Adaptive independence samplers

Markov chainMonte Carlo (MCMC) is an importantcomputational technique for generating samples fromnon-standard probability distributions. A major challenge inthe design of practical MCMC samplers is to achieve efficientconvergence and mixing properties. One way to accelerateconvergence and mixing is to adapt the proposaldistribution in light of previously sampled points, thus increasingthe probability of acceptance. In this paper, we proposetwo new adaptive MCMC algorithms based on the IndependentMetropolisHastings algorithm. In the first, weadjust the proposal to minimize an estimate of the crossentropybetween the target and proposal distributions, usingthe experience of pre-runs. This approach provides a generaltechnique for deriving natural adaptive formulae. The secondapproach uses multiple parallel chains, and involves updatingchains individually, then updating a proposal densityby fitting a Bayesian model to the population. An importantfeature of this approach is that adapting the proposal doesnot change the limiting distributions of the chains. Consequently,the adaptive phase of the sampler can be continued