Markov chain Monte Carlo (MCMC) is the engine of modern Bayesian statistics, being used to approximate posterior and derived quantities interest. Despite this, issue how output from a post-processed reported often overlooked. Convergence diagnostics can be control bias via burn-in removal, but these do not account for (common) situations where limited computational budget engenders bias-varianc...

We introduce Bilby-MCMC, a Markov-Chain Monte-Carlo sampling algorithm tuned for the analysis of gravitational waves from merging compact objects. Bilby-MCMC provides parallel-tempered ensemble Metropolis-Hastings sampler with access to block-updating proposal library including problem-specific and machine learning proposals. demonstrate that proposals can produce over 10-fold improvement in ef...

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...