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Markov Chain Monte Carlo (MCMC) algorithms are routinely used to draw samples from distributions with intractable normalization constants. However, standard MCMC algorithms do not apply to doubly-intractable distributions in which there are…

Computation · Statistics 2012-07-02 Iain Murray , Zoubin Ghahramani , David MacKay

A new class of Markov chain Monte Carlo (MCMC) algorithms, based on simulating piecewise deterministic Markov processes (PDMPs), have recently shown great promise: they are non-reversible, can mix better than standard MCMC algorithms, and…

Computation · Statistics 2020-10-23 Augustin Chevallier , Paul Fearnhead , Matthew Sutton

Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble of districting plans which are drawn from a prescribed probability distribution that adheres to a realistic and…

Computation · Statistics 2020-08-19 Gregory Herschlag , Jonathan C. Mattingly , Matthias Sachs , Evan Wyse

A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…

Computation · Statistics 2013-01-18 Matthew T. Harrison , Jeffrey W. Miller

Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood…

Methodology · Statistics 2020-05-26 Guanyu Hu , HaiYing Wang

We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…

Computation · Statistics 2021-08-17 Yves Atchadé , Liwei Wang

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…

Statistical Mechanics · Physics 2024-12-05 Synge Todo

We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient,…

Computation · Statistics 2024-10-03 Guanxun Li , Aaron Smith , Quan Zhou

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…

Statistical Mechanics · Physics 2016-04-27 Marija Vucelja

The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…

Instrumentation and Methods for Astrophysics · Physics 2014-08-19 Yi-Ming Hu , Martin Hendry , Ik Siong Heng

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Numerical Analysis · Mathematics 2017-11-15 Matthias Morzfeld , Marcus S. Day , Ray W. Grout , George Shu Heng Pau , Stefan A. Finsterle , John B. Bell

We introduce a revised derivation of the bitwise Markov Chain Monte Carlo (MCMC) multiple-input multiple-output (MIMO) detector. The new approach resolves the previously reported high SNR stalling problem of MCMC without the need for…

Information Theory · Computer Science 2017-07-13 Jonathan C. Hedstrom , Chung Him , Yuen , Rong-Rong Chen , Behrouz Farhang-Boroujeny

Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…

Methodology · Statistics 2014-11-04 Michael Braun , Paul Damien

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

Discrete Mathematics · Computer Science 2010-03-05 Annabell Berger , Matthias Müller-Hannemann

It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…

Statistical Mechanics · Physics 2019-06-24 Ludovic Berthier , Elijah Flenner , Christopher J. Fullerton , Camille Scalliet , Murari Singh

Monte Carlo rendering algorithms often utilize correlations between pixels to improve efficiency and enhance image quality. For real-time applications in particular, repeated reservoir resampling offers a powerful framework to reuse samples…

Graphics · Computer Science 2022-11-02 Rohan Sawhney , Daqi Lin , Markus Kettunen , Benedikt Bitterli , Ravi Ramamoorthi , Chris Wyman , Matt Pharr

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

Machine Learning · Computer Science 2022-02-11 Jiaming Liang , Yongxin Chen

With sufficient time, double edge-swap Markov chain Monte Carlo (MCMC) methods are able to sample uniformly at random from many different and important graph spaces. For instance, for a fixed degree sequence, MCMC methods can sample any…

Combinatorics · Mathematics 2017-04-07 Joel Nishimura

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky…

Methodology · Statistics 2015-06-22 Clément Gilavert , Saïd Moussaoui , Jérôme Idier

We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…

Probability · Mathematics 2010-07-28 Lucas Gerin