Every day, weather forecasting centres around the world make use of noisy, incomplete observations atmosphere to update their forecasts. This process is known as data assimilation, fusion or state estimation and best expressed Bayesian inference: given a set observations, some prior beliefs model target system, what probability distribution unobserved quantities latent variables at time,...

Markov chain algorithms are ubiquitous in machine learning and statistics many other disciplines. Typically, these can be formulated as acceptance rejection methods. In this work, we present a novel estimator applicable to methods, dubbed importance sampling, which efficiently makes use of rejected proposals. For the unadjusted Langevin algorithm, it provides way correcting discretization error...

We present a versatile Monte Carlo method for estimating multidimensional integrals, with applications to rare-event probability estimation. The method fuses two distinct and popular Monte Carlo simulation methods — Markov chain Monte Carlo and importance sampling — into a single algorithm. We show that for some illustrative and applied numerical examples the proposed Markov Chain importance sa...

Propp & Wilson (1996) described a protocol, called coupling from the past, for exact sampling from a target distribution using a coupled Markov chain Monte Carlo algorithm. In this paper we extend coupling from the past to various MCMC samplers on a continuous state space; rather than following the monotone sampling device of Propp & Wilson, our approach uses methods related to gamma-coupling a...