  The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an
optimal recycling of past simulations in an iterated importance sampling
scheme. The difference with earlier adaptive importance sampling
implementations like Population Monte Carlo is that the importance weights of
all simulated values, past as well as present, are recomputed at each
iteration, following the technique of the deterministic multiple mixture
estimator of Owen and Zhou (2000). Although the convergence properties of the
algorithm cannot be fully investigated, we demonstrate through a challenging
banana shape target distribution and a population genetics example that the
improvement brought by this technique is substantial.
