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Markov chain Monte Carlo (MCMC) algorithms are based on the construction of a Markov chain with transition probabilities leaving invariant a probability distribution of interest. In this work, we look at these transition probabilities as…

Probability · Mathematics 2024-10-01 Rocco Caprio , Adam M. Johansen

We propose a sequential Markov chain Monte Carlo (SMCMC) algorithm to sample from a sequence of probability distributions, corresponding to posterior distributions at different times in on-line applications. SMCMC proceeds as in usual MCMC…

Statistics Theory · Mathematics 2013-08-20 Yun Yang , David B. Dunson

Markov chain Monte Carlo (MCMC) methods are often used in clustering since they guarantee asymptotically exact expectations in the infinite-time limit. In finite time, though, slow mixing often leads to poor performance. Modern computing…

Methodology · Statistics 2022-02-24 Tin D. Nguyen , Brian L. Trippe , Tamara Broderick

Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…

Machine Learning · Computer Science 2019-07-16 Kiarash Shaloudegi , András György

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…

Computation · Statistics 2021-05-27 Peter L Green , Robert E Moore , Ryan J Jackson , Jinglai Li , Simon Maskell

In this paper, we address technical difficulties that arise when applying Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform clustering in the space of latent parameters of subject-wise generative models.…

Quantitative Methods · Quantitative Biology 2020-12-15 Yu Yao , Klaas E. Stephan

We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…

Numerical Analysis · Mathematics 2020-11-25 Zhenghang Xu , Zhijian He , Xiaoqun Wang

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential…

Machine Learning · Statistics 2014-03-31 Elaine Angelino , Eddie Kohler , Amos Waterland , Margo Seltzer , Ryan P. Adams

Multilevel sampling methods, such as multilevel and multifidelity Monte Carlo, multilevel stochastic collocation, or delayed acceptance Markov chain Monte Carlo, have become standard uncertainty quantification (UQ) tools for a wide class of…

Numerical Analysis · Mathematics 2025-10-01 Josef Martínek , Erin Carson , Robert Scheichl

Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the…

Methodology · Statistics 2023-07-04 David Gunawan , Chris Carter , Robert Kohn

Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…

Computation · Statistics 2024-09-09 Adrien Corenflos , Matthew Sutton , Nicolas Chopin

We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for…

Machine Learning · Statistics 2016-12-09 Jost Tobias Springenberg , Aaron Klein , Stefan Falkner , Frank Hutter

We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global…

Computation · Statistics 2022-08-16 Joseph Mathews , Scott C. Schmidler

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms which are primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Single instances of MCMC methods are widely…

Computation · Statistics 2019-05-27 Alessandro Varsi , Lykourgos Kekempanos , Jeyarajan Thiyagalingam , Simon Maskell

This paper addresses the key challenge of estimating the asymptotic covariance associated with the Markov chain central limit theorem, which is essential for visualizing and terminating Markov Chain Monte Carlo (MCMC) simulations. We focus…

Computation · Statistics 2024-08-29 James M. Flegal , Rebecca P. Kurtz-Garcia

We propose a generic Markov Chain Monte Carlo (MCMC) algorithm to speed up computations for datasets with many observations. A key feature of our approach is the use of the highly efficient difference estimator from the survey sampling…

Methodology · Statistics 2017-08-03 Matias Quiroz , Mattias Villani , Robert Kohn

We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…

Computation · Statistics 2019-04-15 Jordan Franks

Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…

Computation · Statistics 2022-03-18 Cosma Rohilla Shalizi

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational…

Machine Learning · Statistics 2025-05-16 Conor Rosato , Harvinder Lehal , Simon Maskell , Lee Devlin , Malcolm Strens

It is widely known that the performance of Markov chain Monte Carlo (MCMC) can degrade quickly when targeting computationally expensive posterior distributions, such as when the sample size is large. This has motivated the search for MCMC…

Computation · Statistics 2024-12-02 James E. Johndrow , Natesh S. Pillai , Aaron Smith