Comparison of MCMC Adaptation Schemes: A Preliminary Empirical Study

Adaptive Markov Chain Monte Carlo (MCMC) adapts the covariance of the proposal distribution to improve the efficiency of Metropolis Hastings (MH). Adaptive Metropolis (AM) is the prime example. Some stochastic optimisation techniques adapt the covariance of the search distribution. Some examples are Gaussian Adaptation (GaA) and (1+1)-Covariance Matrix Adaptation Evolution Strategy (CMAES) that can be turned into MCMC samplers in a straightforward way. However, the adaptation rational used by these samplers differ. AM estimates the covariance of the target distribution based on the generated samples. GaA adapts the covariance such that the entropy of the proposal is increased/decreased when the candidate sample is accepted/rejected while adaptation in CMAES increases the likelihood of generating better search points. We compare the performance of AM, GaA and (1+1)-CMAES samplers on a test suite of target distributions to understand the effectiveness of the adaptation mechanism used.