[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-291166-105":59,"doc-detail-291166-en":123},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","sampling-algorithms-in-statistical-physics-a-guide-for-statistics-and-machine-learning-291166","Sampling algorithms in statistical physics: a guide for statistics and machine learning","","Sampling algorithms in statistical physics are presented using the language and framing of statistics and machine learning. The work introduces key concepts and then studies three classic problems: 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 methods are reviewed alongside cluster algorithms, hybrid Monte Carlo variants, Langevin dynamics, and event chain Monte Carlo, highlighting crossovers with statistical tools and machine-learning perspectives.",{"@graph":69,"@context":115},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/sampling-algorithms-in-statistical-physics-a-guide-for-statistics-and-machine-learning-291166/291166/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/sampling-algorithms-in-statistical-physics-a-guide-for-statistics-and-machine-learning-291166/291166.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"How does the document define or measure algorithm performance?","Question",{"text":113,"@type":114},"Performance is often assessed by how computational steps scale to generate independent samples, and mixing time is also measured; comparisons may relate performance to the dimension of the parameter space.","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},291166,1789643579,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":132,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":122,"read_time":137,"preview_page_count":4},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1794309523707217728","arXiv :2208 .04751v2 [ stat .CO] 9 Jun 2023  \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 Bayesian computation typically strive to establish general-purpose sampling algorithms (most notably Markov chain Monte Carlo) and therefore develop theory concerning how a given sampler behaves in a variety of different settings, characterised by features such as how the tails of a distribution decay (e.g. Jarner and Hansen (2000)) or how much the sampler exploits some particular structure of the model (e.g. Papaspiliopoulos, Roberts and Sköld (2007)) . The main concern for a given algorithm is often the extent to which it can be widely implemented with little problem-specific  \nHH Wills Physics Laboratory, University of Bristol, UK,( [e-mail:](e-mail: michael.faulkner@bristol.ac.uk)[ michael.faulkner@bristol.ac.uk](e-mail: michael.faulkner@bristol.ac.uk)). Department of Statistical Science, University College London, UK,(e-mail: [samuel.livingstone@ucl.ac.uk](samuel.livingstone@ucl.ac.uk)).  \n2  \ntuning. Different samplers are compared by assessing how performance depends on the dimension of the parameter space (e.g. Roberts and Rosenthal (2001)) where `performance' is typically defined as either the mixing time or the asymptotic variance of ergodic averages. Comparisons are usually based on theoretical results, which are complemented with numerical studies to corroborate the theory.  \nIn statistical physics, expectations are studied as functions of the hyperparameters (e.g. the temperature) in order to predict the effect of their variation on the physical system of interest. The prima","cbCaitje2qzev27s","https://ap.wps.com/l/cbCaitje2qzev27s","pdf",1349125,39,"English","# Abstract\n# Key words and phrases\n# 1. Introduction\n## Sampling algorithms in statistics and machine learning\n## Sampling algorithms in statistical physics\n## Comparing sampler performance\n## Multi-modality and anisotropy at low temperature","[{\"question\":\"How does the document define or measure algorithm performance?\",\"answer\":\"Performance is often assessed by how computational steps scale to generate independent samples, and mixing time is also measured; comparisons may relate performance to the dimension of the parameter space.\"}]","Sampling algorithms in statistical physics: a guide for statistics and machine learning | PDF",98]