Anti-tempered layered adaptive importance sampling

Monte Carlo (MC) methods are widely used for Bayesian inference in signal processing, machine learning and statistics. In this work, we introduce an adaptive importance sampler which mixes together the benefits of the Importance Sampling (IS) and Markov Chain Monte Carlo (MCMC) approaches. Different parallel MCMC chains provide the location parameters of the proposal probability density functions (pdfs) used in an IS method. The MCMC algorithms consider a tempered version of the posterior distribution as invariant density. We also provide an exhaustive theoretical support explaining why, in the presented technique, even an anti-tempering strategy (reducing the scaling of the posterior) can be beneficial. Numerical results confirm the advantages of the proposed scheme.