Improving the effectiveness of MCMC through adaptation

Abstract

The Metropolis-Hastings Markov Chain Monte Carlo algorithm uses a proposal distribution to sample from a given target distribution. The proposal distribution has to be tuned beforehand which is an expensive exercise. However, adaptive algorithms automatically tune the proposal distribution based on knowledge from past samples, reducing the tuning cost. In this study we first examine Adaptive Metropolis, Metropolis Gaussian Adaptation and Covariance Matrix Adaptation Evolutionary Strategies. The latter is usually used as an optimization strategy but it is feasible to incorporate it in MCMC.