Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific
computing because of its flexible construction, ease of use, and generality. Indeed, MCMC is …

We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …

The Monte Carlo expectation maximization (MCEM) algorithm is a versatile tool for inference
in incomplete data models, especially when used in combination with Markov chain Monte …

Yang et al. proved that the symmetric random walk Metropolis–Hastings algorithm for
Bayesian variable selection is rapidly mixing under mild high‐dimensional assumptions. We …

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected
value of a function with respect to a, possibly unnormalized, probability distribution. A …

Component-Wise Markov Chain Monte Carlo: Uniform and Geometric Ergodicity under Mixing
and Composition Page 1 Statistical Science 2013, Vol. 28, No. 3, 360–375 DOI …

Markov chain Monte Carlo (MCMC) methods allow us to generate samples from an arbitrary
distribution л known up to a scaling factor; see [46]. The algorithm consists in sampling a …

We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers,
which update their selection probabilities (and perhaps also their proposal distributions) on …

The use of MCMC algorithms in high dimensional Bayesian problems has become routine.
This has spurred so-called convergence complexity analysis, the goal of which is to …

Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical
applications is increasingly recognized. In this paper, we develop general mixing time …