Tempered, Anti-trunctated, Multiple Importance Sampling

We propose a Tempered Anti-truncated Adaptive Multiple Importance Sampling (TAMIS) algorithm to solve the initialization difficulty of the adaptive importance sampling algorithms, without introducing too many evaluations of the target density. We combine a tempering scheme and a new nonlinear transformation of the weights named anti-truncation. As a result, our proposal is an automatically tuned sequential algorithm that is robust to poor initial proposals, doesn't require gradient computations and scales well with the dimension.