Exploring the common concepts of adaptive MCMC and Covariance Matrix Adaptation schemes

In the field of scientific modeling, one is often confronted with the task of drawing samples from a probability distribution that is only known up to a normalizing constant and for which no direct analytical method for sample generation is available. Since the past decade, adaptive Markov Chain Monte Carlo (MCMC) methods gained considerable attention in the statistics community in order to tackle this black-box (or indirect) sampling scenario. Common application domains are Bayesian statistics and statistical physics. Adaptive MCMC methods try to learn an optimal proposal distribution from previously accepted samples in order to efficiently explore the target distribution. Variable metric approaches in black-box optimization, such as the Evolution Strategy with covariance matrix adaptation (CMA-ES) and Gaussian Adaption (GaA), use almost identical ideas to locate putative global optima. This extended abstract summarizes the common concepts in adaptive MCMC and covariance matrix adaptation schemes. We also present how both types of methods can be unified within the Gaussian Adaptation framework and propose a unification of both fields as “grand challenge” for future research.