  Importance sampling is a Monte Carlo method that introduces a proposal
distribution to sample the space according to the target distribution. Yet
calibration of the proposal distribution is essential to achieving efficiency,
thus the resort to adaptive algorithms to tune this distribution. In the paper,
we propose a new adpative importance sampling scheme, named Tempered
Anti-truncated Adaptive Multiple Importance Sampling (TAMIS) algorithm. We
combine a tempering scheme and a new nonlinear transformation of the weights we
named anti-truncation. For efficiency, we were also concerned not to increase
the number of evaluations of the target density. As a result, our proposal is
an automatically tuned sequential algorithm that is robust to poor initial
proposals, does not require gradient computations and scales well with the
dimension.
