Google yields 1.7 million hits. These results stem largely from the ubiquitous use of these algorithms in modern computational statistics, as we shall now describe. MCMC algorithms are used to solve problems in many scientific fields, including physics (where many MCM...

Isolation with Migration model (IM), which jointly estimates divergence times and migration rates between two populations from DNA sequence data, can capture many phenomena when one population splits into two. The parameters inferences for IM are based on Markov Chain Monte Carlo method (MCMC). Standard implementations of MCMC are prone to fall into local optima. Metropolis Coupled MCMC [(MC)3]...

Markov Chain Monte Carlo methods are statistical tools that have been recently proposed for the resolution of the MEG inverse problem [1]. Their main advantages are easy incorporation of a priori knowledge, and an adequate response to the ambiguity of the ill-posed MEG inverse problem. However, since simpler MCMC schemes might have difficulties in escaping from local modes, adequate research is...

An R package mixAK is introduced which implements routines for a semiparametric density estimation through normal mixtures using the Markov chain Monte Carlo (MCMC) methodology. Besides producing the MCMC output, the package computes posterior summary statistics for important characteristics of the fitted distribution or computes and visualizes the posterior predictive density. For the estimate...

Abstract The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is determined by the data. As for most Bayesian nonparametric models, exact posterior inference is intractable—practitioners use Markov chain Monte Carl...