Ensemble preconditioning for Markov chain Monte Carlo simulation

Ensemble preconditioning for Markov chain Monte Carlo simulation

We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotropic sampling problems in high dimensions. Numerical experiments with model p...

Bayesian Generalised Ensemble Markov Chain Monte Carlo

Bayesian generalised ensemble (BayesGE) is a new method that addresses two major drawbacks of standard Markov chain Monte Carlo algorithms for inference in highdimensional probability models: inapplicability to estimate the partition function and poor mixing properties. BayesGE uses a Bayesian approach to iteratively update the belief about the density of states (distribution of the log likelih...

Markov Chain Monte Carlo Simulation Made Simple

Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling

Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery et al. Mon Weather Rev 133:1155–1174, 2005) has recommended the Expec...

Markov Chain Monte Carlo

Markov chain Monte Carlo is an umbrella term for algorithms that use Markov chains to sample from a given probability distribution. This paper is a brief examination of Markov chain Monte Carlo and its usage. We begin by discussing Markov chains and the ergodicity, convergence, and reversibility thereof before proceeding to a short overview of Markov chain Monte Carlo and the use of mixing time...