[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123565-en":3,"doc-seo-123565-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123565,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Sampling algorithms in statistical physics - a guide for statistics and machine learning","The article reviews sampling methods used to draw from unnormalized probability distributions in statistical physics, while framing the discussion through statistics and machine learning terminology. It introduces core concepts and then analyzes three major applications: phase transitions in the Ising model, the melting transition on a two-dimensional plane, and all-atom simulation of liquid water. Classical Metropolis, Glauber, and molecular dynamics samplers are compared with newer approaches including cluster algorithms, hybrid Monte Carlo and Langevin variants, and piece-wise deterministic event-chain Monte Carlo. Cross-disciplinary results and reproducible simulation studies for Ising and XY models are provided, alongside open directions for future collaboration.","Citation (Version of Record):  \nFaulkner, M. F. , & Livingstone, S. (2024) . Sampling algorithms in statistical physics: a guide for statistics and machine learning. Statistical Science, 39(1), 137-164 . [https://doi.org/10.1214/23-sts893](https://doi.org/10.1214/23-sts893)  \nVersion:  \nPeer reviewed version  \nLicense (if available): CC BY  \nLink to published version (if available):  \n10.1214/23-sts893  \nLink to publication record on the Bristol Research Portal:  \nAccess record including PDF (if available)  \nUniversity of Bristol – Bristol Research Portal  \nThis is the accepted author manuscript (AAM) of the article which has been made Open Access under the University of Bristol's Scholarly Works Policy. The final published version (Version of Record) can be found on the publisher's website. The copyright of any third-party content, such as images, remains with the copyright holder.  \nCiting this paper  \nGuidance on citing material from the Bristol Research Portal is available under ‘Manuscripts and Citations’ in the Terms of Use (linked below)  \nTerms of Use  \nFull Terms of Use for the Bristol Research Portal are available online: [https://www.bristol.ac.uk/research](https://www.bristol.ac.uk/research)enterprise-innovation/research-policy/pure/brp-terms/  \nHas this research benefited you?  \nLet us know how reading this research here has been meaningful to you by sharing your story at [https://forms.office.com/e/ffL5CZ0fGT](https://forms.office.com/e/ffL5CZ0fGT)  \nBristol Research Portal Coversheet last updated 21-07-2026  \nSampling algorithms in statistical physics: a guide for statistics and machine learning  \nMichael F. Faulkner and Samuel Livingstone  \nAbstract. We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and concepts ofthe field, before discussing three well-known problems: phase transitions in the Ising model, the melting transition on a two-dimensional plane and simulation of an all-atom model for liquid water.  \nWe review the classical Metropolis, Glauber and molecular dynamics sampling algorithms before discussing several more recent approaches, including cluster algorithms, novel variations of hybrid Monte Carlo and Langevin dynamics and piece-wise deterministic processes such as event chain Monte Carlo. We highlight cross-over with statistics and machine learning throughout and present some results on event chain Monte Carlo and sampling from the Ising model using tools from the statistics literature. We provide a simulation study on the Ising and XY models, with reproducible code freely available online, and following this we discuss several open areas for interaction between the disciplines that have not yet been explored and suggest avenues for doing so.  \nKey words and phrases: Statistical physics, sampling algorithms, Markov chain Monte Carlo, Ising model, Potts model, XY model, hard-disk model, molecular simulation, Metropolis, Glauber dynamics, molecular dynamics, hybrid Monte Carlo, Langevin dynamics, event chain Monte Carlo.  \n1. INTRODUCTION  \nSampling algorithms are commonplace in statistics and machine learning – in particular, in Bayesian computation – and have been used for decades to enable inference, prediction and model comparison in many different settings. They are also widely used in statistical physics, where many popular sampling algorithms first originated (Metropolis et al., 1953 ; Alder and Wainwright, 1957, 1959, 1960) . At a high level, the goals within each discipline are the same – to sample from and approximate expectations with respect to some probability distribution – but the motivations, nomenclature and methods of explanation differ significantly.  \nPractitioners in Bayesian inference estimate parameter expectations based on fixed hyperparameters and input data. To provide for this, researchers in Bayesi","cbCaif8QYBje8Dpe","https://ap.wps.com/l/cbCaif8QYBje8Dpe","pdf",1299892,1,37,"English","en",105,"# Introduction\n## Sampling algorithms across statistics, machine learning, and physics\n## Comparing samplers: mixing time, asymptotic variance, and dimension dependence\n# Statistical physics motivation and inference goals","[{\"question\":\"What problem do the sampling algorithms in the article address?\",\"answer\":\"They address how to sample from unnormalized probability distributions and approximate expectations, a need shared across Bayesian computation, statistical physics, and machine learning.\"},{\"question\":\"Which classical sampling algorithms are reviewed?\",\"answer\":\"The article reviews the Metropolis, Glauber, and molecular dynamics sampling algorithms before moving to more recent approaches.\"},{\"question\":\"What newer methods are discussed beyond classical samplers?\",\"answer\":\"It covers cluster algorithms, variations of hybrid Monte Carlo and Langevin dynamics, and piece-wise deterministic methods such as event chain Monte Carlo.\"}]","Sampling algorithms in statistical physics - 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