Luca Martino (University of Helsinki): An iterated batch importance sampler driven by an MCMC algorithm

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 (e.g., population Monte Carlo). In this work, we introduce an iterated batch importance sampler where the proposal is changed following a random walk generated by an MCMC technique. The novel algorithm provides a global estimation of the variables of interest iteratively, using and all the generated (weighted) samples.

Compared with a traditional IS scheme using with the same number of samples, the performance are strongly improved and the computational cost increases lightly, only for the acceptance step of the MCMC method (for accepting or rejecting the movement). Clearly, the dependence to the choice of the proposal is sensibly reduced. The novel algorithm can be considered as a IS scheme with a population of proposals automatically selected by the used MCMC technique. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error.