MCMC sampling is a methodology that is becoming increasingly important in statistical signal processing. It has been of particular importance to the Bayesian-based approaches to signal processing since it extends signi"cantly the range of problems that they can address. MCMC techniques generate samples from desired distributions by embedding them as limiting distributions of Markov chains. Ther...

The p(2) model is a statistical model for the analysis of binary relational data with covariates, as occur in social network studies. It can be characterized as a multinomial regression model with crossed random effects that reflect actor heterogeneity and dependence between the ties from and to the same actor in the network. Three Markov chain Monte Carlo (MCMC) estimation methods for the p(2)...

Split-Merge MCMC (Monte Carlo Markov Chain) is one of the essential and popular variants of MCMC for problems when an MCMC state consists of an unknown number of components. It is well known that state-of-the-art methods for split-merge MCMC do not scale well. Strategies for rapid mixing requires smart and informative proposals to reduce the rejection rate. However, all known smart proposals in...

Many problems in statistical physics, machine learning and statistical inference require us to draw samples from (potentially very) high-dimensional distributions, P (~x). Often, one does not have an explicit expression for the probability distribution but (as we will see) can evaluate a function f(~x) ∝ P (~x). Markov Chain Monte Carlo is a way of sequentially generating samples (in a “chain”)...

UNLABELLED A key element to a successful Markov chain Monte Carlo (MCMC) inference is the programming and run performance of the Markov chain. However, the explicit use of quality assessments of the MCMC simulations-convergence diagnostics-in phylogenetics is still uncommon. Here, we present a simple tool that uses the output from MCMC simulations and visualizes a number of properties of primar...

With gravitational-wave detection on the horizon, astronomers look for ways of extracting useful information from a detected gravitational wave. Like its electromagnetic cousin, a gravitational wave carries important information about the characteristics of its source, and these characteristics can be recovered through numerical analysis. Using one promising technique known as a Metropolis-Hast...

In mixed models, posterior densities are too difficult to work with directly. With the Markov chain Monte Carlo (MCMC) methods, to do statistical inference requires the convergence of the MCMC chain to its stationary distribution. To assess convergence of Markov chain has not a specific way. Assessing convergence of Markov chain has been developed many techniques. Although increasingly populari...

The conventional Markov chain Monte Carlo (MCMC) method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis (AM) algorithm and delayed rejection (DR) algor...