Asymptotically Independent Markov Sampling: A New Markov Chain Monte Carlo Scheme for Bayesian Interference

摘要

In Bayesian statistics, many problems can be expressed as the evaluation of theudexpectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered posterioruddistributions cannot be sampled directly. In this case, the most popular strategies are the importance sampling method, Markov chain Monte Carlo, and annealing. Inudthis paper, we introduce a new scheme for Bayesian inference, called Asymptotically Independent Markov Sampling (AIMS), which is based on the above methods. Weudderive important ergodic properties of AIMS. In particular, it is shown that, under certain conditions, the AIMS algorithm produces a uniformly ergodic Markov chain.udThe choice of the free parameters of the algorithm is discussed and recommendations are provided for this choice, both theoretically and heuristically based. Theudefficiency of AIMS is demonstrated with three numerical examples, which include both multimodal and higher-dimensional target posterior distributions.