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In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

Methodology · Statistics 2022-10-03 Robert Millar , Jinglai Li , Hui Li

Population annealing Monte Carlo is an efficient sequential algorithm for simulating k-local Boolean Hamiltonians. Because of its structure, the algorithm is inherently parallel and therefore well suited for large-scale simulations of…

Disordered Systems and Neural Networks · Physics 2018-11-26 Amin Barzegar , Christopher Pattison , Wenlong Wang , Helmut G. Katzgraber

Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this…

Computation · Statistics 2024-11-07 Haoxuan Chen , Lexing Ying

Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…

Methodology · Statistics 2013-02-11 Cheng-Der Fuh , Huei-Wen Teng , Ren-Her Wang

This paper introduces a class of Monte Carlo algorithms which are based upon the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current…

Methodology · Statistics 2020-04-14 Murray Pollock , Paul Fearnhead , Adam M. Johansen , Gareth O. Roberts

We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…

Statistical Mechanics · Physics 2009-11-07 P. Grassberger

This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…

Computation · Statistics 2016-03-04 Pierre Del Moral , Ajay Jasra , Kody Law , Yan Zhou

Casella and Robert [Biometrika 83 (1996) 81--94] presented a general Rao--Blackwellization principle for accept-reject and Metropolis--Hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at…

Computation · Statistics 2011-03-09 Randal Douc , Christian P. Robert

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…

Computation · Statistics 2012-02-27 Brendon J. Brewer , Livia B. Pártay , Gábor Csányi

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…

Methodology · Statistics 2016-12-08 Blazej Miasojedow , Wojciech Niemiro , Jan Palczewski , Wojciech Rejchel

This paper presents a control variate-based Markov chain Monte Carlo algorithm for efficient sampling from the probability simplex, with a focus on applications in large-scale Bayesian models such as latent Dirichlet allocation. Standard…

Methodology · Statistics 2024-10-02 Francesco Barile , Christopher Nemeth

We study control variate methods for Markov chain Monte Carlo (MCMC) in the setting of deterministic sweep sampling using $K\geq 2$ transition kernels. New variance reduction results are provided for MCMC averages based on sweeps over…

Statistics Theory · Mathematics 2019-12-17 Stephen Berg , Jun Zhu , Murray K. Clayton

In the last decade, sequential Monte-Carlo methods (SMC) emerged as a key tool in computational statistics. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted…

Statistics Theory · Mathematics 2007-06-13 R. Douc , France E. Moulines

We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm, and show that this variant can be considered as a sequential Monte Carlo sampler with a modified mutation kernel. We prove that the new sampler…

Computation · Statistics 2009-11-11 G. W. Peters , Y. Fan , S. A. Sisson

Acceptance-rejection (AR), Independent Metropolis Hastings (IMH) or importance sampling (IS) Monte Carlo (MC) simulation algorithms all involve computing ratios of probability density functions (pdfs). On the other hand, classifiers…

Methodology · Statistics 2023-09-11 Elouan Argouarc'h , François Desbouvries

This paper focuses on the study of an original combination of the Multilevel Monte Carlo method introduced by Giles [10] and the popular importance sampling technique. To compute the optimal choice of the parameter involved in the…

Probability · Mathematics 2017-09-05 Mohamed Ben Alaya , Kaouther Hajji , Ahmed Kebaier

Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and…

Econometrics · Economics 2024-09-10 Marko Mlikota , Frank Schorfheide

We propose a new Monte Carlo algorithm for complex discrete distributions. The algorithm is motivated by the N-Fold Way, which is an ingenious event-driven MCMC sampler that avoids rejection moves at any specific state. The N-Fold Way can…

Computation · Statistics 2012-06-26 Firas Hamze , Nando de Freitas

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…

Computation · Statistics 2009-08-18 Olivier Cappé , Randal Douc , Arnaud Guillin , Jean-Michel Marin , Christian P. Robert

Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…

Probability · Mathematics 2007-05-23 Andreas Eberle , Carlo Marinelli