8. MCMC-Driven Adaptive Multiple Importance Sampling

Monte Carlo (MC) methods are widely used for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling (IS) and its adaptive extensions (such as adaptive multiple IS and population MC). In this work, we introduce an iterated batch importance sampler using a population of proposal densities, which are adapted according to a Markov Chain Monte Carlo (MCMC) technique over the population of location parameters. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the generated samples weighted according to the so-called deterministic mixture scheme. Compared with a traditional multiple IS scheme with the same number of samples, the performance is substantially improved at the expense of a slight increase in the computational cost due to the additional MCMC steps. Moreover, the dependence on the choice of the cloud of proposals is sensibly reduced, since the proposal density in the MCMC method can be adapted in order to optimize the performance. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error.