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The effective sample size (ESS) is widely used in sample‐based simulation methods for assessing the quality of a Monte Carlo approximation of a given distribution and of related integrals. In this paper, we revisit the approximation of the ESS in the specific context of importance sampling. The derivation of this approximation, that we will denote as
, is partially available in a 1992 foundational...
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized...
The Effective Sample Size (ESS) is an important measure of efficiency of Monte Carlo methods such as Markov Chain Monte Carlo (MCMC) and Importance Sampling (IS) techniques. In the IS context, an approximation ESS^ of the theoretical ESS definition is widely applied, involving the inverse of the sum of the squares of the normalized importance weights. This formula, ESS^, has become an essential piece...
In this work, we focus on advancing the theory and practice of a class of Monte Carlo methods, population Monte Carlo (PMC) sampling, for dealing with inference problems with static parameters. We devise a new method for efficient adaptive learning from past samples and weights to construct improved proposal functions. It is based on assuming that, at each iteration, there is an intermediate target...
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