[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119428-en":3,"doc-seo-119428-105":30,"detail-sidebar-cat-0-en-105":92},{"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},119428,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Statistics and machine learning for high-energy physics - lecture notes","Lecture notes covering frequentist and Bayesian statistics and the foundations of supervised machine learning for high-energy physics. The probabilistic interpretation of machine learning is emphasized, with explanations grounded in particle-physics examples. Key topics include samples and populations, statistical inference, likelihood and confidence intervals, profile likelihood and hypothesis tests, then Bayesian analysis with model selection and an application to 4-lepton data. An overview of supervised learning and transformers connects probabilistic modeling to modern architectures.","Statistics and machine learning for high-energy physics  \nHarrison B. Prosper  \nDepartment of Physics, Florida State University, Tallahassee, FL 32306, USA  \nThese lectures introduce some of the main ideas of frequentist and Bayesian statistics as well as supervised machine learning with a focus on the probabilistic interpretation of the latter. The ideas are illustrated using simple examples from particle physics.  \n1 Introduction ........................................ 151  \n1.1 Samples ...................................... 152  \n1.2 Populations .................................... 153  \n1.3 Statistical inference ................................ 154  \n2 Frequentist analysis .................................... 155  \n2.1 The statistical model ............................... 155  \n2.2 The likelihood function .............................. 158  \n2.3 The frequentist principle ............................. 159  \n2.4 Confidence intervals ................................ 160  \n2.5 The profile likelihood ............................... 164  \n2.6 Hypothesis tests .................................. 168  \n3 Bayesian analysis ..................................... 172  \n3.1 Model selection .................................. 176  \n3.2 Bayesian analysis of 4-lepton data ........................ 177  \n4 Introduction to supervised machine learning ....................... 180  \n4.1 A bird’s eye view of supervised machine learning ................ 181  \n4.2 Transformers ................................... 190  \n1 Introduction  \nThese lectures cover some of the key concepts and practices of statistics as well as the basic ideas of supervised machine learning. We aim to provide just enough detail to make the lectures self-contained. In discussing supervised machine learning, the focus is on foundational ideas rather than the nuts and bolts so that you gain an understanding of the probabilistic nature of machine learning. Given the striking abilities of computational models such the transformer, which powers systems like ChatGPT, it may not be immediately obvious where probability enters. But, as we shall see, systems like ChatGPT are“merely” highly sophisticated probabilistic machines.  \nThis article should be cited as: Statistics and machine learning for high-energy physics, Harrison Prosper, DOI: 10.23730/CYRSP-2025-002.151, in: Proceedings of the 2023 CERN Latin-American School of High-Energy Physics, CERN Yellow Reports: School Proceedings, CERN-2025-002, DOI: 10.23730/CYRSP-2025-002, p. 151.  \n© CERN, 2024 . Published by CERN under the Creative Commons Attribution 4.0 license.  \nStatistics, like physics, is based on a set of mathematical rules. However, unlike physics, the rules of statistics are not informed by Nature and, consequently, we cannot appeal to Nature to adjudicate disagreements about whether a proposed statistical rule is valid or not. The primary cause of the disagreements among professional statisticians, which have lingered for more than two centuries, can be traced to the differing views about the interpretation of probability. In these lectures, we consider the two most important interpretations: relative frequency and degree of belief. The former interpretation is the basis of the frequentist approach to statistics, while the latter underpins the Bayesian approach. These interpretations are discussed later in this section.  \nThe point of mentioning the disagreements is to alert you of the fact that in statistics there is no such thing as “the answer”; rather there are “answers”, which often agree closely but sometimes do not. Therefore, in the practice of statistics a degree of pragmatism is necessary to avoid fruitless arguments about statistical practice that are ultimately about intellectual taste rather than mathematical correctness.  \nThe lecture notes are organized as follows. The rest of the Introduction introduces some basic terminology. Section 2 covers the frequentist approach to statistics, while Section 3 int","cbCaiqB31KNzu8bl","https://ap.wps.com/l/cbCaiqB31KNzu8bl","pdf",2414123,1,45,"English","en",105,"# Introduction\n## Samples\n## Populations\n## Statistical inference\n# Frequentist analysis\n## The statistical model\n## The likelihood function\n## The frequentist principle\n## Confidence intervals\n## The profile likelihood\n## Hypothesis tests\n# Bayesian analysis\n## Model selection\n## Bayesian analysis of 4-lepton data\n# Introduction to supervised machine learning\n## A bird’s eye view of supervised machine learning\n## Transformers","[{\"question\":\"What are the two main interpretations of probability used in these lectures?\",\"answer\":\"The lectures contrast relative frequency (basis of the frequentist approach) with degree of belief (underpinning Bayesian methods).\"},{\"question\":\"Which frequentist tools are covered for statistical inference?\",\"answer\":\"They cover the statistical model and likelihood, confidence intervals, profile likelihood, and hypothesis tests.\"},{\"question\":\"How does the lecture introduce supervised machine learning in a physics context?\",\"answer\":\"It provides a bird’s-eye view of supervised machine learning, highlighting its probabilistic nature, and then introduces transformers as a key example.\"}]","Statistics and machine learning for high-energy physics - 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