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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. The method is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performances of the proposed scheme are studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.
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
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
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 inc
Monte Carlo (MC) methods have become very popular in signal processing during the past decades. The adaptive rejection sampling (ARS) algorithms are well-known MC technique which draw efficiently independent samples from univariate target densities.