Many Bayesian inference problems involve target distributions whose density functions are computationally expensive to evaluate. Replacing the with a local approximation based on small number of carefully chosen evaluations can significantly reduce computational expense Markov chain Monte Carlo (MCMC) sampling. Moreover, continual refinement guarantee asymptotically exact We devise new strategy...

In recent years, stochastic gradient Markov Chain Monte Carlo (SG-MCMC) methods have been raised to process large-scale dataset by iterative learning from small minibatches. However, the high variance caused by naive subsampling usually slows down the convergence to the desired posterior distribution. In this paper, we propose an effective subsampling strategy to reduce the variance based on a ...

Sampling from the posterior distribution using Markov chain Monte Carlo (MCMC) methods can require an exhaustive number of iterations to fully explore the correct posterior. This is often the case when the posterior of interest is multi-modal, as the MCMC sampler can become trapped in a local mode for a large number of iterations. In this paper, we introduce the pseudo-extended MCMC method as a...

The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore a high-dimensional space for accurate inference. This struggle is compounded in physical applications when the nonlinear forward model is computationally expensive. One approach to acce...

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...