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Related papers: Optimality in importance sampling: a gentle survey

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The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…

Computation · Statistics 2017-01-17 S. Agapiou , O. Papaspiliopoulos , D. Sanz-Alonso , A. M. Stuart

In this work, we propose a smart idea to couple importance sampling and Multilevel Monte Carlo (MLMC). We advocate a per level approach with as many importance sampling parameters as the number of levels, which enables us to compute the…

Probability · Mathematics 2017-07-10 Ahmed Kebaier , Jérôme Lelong

We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to…

Computation · Statistics 2019-09-18 Giacomo Zanella , Gareth Roberts

Large deviation theory has provided important clues for the choice of importance sampling measures for Monte Carlo evaluation of exceedance probabilities. However, Glasserman and Wang [Ann. Appl. Probab. 7 (1997) 731--746] have given…

Probability · Mathematics 2007-05-23 Hock Peng Chan , Tze Leung Lai

We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…

Computation · Statistics 2018-07-12 Matthias C. M. Troffaes

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows…

Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…

Computational Finance · Quantitative Finance 2011-04-28 Bernard Lapeyre , Jérôme Lelong

We present an aid for importance sampling in Monte Carlo integration, which is of the general-purpose type in the sense that it in principle deals with any quadratically integrable integrand on a unit hyper-cube of arbitrary dimension. In…

High Energy Physics - Phenomenology · Physics 2009-07-29 A. van Hameren

Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…

Computation · Statistics 2022-01-17 Víctor Elvira , Luca Martino , David Luengo , Mónica F. Bugallo

An importance sampling approach for sampling copula models is introduced. We propose two algorithms that improve Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at…

Computation · Statistics 2015-04-08 Philipp Arbenz , Mathieu Cambou , Marius Hofert

We consider selecting the top-$m$ alternatives from a finite number of alternatives via Monte Carlo simulation. Under a Bayesian framework, we formulate the sampling decision as a stochastic dynamic programming problem, and develop a…

Optimization and Control · Mathematics 2023-08-22 Gongbo Zhang , Yijie Peng , Jianghua Zhang , Enlu Zhou

We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…

Computation · Statistics 2019-11-05 Siddhant Wahal , George Biros

Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the…

Statistics Theory · Mathematics 2021-11-01 Anna Korba , François Portier

We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling…

Methodology · Statistics 2015-01-12 Ernest K. Ryu , Stephen P. Boyd

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of…

Numerical Analysis · Mathematics 2018-04-04 Joakim Beck , Ben Mansour Dia , Luis FR Espath , Quan Long , Raul Tempone

We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…

Probability · Mathematics 2011-09-20 Noufel Frikha , Abass Sagna

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…

Machine Learning · Statistics 2022-06-08 Yi-An Ma , Yuansi Chen , Chi Jin , Nicolas Flammarion , Michael I. Jordan

In this work, we analyze the noisy importance sampling (IS), i.e., IS working with noisy evaluations of the target density. We present the general framework and derive optimal proposal densities for noisy IS estimators. The optimal…

Machine Learning · Statistics 2022-01-24 Fernando Llorente , Luca Martino , Jesse Read , David Delgado-Gómez

Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…

Computational Physics · Physics 2010-11-22 John Robert Trail , Ryo Maezono

Any data modeling exercise has two main components: parameter estimation and model selection. The latter will be the topic of this lecture note. More concretely we will introduce several Monte-Carlo sampling-based rules for model selection…

Methodology · Statistics 2022-09-28 Petre Stoica , Xiaolei Shang , Yuanbo Cheng