Coalescent-based Bayesian Markov chain Monte Carlo (MCMC) inference generates estimates of evolutionary parameters and their posterior probability distributions. As the number of sequences increases, the length of time taken to complete an MCMC analysis increases as well. Here, we investigate an approach to distribute the MCMC analysis across a cluster of computers. To do this, we use bootstrap...

Error bars for MCMC are harder than for direct Monte Carlo. It is harder to estimate error bars from MCMC data, and it is harder to predict them from theory. The estimation and theory are more important because MCMC estimation errors can be much larger than you might expect based on the run time. The fundamental formula for MCMC error bars is as follows. Suppose Xk is a sequence of MCMC samples...

Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or M...

Monte Carlo (MC) methods are widely used in statistics, signal processing and machinelearning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC)algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have beenrecently introduced. In this work, ...

We develop a novel Markov chain Monte Carlo (MCMC) method that exploits hierarchy of models increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the rewrites multilevel MCMC approach Dodwell et al. [SIAM/ASA J. Un-certain. Quantif., 3 (2015), pp. 1075–1108] in terms delayed acceptance Christen and Fox [J. Comput. Graph. Statist., 14 (2005), 79...

We apply coarse-to-fine MCMC to perform Bayesian inference for a seismic monitoring system. While traditional MCMC has difficulty moving between local optima, by applying coarse-to-fine MCMC, we can adjust the resolution of the model and this allows the state to jump between different optima more easily. It is quite similar to simulated annealing. We will use a 1D model as an example, and then ...

Markov Chain Monte Carlo (MCMC) methods are increasingly popular among epidemiologists. The reason for this may in part be that MCMC offers an appealing approach to handling some difficult types of analyses. Additionally, MCMC methods are those most commonly used for Bayesian analysis. However, epidemiologists are still largely unfamiliar with MCMC. They may lack familiarity either with he impl...