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Markov chain Monte Carlo (MCMC) methods are one of the most popular classes of algorithms for sampling from a target probability distribution. A rising trend in recent years consists in analyzing the convergence of MCMC algorithms using…

概率论 · 数学 2025-04-30 Federica Milinanni

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…

高能物理 - 唯象学 · 物理学 2023-09-06 N. T. Hunt-Smith , W. Melnitchouk , F. Ringer , N. Sato , A. W Thomas , M. J. White

Markov Chain Monte Carlo (MCMC) methods are a powerful tool for computation with complex probability distributions. However the performance of such methods is critically dependant on properly tuned parameters, most of which are difficult if…

统计计算 · 统计学 2021-10-27 James A. Brofos , Marylou Gabrié , Marcus A. Brubaker , Roy R. Lederman

The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…

统计方法学 · 统计学 2026-03-10 Estevão Prado , Christopher Nemeth , Chris Sherlock

Motivated by the physics of strings and branes, we develop a class of Markov chain Monte Carlo (MCMC) algorithms involving extended objects. Starting from a collection of parallel Metropolis-Hastings (MH) samplers, we place them on an…

计算物理 · 物理学 2017-09-13 Jonathan J. Heckman , Jeffrey G. Bernstein , Ben Vigoda

Markov Chain Monte Carlo (MCMC) is a class of algorithms to sample complex and high-dimensional probability distributions. The Metropolis-Hastings (MH) algorithm, the workhorse of MCMC, provides a simple recipe to construct reversible…

Markov Chain Monte Carlo (MCMC) algorithms are widely used for stochastic optimization, sampling, and integration of mathematical objective functions, in particular, in the context of Bayesian inverse problems and parameter estimation. For…

数据分析、统计与概率 · 物理学 2020-10-12 Shashank Kumbhare , Amir Shahmoradi

We propose a new class of learning algorithms that combines variational approximation and Markov chain Monte Carlo (MCMC) simulation. Naive algorithms that use the variational approximation as proposal distribution can perform poorly…

机器学习 · 计算机科学 2013-01-14 Nando de Freitas , Pedro Hojen-Sorensen , Michael I. Jordan , Stuart Russell

An informal observation, made by several authors, is that the adaptive design of a Markov transition kernel has the flavour of a reinforcement learning task. Yet, to-date it has remained unclear how to actually exploit modern reinforcement…

统计计算 · 统计学 2024-05-24 Congye Wang , Wilson Chen , Heishiro Kanagawa , Chris. J. Oates

The multiple-try Metropolis (MTM) algorithm is a generalization of the Metropolis-Hastings algorithm in which the transition kernel uses a compound proposal consisting of multiple candidate draws. Since its seminal paper there have been…

统计计算 · 统计学 2025-03-17 Renny Doig , Liangliang Wang

Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…

机器学习 · 统计学 2019-08-29 Tung-Yu Wu , Y. X. Rachel Wang , Wing H. Wong

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the…

统计理论 · 数学 2015-11-03 Yi-An Ma , Tianqi Chen , Emily B. Fox

Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we…

机器学习 · 计算机科学 2015-02-25 Jacob Steinhardt , Percy Liang

Stochastic gradient Markov Chain Monte Carlo (SGMCMC) is considered the gold standard for Bayesian inference in large-scale models, such as Bayesian neural networks. Since practitioners face speed versus accuracy tradeoffs in these models,…

机器学习 · 计算机科学 2022-07-19 Antonios Alexos , Alex Boyd , Stephan Mandt

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…

统计方法学 · 统计学 2024-06-21 Luca Martino , Victor Elvira

Metropolis-Hastings (MH) is a foundational Markov chain Monte Carlo (MCMC) algorithm. In this paper, we ask whether it is possible to formulate and analyse MH in terms of categorical probability, using a recent involutive framework for…

统计计算 · 统计学 2026-02-02 Rob Cornish , Andi Q. Wang

One of the most widely used samplers in practice is the component-wise Metropolis-Hastings (CMH) sampler that updates in turn the components of a vector valued Markov chain using accept-reject moves generated from a proposal distribution.…

统计计算 · 统计学 2017-03-22 Jinyoung Yang , Evgeny Levi , Radu V. Craiu , Jeffrey S. Rosenthal

Stochastic gradient Markov Chain Monte Carlo algorithms are popular samplers for approximate inference, but they are generally biased. We show that many recent versions of these methods (e.g. Chen et al. (2014)) cannot be corrected using…

机器学习 · 统计学 2021-02-03 Adrià Garriga-Alonso , Vincent Fortuin

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…

机器学习 · 计算机科学 2025-03-04 Hyunsu Kim , Giung Nam , Chulhee Yun , Hongseok Yang , Juho Lee

Markov Chain Monte Carlo (MCMC) algorithms are frequently used to perform inference under a Bayesian modeling framework. Convergence diagnostics, such as traceplots, the Gelman-Rubin potential scale reduction factor, and effective sample…

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