Metropolis Sampling

Abstract

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based sampling's world.

Wiley StatsRef-Statistics Reference Online, 2017

References in corpus (8)

• The pseudo-marginal approach for efficient Monte Carlo computations
• MCMC for doubly-intractable distributions
• Layered Adaptive Importance Sampling
• Orthogonal parallel MCMC methods for sampling and optimization
• Efficient Multiple Importance Sampling Estimators
• Non-reversible Metropolis-Hastings
• Adaptive independent Metropolis--Hastings
• Heretical Multiple Importance Sampling

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• Nearly Consistent Finite Particle Estimates in Streaming Importance Sampling