We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely difficult, even when using the Bayesian approach combined with Markov chain Monte Carlo (MCMC). The Sequential Monte Carlo sampler (SMC) is a new and general...

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]...

In radar tracking application, the observation noise is highly non-Gaussian, which is also referred as glint noise. The performance of extended Kalman filter degrades severely in the presence of glint noise. In this paper, an improved particle filter, Markov chain Monte Carlo particle filter (MCMC-PF), is introduced to cope with radar target tracking in glint noise environment. The Monte Carlo ...

As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, S...

In this note we attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940’s through its use today. We see how the earlier stages of the Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More importantly, we see how the development of this methodology has not only changed our solutions to problems, but...

Bayesian credible bounds produced from Markov chain Monte Carlo (MCMC) procedures contain Monte Carlo error and thus may require a long chain in order to have a reasonable degree of repeatability. This is especially true when there is a substantial amount of autocorrelation in the chain realization. Repeatability would be important in some applications where it would be undesirable to report nu...

Assessing the Convergence of Markov Chain Monte Carlo Methods for Bayesian Inference of Phylogenetic Trees In biology, it is commonly of interest to investigate the ancestral pattern that gave rise to a currently existing group of individuals, such as genes or species. This ancestral pattern is frequently represented pictorially by a phylogenetic tree. Due to the growing popularity of Bayesian ...

Motivated by the success of genetic algorithms and simulated annealing in hard optimization problems, the authors propose a new Markov chain Monte Carlo (MCMC) algorithm called an evolutionary Monte Carlo algorithm. This algorithm has incorporated several attractive features of genetic algorithms and simulated annealing into the framework of MCMC. It works by simulating a population of Markov c...

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...