03690nam 22007095 450 991034932740332120230123161333.0981-329-593-710.1007/978-981-32-9593-3(CKB)4100000009606197(MiAaPQ)EBC5946132(DE-He213)978-981-32-9593-3(PPN)241116740(EXLCZ)99410000000960619720191016d2019 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierIntroduction to a Renormalisation Group Method /by Roland Bauerschmidt, David C. Brydges, Gordon Slade1st ed. 2019.Singapore :Springer Singapore :Imprint: Springer,2019.1 online resource (xii, 283 pages) illustrationsLecture Notes in Mathematics,0075-8434 ;2242981-329-591-0 Includes bibliographical references and index.This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.Lecture Notes in Mathematics ;2242.Mathematical physicsQuantum field theoryString modelsStatistical physicsPhysicsDynamicsMathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Quantum Field Theories, String Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P19048Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Mathematical physics.Quantum field theory.String models.Statistical physics.Physics.Dynamics.Mathematical Physics.Quantum Field Theories, String Theory.Statistical Physics and Dynamical Systems.Mathematical Methods in Physics.Complex Systems.530.1430151Bauerschmidt Rolandauthttp://id.loc.gov/vocabulary/relators/aut769120Brydges David Cauthttp://id.loc.gov/vocabulary/relators/autSlade Gordonauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910349327403321Introduction to a Renormalisation Group Method2513903UNINA05462nam 2200685Ia 450 991081442290332120200520144314.09786612548406978128254840412825484099780470665084047066508497804706650770470665076(CKB)2670000000014732(EBL)514398(OCoLC)609862743(SSID)ssj0000358663(PQKBManifestationID)11257130(PQKBTitleCode)TC0000358663(PQKBWorkID)10380479(PQKB)10877076(MiAaPQ)EBC514398(Perlego)2756989(EXLCZ)99267000000001473220100121d2010 uy 0engur|n|---|||||txtccrData analysis in forensic science a Bayesian decision perspective /Franco Taroni ... [et al.]Chichester John Wiley and Sons20101 online resource (389 p.)Statistics in practiceDescription based upon print version of record.9780470998359 0470998350 Includes bibliographical references and index.Data Analysis in Forensic Science; Contents; Foreword; Preface; I The Foundations of Inference and Decision in Forensic Science; 1 Introduction; 1.1 The Inevitability of Uncertainty; 1.2 Desiderata in Evidential Assessment; 1.3 The Importance of the Propositional Framework and the Nature of Evidential Assessment; 1.4 From Desiderata to Applications; 1.5 The Bayesian Core of Forensic Science; 1.6 Structure of the Book; 2 Scientific Reasoning and Decision Making; 2.1 Coherent Reasoning Under Uncertainty; 2.1.1 A rational betting policy; 2.1.2 A rational policy for combining degrees of belief2.1.3 A rational policy for changing degrees of belief2.2 Coherent Decision Making Under Uncertainty; 2.2.1 A method for measuring the value of consequences; 2.2.2 The consequences of rational preferences; 2.2.3 Intermezzo: some more thoughts about rational preferences; 2.2.4 The implementation of coherent decision making under uncertainty: Bayesian networks; 2.2.5 The connection between pragmatic and epistemic standards of reasoning; 2.3 Scientific Reasoning as Coherent Decision Making; 2.3.1 Bayes' theorem; 2.3.2 The theories' race; 2.3.3 Statistical reasoning: the models' race2.3.4 Probabilistic model building: betting on random quantities2.4 Forensic Reasoning as Coherent Decision Making; 2.4.1 Likelihood ratios and the 'weight of evidence'; 2.4.2 The expected value of information; 2.4.3 The hypotheses' race in the law; 3 Concepts of Statistical Science and Decision Theory; 3.1 Random Variables and Distribution Functions; 3.1.1 Univariate random variables; 3.1.2 Measures of location and variability; 3.1.3 Multiple random variables; 3.2 Statistical Inference and Decision Theory; 3.2.1 Utility theory; 3.2.2 Maximizing expected utility; 3.2.3 The loss function3.3 The Bayesian Paradigm3.3.1 Sequential use of Bayes' theorem; 3.3.2 Principles of rational inference in statistics; 3.3.3 Prior distributions; 3.3.4 Predictive distributions; 3.3.5 Markov Chain Monte Carlo methods (MCMC); 3.4 Bayesian Decision Theory; 3.4.1 Optimal decisions; 3.4.2 Standard loss functions; 3.5 R Code; II Forensic Data Analysis; 4 Point Estimation; 4.1 Introduction; 4.2 Bayesian Decision for a Proportion; 4.2.1 Estimation when there are zero occurrences in a sample; 4.2.2 Prior probabilities; 4.2.3 Prediction4.2.4 Inference for 0 in the presence of background data on the number of successes4.2.5 Multinomial variables; 4.3 Bayesian Decision for a Poisson Mean; 4.3.1 Inference about the Poisson parameter in the absence of background events; 4.3.2 Inference about the Poisson parameter in the presence of background events; 4.3.3 Forensic inference using graphical models; 4.4 Bayesian Decision for Normal Mean; 4.4.1 Case with known variance; 4.4.2 Case with unknown variance; 4.4.3 Estimation of the mean in the presence of background data; 4.5 R Code; 5 Credible Intervals; 5.1 Introduction5.2 Credible Intervals and Lower BoundsThis is the first text to examine the use of statistical methods in forensic science and bayesian statistics in combination. The book is split into two parts: Part One concentrates on the philosophies of statistical inference. Chapter One examines the differences between the frequentist, the likelihood and the Bayesian perspectives, before Chapter Two explores the Bayesian decision-theoretic perspective further, and looks at the benefits it carries. Part Two then introduces the reader to the practical aspects involved: the application, interpretation, summary and presentation of data analyStatistics in practice.Forensic sciencesStatistical methodsBayesian statistical decision theoryForensic sciencesStatistical methods.Bayesian statistical decision theory.363.2501/519542Taroni Franco1709604MiAaPQMiAaPQMiAaPQBOOK9910814422903321Data analysis in forensic science4099466UNINA