Statistical Decision Theory and Bayesian Analysis

Author: James O. Berger
Publisher: Springer Science & Business Media
ISBN: 9781475742862
Release Date: 2013-03-14
Genre: Mathematics

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.

Frontiers of Statistical Decision Making and Bayesian Analysis

Author: Ming-Hui Chen
Publisher: Springer Science & Business Media
ISBN: 1441969446
Release Date: 2010-07-24
Genre: Mathematics

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

Statistical Decision Theory and Related Topics IV

Author: Shanti S. Gupta
Publisher: Springer
ISBN: 1461387701
Release Date: 2011-11-08
Genre: Mathematics

The Fourth Purdue Symposium on Statistical Decision Theory and Related Topics was held at Purdue University during the period June 15-20, 1986. The symposium brought together many prominent leaders and younger researchers in statistical decision theory and related areas. The 65 invited papers and discussions presented at the symposium are collected in this two-volume work. The papers are grouped into a total of seven parts. Volume I has three parts: Part 1 -Conditioning and Likelihood; Part f! - Bayes and Empirical Bayes Analysis; and Part 9 -Decision Theoretic Estimation. Part 1 contains the proceedings of a Workshop on Conditioning, which was held during the symposium. Most of the articles in Volume I involve either conditioning or Bayesian ideas, resulting in a volume of considerable interest to conditionalists and Bayesians as well as to decision-theorists. Volume II has four parts: Part 1 -Selection, Ranking, and Multiple Com parisons; fart f! -Asymptotic and Sequential Analysis; Part 9 -Estimation and Testing; and Part -4 -Design and Comparison of Experiments and Distributions. These articles encompass the leading edge of much current research in math ematical statistics, with decision theory, of course, receiving special emphasis. It should be noted that the papers in these two volumes are by no means all theoretical; many are applied in nature or are creative review papers.

Handbuch Modellbildung und Simulation in den Sozialwissenschaften

Author: Norman Braun
Publisher: Springer-Verlag
ISBN: 9783658011642
Release Date: 2014-10-29
Genre: Social Science

Das Handbuch Modellbildung und Simulation in den Sozialwissenschaften bietet in 37 Artikeln einen umfassenden Überblick über sozialwissenschaftliche Modellbildung und Simulation. Es vermittelt wissenschaftstheoretische und methodische Grundlagen sowie den Stand der Forschung in den wichtigsten Anwendungsgebieten. Behandelt werden realistische, strukturalistische und konstruktivistische Zugriffe auf Modellbildung und Simulation, bedeutende Methoden und Typen der Modellierung (u.a. stochastische Prozesse und Bayes-Verfahren, nutzen- und spieltheoretische Modellierungen) und Ansätze der Computersimulation (z.B. Multi-Agenten-Modelle, zelluläre Automaten, neuronale Netze, Small Worlds). Die Anwendungskapitel befassen sich u.a. mit sozialen Dilemmata, sozialen Normen, Innovation und Diffusion, Herrschaft und Organisation, Gewalt und Krieg.

Einf hrung in Statistik und Messwertanalyse f r Physiker

Author: G. Bohm
ISBN: 3540257594
Release Date: 2006

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.

Statistical Decision Theory

Author: Nicholas T. Longford
Publisher: Springer Science & Business Media
ISBN: 9783642404337
Release Date: 2013-10-17
Genre: Mathematics

This monograph presents a radical rethinking of how elementary inferences should be made in statistics, implementing a comprehensive alternative to hypothesis testing in which the control of the probabilities of the errors is replaced by selecting the course of action (one of the available options) associated with the smallest expected loss. Its strength is that the inferences are responsive to the elicited or declared consequences of the erroneous decisions, and so they can be closely tailored to the client’s perspective, priorities, value judgments and other prior information, together with the uncertainty about them.

Lie Gruppen und Lie Algebren

Author: Joachim Hilgert
Publisher: Springer-Verlag
ISBN: 9783322802705
Release Date: 2013-03-12
Genre: Education

Dieses Buch versteht sich als Einführung in die Theorie der Lie-Gruppen. Der Begriff der Lie-Gruppen wird ausgehend von den einfachsten Beispielen, den Matrizengruppen, entwickelt. Eine große Anzahl von Problemen für Lie-Gruppen kann man durch Übertragung auf die zugehörigen Lie-Algebren lösen. Dies ist der Leitgedanke des Buches. Vorausgesetzt werden Kenntnisse in der Linearen Algebra, der Differentialrechnung mehrerer Variablen und der elementaren Gruppentheorie.

Advances in Statistical Decision Theory and Applications

Author: S. Panchapakesan
Publisher: Springer Science & Business Media
ISBN: 9781461223085
Release Date: 2012-12-06
Genre: Mathematics

Shanti S. Gupta has made pioneering contributions to ranking and selection theory; in particular, to subset selection theory. His list of publications and the numerous citations his publications have received over the last forty years will amply testify to this fact. Besides ranking and selection, his interests include order statistics and reliability theory. The first editor's association with Shanti Gupta goes back to 1965 when he came to Purdue to do his Ph.D. He has the good fortune of being a student, a colleague and a long-standing collaborator of Shanti Gupta. The second editor's association with Shanti Gupta began in 1978 when he started his research in the area of order statistics. During the past twenty years, he has collaborated with Shanti Gupta on several publications. We both feel that our lives have been enriched by our association with him. He has indeed been a friend, philosopher and guide to us.

Statistical Decision Theory and Related Topics III

Author: Shanti S. Gupta
Publisher: Academic Press
ISBN: 9781483259550
Release Date: 2014-05-10
Genre: Mathematics

Statistical Decision Theory and Related Topics III, Volume 2 is a collection of papers presented at the Third Purdue Symposium on Statistical Decision Theory and Related Topics, held at Purdue University in June 1981. The symposium brought together many prominent leaders and a number of younger researchers in statistical decision theory and related areas. This volume contains the research papers presented at the symposium and includes works on general decision theory, multiple decision theory, optimum experimental design, sequential and adaptive inference, Bayesian analysis, robustness, and large sample theory. These research areas have seen rapid developments since the preceding Purdue Symposium in 1976, developments reflected by the variety and depth of the works in this volume. Statisticians and mathematicians will find the book very insightful.

Statistical Decision Theory

Author: James Berger
Publisher: Springer Science & Business Media
ISBN: 9781475717273
Release Date: 2013-04-17
Genre: Mathematics

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.

Statistik II f r Dummies

Author: Deborah J. Rumsey
Publisher: John Wiley & Sons
ISBN: 9783527669240
Release Date: 2013-03-25
Genre: Mathematics

Vom Absolutrang bis zum Zweifach-Varianzanalysemodell – alles, was Sie über weiterführende Statistik wissen sollten Es gibt Qualen, große Qualen und Statistik, so sehen es viele Studenten. Mit diesem Buch lernen Sie weiterführende Statistik so leicht wie möglich. Deborah Rumsey zeigt Ihnen, wie Sie Varianzanalysen und Chi-Quadrat-Tests berechnen, wie Sie mit Regressionen arbeiten, ein Modell erstellen, Korrelationen bilden, nichtparametrische Prozeduren durchführen und vieles mehr. Aber auch die Grundlagen der Statistik bleiben nicht außen vor und deshalb erklärt Ihnen die Autorin, was Sie zu Mittelwerten, Vertrauensintervallen und Co wissen sollten. So lernen Sie die Methoden, die Sie brauchen, und erhalten das Handwerkszeug, um erfolgreich Ihre Statistikprüfungen zu bestehen. Sie erfahren: • Wie Sie mit multiplen Regressionen umgehen • Was es mit dem Vorzeichentest und dem Vorzeichenrangtest auf sich hat • Wie Sie sich innerhalb der statistischen Techniken zurechtfinden • Was das richtige Regressionsmodell für Ihre Analyse ist • Wie Regression und ANOVA zusammenhängen

Decision Theory

Author: Giovanni Parmigiani
Publisher: John Wiley & Sons
ISBN: 9780470746677
Release Date: 2009-04-15
Genre: Mathematics

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.

An Introduction to Bayesian Analysis

Author: Jayanta K. Ghosh
Publisher: Springer Science & Business Media
ISBN: 9780387354330
Release Date: 2007-07-03
Genre: Mathematics

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.