[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123564-en":3,"doc-seo-123564-105":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":4,"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},123564,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Likelihood-Free Frequentist Inference - Bridging Classical Statistics and Machine Learning in Simulation and Uncertainty Quantification","Many areas of science rely on computer simulators that implicitly encode likelihood functions, creating likelihood-free inference (LFI) problems where classical tools struggle outside narrow asymptotic or low-dimensional settings. Recent machine learning advances improve sample efficiency, yet uncertainty quantification reliability remains unclear. This paper proposes a unified framework, likelihood-free frequentist inference (LF2I), enabling frequentist confidence sets and hypothesis tests with finite-sample nominal coverage, plus diagnostics to assess empirical coverage across the parameter space, using plug-in test statistics without fixed-parameter Monte Carlo.","arXiv :2 107 .03920v2 [ stat .ML] 19 Jul 2021  \nLikelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning in Simulation and Uncertainty Quanti􀀌cation  \nNiccol􀀒o Dalmasso 􀀃y [niccolo.dalmasso@gmail.com](niccolo.dalmasso@gmail.com)  \nDavid Zhao 􀀃y [davidzhao@stat.cmu.edu](davidzhao@stat.cmu.edu)  \nRafael Izbicki [z](z rafaelizbicki@gmail.com)[ rafaelizbicki@gmail.com](z rafaelizbicki@gmail.com)  \n[Ann B. Lee](Ann B. Lee y annlee@stat.cmu.edu)[ y](Ann B. Lee y annlee@stat.cmu.edu)[ annlee@stat.cmu.edu](Ann B. Lee y annlee@stat.cmu.edu)  \nAbstract  \nMany areas of science make extensive use of computer simulators that implicitly encode likelihood functions of complex systems. Classical statistical methods are poorly suited for these so-called likelihood-free inference (LFI) settings, outside the asymptotic and lowdimensional regimes. Although new machine learning methods, such as normalizing 􀀍ows, have revolutionized the sample e􀀎ciency and capacity of LFI methods, it remains an open question whether they produce reliable measures of uncertainty.  \nThis paper presents a statistical framework for LFI that uni􀀌es classical statistics with modern machine learning to: (1) e􀀎ciently construct frequentist con􀀌dence sets and hypothesis tests with 􀀌nite-sample guarantees of nominal coverage (type I error control) and power; (2) provide practical diagnostics for assessing empirical coverage over the entire parameter space. We refer to our framework as likelihood-free frequentist inference (LF2I) . Any method that estimates a test statistic, like the likelihood ratio, can be plugged into our framework to create valid con􀀌dence sets and compute diagnostics, without costly Monte Carlo samples at 􀀌xed parameter settings. In this work, we speci􀀌cally study the power of two test statistics (ACORE and BFF), which, respectively, maximize versus integrate an odds function over the parameter space. Our study o􀀋ers multifaceted perspectives on the challenges in LF2I.  \nKeywords: likelihood-free inference, simulation-based inference, frequentist coverage, con􀀌dence sets, hypothesis testing  \n1. Introduction  \nHypothesis testing and uncertainty quanti􀀌cation are the hallmarks of scienti􀀌c inference. Methods that achieve good statistical performance (e.g., high power) often rely on being able to explicitly evaluate a likelihood function, which relates parameters of the data-generating process to observed data. However, in many areas of science and engineering, complex phenomena are modeled by forward simulators that implicitly de􀀌ne a likelihood function. For example, given input parameters 􀀒, a stochastic model may encode the interaction of atoms or elementary particles, or the transport of radiation through the atmosphere  \n∗ . Equal Contribution  \n†. Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, USA ‡. Department of Statistics, Federal University of Sao Carlos, Sao Paulo, Brazil  \n©2021 Niccol􀀒o Dalmasso, David Zhao, Rafael Izbicki, and Ann B. Lee.  \nLicense: CC-BY 4.0, see [https://creativecommons.org/licenses/by/4.0/](https://creativecommons.org/licenses/by/4.0/) .  \nDalmasso, Zhao, Izbicki, and Lee  \nor through matter in the Universe, by combining deterministic dynamics with random 􀀍uctuations and measurement errors to produce synthetic data X.  \nSimulation-based inference without an explicit likelihood is commonly referred to as likelihood-free inference (LFI) . The most well-known approach to LFI is Approximate Bayesian Computation (ABC; see Beaumont et al. 2002; Marin et al. 2012; Sisson et al. 2018 for areview) . These methods use simulations su􀀎ciently close to the observed data D to infer the underlying parameters, or more precisely, the posterior distribution p (􀀒jD) . Recently, the arsenal of LFI methods has been expanded with new machine learning algorithms (such as neural density estimators) that instead use the output from simulators as training data. The objective here","cbCaiqkC2CW8RAjS","https://ap.wps.com/l/cbCaiqkC2CW8RAjS","pdf",7142764,1,49,"English","en",105,"# Introduction\n## Likelihood-free inference and its motivation\n## Simulation-based inference and machine learning surrogates","[{\"question\":\"What problem does likelihood-free inference address?\",\"answer\":\"Likelihood-free inference applies when simulators generate data but do not allow explicit evaluation of a likelihood function, making classical inference difficult in many high-dimensional settings.\"},{\"question\":\"What does the LF2I framework enable?\",\"answer\":\"LF2I unifies classical statistics with machine learning to construct frequentist confidence sets and hypothesis tests with finite-sample guarantees of nominal coverage and to provide diagnostics for empirical coverage over the full parameter space.\"},{\"question\":\"How can the proposed methods avoid costly Monte Carlo at fixed parameter settings?\",\"answer\":\"LF2I allows any method that estimates an appropriate test statistic to be plugged in, producing valid confidence sets and diagnostics without requiring large numbers of Monte Carlo experiments at fixed parameter points.\"}]","Likelihood-Free Frequentist Inference - Bridging Classical Statistics and Machine Learning in Simulation and Uncertainty Quantification | PDF",1785817369,123,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"likelihood-free-frequentist-inference-bridging-classical-statistics-and-machine-learning-in-simulation-and-uncertainty-quantification","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/likelihood-free-frequentist-inference-bridging-classical-statistics-and-machine-learning-in-simulation-and-uncertainty-quantification/123564/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does likelihood-free inference address?","Question",{"text":75,"@type":76},"Likelihood-free inference applies when simulators generate data but do not allow explicit evaluation of a likelihood function, making classical inference difficult in many high-dimensional settings.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What does the LF2I framework enable?",{"text":80,"@type":76},"LF2I unifies classical statistics with machine learning to construct frequentist confidence sets and hypothesis tests with finite-sample guarantees of nominal coverage and to provide diagnostics for empirical coverage over the full parameter space.",{"name":82,"@type":73,"acceptedAnswer":83},"How can the proposed methods avoid costly Monte Carlo at fixed parameter settings?",{"text":84,"@type":76},"LF2I allows any method that estimates an appropriate test statistic to be plugged in, producing valid confidence sets and diagnostics without requiring large numbers of Monte Carlo experiments at fixed parameter points.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]