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Importance sampling (IS) is a Monte Carlo technique for the approximation of intractable distributions and integrals with respect to them. The origin of IS dates from the early 1950s. In the last decades, the rise of the Bayesian paradigm and the increase of the available computational resources have propelled the interest in this theoretically sound methodology. In this paper, we first describe the basic IS algorithm and then revisit the recent advances in this methodology. We pay particular attention to two sophisticated lines. First, we focus on multiple IS (MIS), the case where more than one proposal is available. Second, we describe adaptive IS (AIS), the generic methodology for adapting one or more proposals.
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
Monte Carlo methods represent the de facto standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use simpler pro
In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the importance sampling performances, as measured by an entropy criterion. T
Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a sign
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals