This book comprehensively presents the basic concepts of probability and Bayesian inference with sufficient generality to make them applicable to current problems in scientific research. The first chapter provides the fundamentals of probability theory that are essential for the analysis of random phenomena. The second chapter includes a full and pragmatic review of the Bayesian methods that constitute a natural and coherent framework with enough freedom to analyze all the information available from experimental data in a conceptually simple manner. The third chapter presents the basic Monte Carlo techniques used in scientific research, allowing a large variety of problems to be handled difficult to tackle by other procedures. The author also introduces a basic algorithm, which enables readers to simulate samples from simple distribution, and describes useful cases for researchers in particle physics.The final chapter is devoted to the basic ideas of Information Theory, which are important in the Bayesian methodology. This highly readable book is appropriate for graduate-level courses, while at the same time being useful for scientific researches in general and for physicists in particular since most of the examples are from the field of Particle Physics.
Die Einf]hrung in die Statistik und Messwertanalyse f]r Physiker richtet sich weniger an mathematischen \berlegungen aus, sondern stellt die praktische Anwendung in den Vordergrund und schdrft die Intuition experimentelle Ergebnisse richtig einzuschdtzen. Zahlreiche ausf]hrlich betrachtete Beispiele dienen dazu, hdufig bei der Datenanalyse gemachte Fehler zu vermeiden (unsinnige Anwendung des Chi-Quadrattests, Funktionenanpassung bei falscher Parametrisierung, Entfaltung mit willk]rlicher Regularisierung). Ein besonderes Augenmerk wird auf den Vergleich von Daten mit Monte-Carlo-Simulationen gelenkt. Moderne Experimente kommen nicht ohne Simulation aus. Deshalb ist es wichtig zu wissen, wie Parameteranpassungen und Entfaltungen in diesem Fall durchgef]rt werden. Au_erdem werden den Studierenden moderne Entwicklungen der Statistik nahegebracht, die in dlteren Lehrb]chern nicht behandelt werden.
This concise set of course-based notes provides the reader with the main concepts and tools needed to perform statistical analyses of experimental data, in particular in the field of high-energy physics (HEP). First, the book provides an introduction to probability theory and basic statistics, mainly intended as a refresher from readers’ advanced undergraduate studies, but also to help them clearly distinguish between the Frequentist and Bayesian approaches and interpretations in subsequent applications. More advanced concepts and applications are gradually introduced, culminating in the chapter on both discoveries and upper limits, as many applications in HEP concern hypothesis testing, where the main goal is often to provide better and better limits so as to eventually be able to distinguish between competing hypotheses, or to rule out some of them altogether. Many worked-out examples will help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical concepts to actual data. This new second edition significantly expands on the original material, with more background content (e.g. the Markov Chain Monte Carlo method, best linear unbiased estimator), applications (unfolding and regularization procedures, control regions and simultaneous fits, machine learning concepts) and examples (e.g. look-elsewhere effect calculation).
Svetlozar T. Rachev,Markus Hoechstoetter,Frank J. Fabozzi, CFA,Sergio M. Focardi
Author: Svetlozar T. Rachev,Markus Hoechstoetter,Frank J. Fabozzi, CFA,Sergio M. Focardi
Publisher: John Wiley & Sons
Category: Business & Economics
A comprehensive look at how probability and statistics is applied to the investment process Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before. In order to keep up, you need a firm understanding of this discipline. Probability and Statistics for Finance addresses this issue by showing you how to apply quantitative methods to portfolios, and in all matter of your practices, in a clear, concise manner. Informative and accessible, this guide starts off with the basics and builds to an intermediate level of mastery. • Outlines an array of topics in probability and statistics and how to apply them in the world of finance • Includes detailed discussions of descriptive statistics, basic probability theory, inductive statistics, and multivariate analysis • Offers real-world illustrations of the issues addressed throughout the text The authors cover a wide range of topics in this book, which can be used by all finance professionals as well as students aspiring to enter the field of finance.
This book is a guide to the practical application of statistics in data analysis as typically encountered in the physical sciences. It is primarily addressed at students and professionals who need to draw quantitative conclusions from experimental data. Although most of the examples are taken from particle physics, the material is presented in a sufficiently general way as to be useful to people from most branches of the physical sciences. The first part of the book describes the basic tools of data analysis: concepts of probability and random variables, Monte Carlo techniques, statistical tests, and methods of parameter estimation. The last three chapters are somewhat more specialized than those preceding, covering interval estimation, characteristic functions, and the problem of correcting distributions for the effects of measurement errors (unfolding).
A treatment of the experimental techniques and instrumentation most often used in nuclear and particle physics experiments as well as in various other experiments, providing useful results and formulae, technical know-how and informative details. This second edition has been revised, while sections on Cherenkov radiation and radiation protection have been updated and extended.
Der Leser erhält einen umfassenden Überblick über Aufbau und Funktionsweise von Teilchendetektoren. In der 4. Auflage werden neuere Entwicklungen wie Silizium-Streifendetektoren, Pixeldetektoren, szintillierende Fasern, neue elektromagnetische Kalorimeter und kompensierende Hadronkalorimeter behandelt. Vertiefend wird nun auch auf aktuelle Forschungsgebiete wie Astroteilchenphysik, kosmische Strahlung, Neutrinophysik und die dunkle Materie im Kosmos eingegangen.
A Guide to the Use of Statistical Methods in the Physical Sciences
Author: R. J. Barlow
Publisher: John Wiley & Sons
The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A.C. Phillips Computing for Scientists R. J. Barlow and A. R. Barnett Written by a physicist, Statistics is tailored to the needs of physical scientists, containing and explaining all they need to know. It concentrates on parameter estimation, especially the methods of Least Squares and Maximum Likelihood, but other techniques, such as hypothesis testing, Bayesian statistics and non-parametric methods are also included. Intended for reasonably numerate scientists it contains all the basic formulae, their derivations and applications, together with some more advanced ones. Statistics features: * Comprehensive coverage of the essential techniques physical scientists are likely to need. * A wealth of examples, and problems with their answers. * Flexible structure and organisation allows it to be used as a course text and a reference. * A review of the basics, so that little prior knowledge is required.
These proceedings comprise current statistical issues in analyzing data in particle physics, astrophysics and cosmology, as discussed at the PHYSTAT05 conference in Oxford. This is a continuation of the popular PHYSTAT series; previous meetings were held at CERN (2000), Fermilab (2000), Durham (2002) and Stanford (2003).In-depth discussions on topical issues are presented by leading statisticians and research workers in their relevant fields. Included are invited reviews and contributed research papers presenting the latest, state-of-the-art techniques.
This book is designed as a practical and intuitive introduction to probability, statistics and random quantities for physicists. The book aims at getting to the main points by a clear, hands-on exposition supported by well-illustrated and worked-out examples. A strong focus on applications in physics and other natural sciences is maintained throughout. In addition to basic concepts of random variables, distributions, expected values and statistics, the book discusses the notions of entropy, Markov processes, and fundamentals of random number generation and Monte-Carlo methods.
The first edition of this classic book has become the authoritative reference for physicists desiring to master the finer points of statistical data analysis. This second edition contains all the important material of the first, much of it unavailable from any other sources. In addition, many chapters have been updated with considerable new material, especially in areas concerning the theory and practice of confidence intervals, including the important Feldman-Cousins method. Both frequentist and Bayesian methodologies are presented, with a strong emphasis on techniques useful to physicists and other scientists in the interpretation of experimental data and comparison with scientific theories. This is a valuable textbook for advanced graduate students in the physical sciences as well as a reference for active researchers.
Von den Grundlagen bis zur Streutheorie – das Wichtigste zur Quantenmechanik Die Quantenphysik ist ein zentrales und spannendes, wenn auch von vielen Schülern und Studenten ungeliebtes Thema der Physik. Aber keine Sorge! Steven Holzner erklärt Ihnen verständlich und lebendig, was Sie über Quantenphysik wissen müssen. Er erläutert die Grundlagen von Drehimpuls und Spin, gibt Ihnen Tipps, wie Sie komplexe Gleichungen lösen und nimmt den klassischen Problemen der Quantenphysik den Schrecken. Dabei arbeitet er mit Beispielen, die er ausführlich erklärt und gibt Ihnen so zusätzliche Sicherheit auf einem vor Unschärfen wimmelnden Feld.
Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.
All macroscopic systems consist ultimately of atoms obeying the laws of quantum mechanics. That premise forms the basis for this comprehensive text, intended for a first upper-level course in statistical and thermal physics. Reif emphasizes that the combination of microscopic concepts with some statistical postulates leads readily to conclusions on a purely macroscopic level. The authors writing style and penchant for description energize interest in condensed matter physics as well as provide a conceptual grounding with information that is crystal clear and memorable. Reif first introduces basic probability concepts and statistical methods used throughout all of physics. Statistical ideas are then applied to systems of particles in equilibrium to enhance an understanding of the basic notions of statistical mechanics, from which derive the purely macroscopic general statements of thermodynamics. Next, he turns to the more complicated equilibrium situations, such as phase transformations and quantum gases, before discussing nonequilibrium situations in which he treats transport theory and dilute gases at varying levels of sophistication. In the last chapter, he addresses some general questions involving irreversible processes and fluctuations. A large amount of material is presented to facilitate students later access to more advanced works, to allow those with higher levels of curiosity to read beyond the minimum given on a topic, and to enhance understanding by presenting several ways of looking at a particular question. Formatting within the text either signals material that instructors can assign at their own discretion or highlights important results for easy reference to them. Additionally, by solving many of the 230 problems contained in the text, students activate and embed their knowledge of the subject matter.
The book is written for advanced graduate students. The topics have been selected to present methods and models that have applications in both particle physics and polymer physics. The lectures may serve as a guide through more recent research activities and illustrate the applicability of joint methods in different contexts. The book deals with analytic tools (e.g. random walk models, polymer expansion), numerical tools (e.g. Langevin dynamics), and common models (the three-dimensional Gross-Neveu-Model).
Modern analysis of HEP data needs advanced statistical tools to separate signal from background. This is the first book which focuses on machine learning techniques. It will be of interest to almost every high energy physicist, and, due to its coverage, suitable for students.