Efficient Adaptive Multiple Importance Sampling

The adaptive multiple importance sampling (AMIS) algorithm is a powerful Monte Carlo tool for Bayesian estimation in intractable models. The uniqueness of this methodology from other adaptive importance sampling (AIS) schemes is in the
weighting procedure, where at each iteration of the algorithm, all samples are re-weighted according to the temporal deterministic mixture approach. This re-weighting allows for substantial variance reduction of the AMIS estimator, at the expense of an increased computational cost that grows quadratically with
the number of iterations. In this paper, we propose a novel AIS methodology which obtains most of the AMIS variance reduction while improving upon its computational complexity. The proposed method implements an approximate version of the temporal deterministic mixture approach and requires substantially less computation. Advantages are shown empirically through a numerical example, where the novel method is able to attain a desired mean-squared error with much less computation.