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Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…

Computation · Statistics 2018-04-12 Christian P. Robert , Victor Elvira , Nick Tawn , Changye Wu

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…

Computation · Statistics 2017-08-30 James E. Johndrow , Jonathan C. Mattingly , Sayan Mukherjee , David Dunson

Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…

Artificial Intelligence · Computer Science 2013-01-07 Bhaskara Marthi , Hanna Pasula , Stuart Russell , Yuval Peres

This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…

Probability · Mathematics 2021-09-03 Yu Hang Jiang , Tong Liu , Zhiya Lou , Jeffrey S. Rosenthal , Shanshan Shangguan , Fei Wang , Zixuan Wu

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 present a Markov chain Monte Carlo scheme based on merges and splits of groups that is capable of efficiently sampling from the posterior distribution of network partitions, defined according to the stochastic block model (SBM). We…

Physics and Society · Physics 2020-07-14 Tiago P. Peixoto

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…

Probability · Mathematics 2017-11-16 James E. Johndrow , Jonathan C. Mattingly

Markov chain Monte Carlo (MCMC) is one of the most useful approaches to scientific computing because of its flexible construction, ease of use and generality. Indeed, MCMC is indispensable for performing Bayesian analysis. Two critical…

Computation · Statistics 2019-10-18 Vivekananda Roy

We connect the problem of semi-supervised clustering to constrained Markov aggregation, i.e., the task of partitioning the state space of a Markov chain. We achieve this connection by considering every data point in the dataset as an…

Machine Learning · Computer Science 2022-05-11 Sophie Steger , Bernhard C. Geiger , Marek Smieja

Markov Chain Monte Carlo (MCMC) is a flexible approach to approximate sampling from intractable probability distributions, with a rich theoretical foundation and comprising a wealth of exemplar algorithms. While the qualitative correctness…

Computation · Statistics 2025-11-27 Sam Power , Giorgos Vasdekis

It is commonly admitted that non-reversible Markov chain Monte Carlo (MCMC) algorithms usually yield more accurate MCMC estimators than their reversible counterparts. In this note, we show that in addition to their variance reduction…

Computation · Statistics 2019-08-27 Marie Vialaret , Florian Maire

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

An important problem in the implementation of Markov Chain Monte Carlo algorithms is to determine the convergence time, or the number of iterations before the chain is close to stationarity. For many Markov chains used in practice this time…

Data Structures and Algorithms · Computer Science 2010-07-02 Nayantara Bhatnagar , Andrej Bogdanov , Elchanan Mossel

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the…

Machine Learning · Computer Science 2014-11-13 Xianghang Liu , Justin Domke

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…

Instrumentation and Methods for Astrophysics · Physics 2018-05-23 David W. Hogg , Daniel Foreman-Mackey

We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters…

Social and Information Networks · Computer Science 2023-03-28 Yufan Huang , C. Seshadhri , David F. Gleich

Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…

Computation · Statistics 2015-10-30 Christophe Andrieu , Matti Vihola

Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…

Computation · Statistics 2008-07-22 Ioana A. Cosma , Masoud Asgharian

In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in…

Discrete Mathematics · Computer Science 2016-09-15 Steffen Rechner , Annabell Berger

Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed…

Probability · Mathematics 2025-07-16 Patrick Sonnentag