Statistical Decision Theory
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Introduction To Statistical Decision Theory
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Author : John Pratt
language : en
Publisher: MIT Press
Release Date : 2008-01-25
Introduction To Statistical Decision Theory written by John Pratt and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-25 with Business & Economics categories.
The Bayesian revolution in statistics—where statistics is integrated with decision making in areas such as management, public policy, engineering, and clinical medicine—is here to stay. Introduction to Statistical Decision Theory states the case and in a self-contained, comprehensive way shows how the approach is operational and relevant for real-world decision making under uncertainty. Starting with an extensive account of the foundations of decision theory, the authors develop the intertwining concepts of subjective probability and utility. They then systematically and comprehensively examine the Bernoulli, Poisson, and Normal (univariate and multivariate) data generating processes. For each process they consider how prior judgments about the uncertain parameters of the process are modified given the results of statistical sampling, and they investigate typical decision problems in which the main sources of uncertainty are the population parameters. They also discuss the value of sampling information and optimal sample sizes given sampling costs and the economics of the terminal decision problems. Unlike most introductory texts in statistics, Introduction to Statistical Decision Theory integrates statistical inference with decision making and discusses real-world actions involving economic payoffs and risks. After developing the rationale and demonstrating the power and relevance of the subjective, decision approach, the text also examines and critiques the limitations of the objective, classical approach.
Statistical Decision Theory
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Author : F. Liese
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-30
Statistical Decision Theory written by F. Liese and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-30 with Mathematics categories.
For advanced graduate students, this book is a one-stop shop that presents the main ideas of decision theory in an organized, balanced, and mathematically rigorous manner, while observing statistical relevance. All of the major topics are introduced at an elementary level, then developed incrementally to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. With its broad coverage of decision theory, this book fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory.
Statistical Decision Theory And Bayesian Analysis
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Author : James O. Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 1985-08-21
Statistical Decision Theory And Bayesian Analysis written by James O. Berger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08-21 with Business & Economics categories.
"The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library." -Bulletin of the American Mathematical Society In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.
Introduction To Statistical Decision Theory
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Author : Silvia Bacci
language : en
Publisher: CRC Press
Release Date : 2019-07-11
Introduction To Statistical Decision Theory written by Silvia Bacci and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-11 with Mathematics categories.
Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory
Introduction To Statistical Decision Theory
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Author : Silvia Bacci
language : en
Publisher: CRC Press
Release Date : 2019-07-11
Introduction To Statistical Decision Theory written by Silvia Bacci and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-11 with Mathematics categories.
Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory
Asymptotic Methods In Statistical Decision Theory
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Author : Lucien Le Cam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Methods In Statistical Decision Theory written by Lucien Le Cam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.
Statistics For Making Decisions
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Author : Nicholas T. Longford
language : en
Publisher: CRC Press
Release Date : 2021-03-30
Statistics For Making Decisions written by Nicholas T. Longford and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-30 with Mathematics categories.
Making decisions is a ubiquitous mental activity in our private and professional or public lives. It entails choosing one course of action from an available shortlist of options. Statistics for Making Decisions places decision making at the centre of statistical inference, proposing its theory as a new paradigm for statistical practice. The analysis in this paradigm is earnest about prior information and the consequences of the various kinds of errors that may be committed. Its conclusion is a course of action tailored to the perspective of the specific client or sponsor of the analysis. The author’s intention is a wholesale replacement of hypothesis testing, indicting it with the argument that it has no means of incorporating the consequences of errors which self-evidently matter to the client. The volume appeals to the analyst who deals with the simplest statistical problems of comparing two samples (which one has a greater mean or variance), or deciding whether a parameter is positive or negative. It combines highlighting the deficiencies of hypothesis testing with promoting a principled solution based on the idea of a currency for error, of which we want to spend as little as possible. This is implemented by selecting the option for which the expected loss is smallest (the Bayes rule). The price to pay is the need for a more detailed description of the options, and eliciting and quantifying the consequences (ramifications) of the errors. This is what our clients do informally and often inexpertly after receiving outputs of the analysis in an established format, such as the verdict of a hypothesis test or an estimate and its standard error. As a scientific discipline and profession, statistics has a potential to do this much better and deliver to the client a more complete and more relevant product. Nicholas T. Longford is a senior statistician at Imperial College, London, specialising in statistical methods for neonatal medicine. His interests include causal analysis of observational studies, decision theory, and the contest of modelling and design in data analysis. His longer-term appointments in the past include Educational Testing Service, Princeton, NJ, USA, de Montfort University, Leicester, England, and directorship of SNTL, a statistics research and consulting company. He is the author of over 100 journal articles and six other monographs on a variety of topics in applied statistics.
Statistical Decision Theory
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Author : James Berger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Statistical Decision Theory written by James Berger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Decision theory is generally taught in one of two very different ways. When of opti taught by theoretical statisticians, it tends to be presented as a set of mathematical techniques mality principles, together with a collection of various statistical procedures. When useful in establishing the optimality taught by applied decision theorists, it is usually a course in Bayesian analysis, showing how this one decision principle can be applied in various practical situations. The original goal I had in writing this book was to find some middle ground. I wanted a book which discussed the more theoretical ideas and techniques of decision theory, but in a manner that was constantly oriented towards solving statistical problems. In particular, it seemed crucial to include a discussion of when and why the various decision prin ciples should be used, and indeed why decision theory is needed at all. This original goal seemed indicated by my philosophical position at the time, which can best be described as basically neutral. I felt that no one approach to decision theory (or statistics) was clearly superior to the others, and so planned a rather low key and impartial presentation of the competing ideas. In the course of writing the book, however, I turned into a rabid Bayesian. There was no single cause for this conversion; just a gradual realization that things seemed to ultimately make sense only when looked at from the Bayesian viewpoint.
Decision Theory
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Author : Giovanni Parmigiani
language : en
Publisher: John Wiley & Sons
Release Date : 2009-04-15
Decision Theory written by Giovanni Parmigiani and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-15 with Mathematics categories.
Decision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice. The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives. This book: Provides a rich collection of techniques and procedures. Discusses the foundational aspects and modern day practice. Links foundations to practical applications in biostatistics, computer science, engineering and economics. Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. Decision Theory is fundamental to all scientific disciplines, including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.
Applied Statistical Decision Theory
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Author : Howard Raiffa
language : en
Publisher: John Wiley & Sons
Release Date : 2000-06-02
Applied Statistical Decision Theory written by Howard Raiffa and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-02 with Mathematics categories.
"In the field of statistical decision theory, Raiffa and Schlaifer have sought to develop new analytic techniques by which the modern theory of utility and subjective probability can actually be applied to the economic analysis of typical sampling problems." —From the foreword to their classic work Applied Statistical Decision Theory. First published in the 1960s through Harvard University and MIT Press, the book is now offered in a new paperback edition from Wiley