Bayesian statistics is based on the intuitivetive idea that probability quantifies the degree of belief in the occurrence of an event. Many cases of evaluation of measurement uncertainty are considered in detail in this report.

This book provides a multi-level introduction to Bayesian reasoning (as opposed to “conventional statistics”) and its applications to data analysis. The basic ideas of this “new” approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and are shown often to coincide — under well-defined assumptions! — with “standard” methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework.

The ninth Advanced Study Institute (AS!) on Techniques and Concepts of High Energy Physics was almost canceled before ifbegan! A certain visitor to the area (Hurricane Bertha) arrived unexpectedly early in 1996. It was the first hur ricane in memory to menace the Caribbean in early July! Fortunately, it passed St. Croix several days before our meeting, and left very little damage. (The Altar ellis survived the eye of the storm in the in the British West Islands!) The meeting was held once again at the hotel on the Cay, on that spec of land in the harbor ofChrirtiansted, St. Croix, U. S. Virgin Islands. After the first two days of, at times, outrageous downpour, the 71 participants from 26 coun tries began to relax and enjoy the lectures and the lovely surroundings of the In stitute. The primary support for the meeting was provided by the ~cientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was cosponsored by the U. S. department of Energy, by the Fermi National Accelera tor Laboratory (Fermi-lab), by the U. S. National Science Foundation, and by the University of Rochester. In addition, the International Science Foundation con tributed to the support of a participant from Russia. As in the case of the previous ASIs, the scientific program was designed for advanced graduate students and recent Ph. D. recipients in experimental parti cle physics.

This practical guide covers the essential tasks in statistical data analysis encountered in high energy physics and provides comprehensive advice for typical questions and problems. The basic methods for inferring results from data are presented as well as tools for advanced tasks such as improving the signal-to-background ratio, correcting detector effects, determining systematics and many others. Concrete applications are discussed in analysis walkthroughs. Each chapter is supplemented by numerous examples and exercises and by a list of literature and relevant links. The book targets a broad readership at all career levels - from students to senior researchers. An accompanying website provides more algorithms as well as up-to-date information and links. * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

In 1978 Edwin T. Jaynes and Myron Tribus initiated a series of workshops to exchange ideas and recent developments in technical aspects and applications of Bayesian probability theory. The first workshop was held at the University of Wyoming in 1981 organized by C.R. Smith and W.T. Grandy. Due to its success, the workshop was held annually during the last 18 years. Over the years, the emphasis of the workshop shifted gradually from fundamental concepts of Bayesian probability theory to increasingly realistic and challenging applications. The 18th international workshop on Maximum Entropy and Bayesian Methods was held in Garching / Munich (Germany) (27-31. July 1998). Opening lectures by G. Larry Bretthorst and by Myron Tribus were dedicated to one of th the pioneers of Bayesian probability theory who died on the 30 of April 1998: Edwin Thompson Jaynes. Jaynes revealed and advocated the correct meaning of 'probability' as the state of knowledge rather than a physical property. This inter pretation allowed him to unravel longstanding mysteries and paradoxes. Bayesian probability theory, "the logic of science" - as E.T. Jaynes called it - provides the framework to make the best possible scientific inference given all available exper imental and theoretical information. We gratefully acknowledge the efforts of Tribus and Bretthorst in commemorating the outstanding contributions of E.T. Jaynes to the development of probability theory.

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).

This book provides a multi-level introduction to Bayesian reasoning (as opposed to OC conventional statisticsOCO) and its applications to data analysis. The basic ideas of this OC newOCO approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and are shown often to coincide OCo under well-defined assumptions! OCo with OC standardOCO methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework.

Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.

Ask a traditional mathematician the likely outcome of a coin-toss, and he will reply that no evidence exists on which to base such a prediction. Ask a Bayesian, and he will examine the coin, conclude that it was probably not tampered with, and predict five hundred heads in a thousand tosses; a subsequent experiment would then be used to refine this prediction. The Bayesian approach, in other words, permits the use of prior knowledge when testing a hypothesis. Long the province of mathematicians and statisticians, Bayesian methods are applied in this ground-breaking book to problems in cutting-edge physics. Joerg Lemm offers practical examples of Bayesian analysis for the physicist working in such areas as neural networks, artificial intelligence, and inverse problems in quantum theory. The book also includes nonparametric density estimation problems, including, as special cases, nonparametric regression and pattern recognition. Thought-provoking and sure to be controversial, Bayesian Field Theory will be of interest to physicists as well as to other specialists in the rapidly growing number of fields that make use of Bayesian methods.

Covering theoretical methods and computational techniques in biomolecular research, this book focuses on approaches for the treatment of macromolecules, including proteins, nucleic acids, and bilayer membranes. It uses concepts in free energy calculations, conformational analysis, reaction rates, and transition pathways to calculate and interpret b