Solving a longstanding problem in the physical sciences, this text and reference generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. The text is written at introductory level, with many examples and exercises.
Bayesian Inference: Parameter Estimation and Decisions
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Book Description
Editorial Reviews
Review
From the reviews: "The book under review combines features of a textbook and a monograph. … Arguments are presented as explicitly as possible with the aid of appendices … . There are numerous examples and illustrations, often taken from physics research. Problems are posed and their solutions are provided." (Joseph Melamed, Zentralblatt MATH, Vol. 1019, 2003)
From the Back Cover
The book provides a generalization of Gaussian error intervals to situations where the data follow non-Gaussian distributions. This usually occurs in frontier science, where the observed parameter is just above background or the histogram of multiparametric data contains empty bins. Then the validity of a theory cannot be decided by the chi-squared-criterion, but this long-standing problem is solved here. The book is based on Bayes' theorem, symmetry and differential geometry. In addition to solutions of practical problems, the text provides an epistemic insight: The logic of quantum mechanics is obtained as the logic of unbiased inference from counting data. However, no knowledge of quantum mechanics is required. The text, examples and exercises are written at an introductory level.
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Inside This Book
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First Sentence:
Science does not prove anything. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
marginalisation paradox, incoherent alternative, commuting parameters, parameters commute, uninteresting parameters, silent parameter, form invariance, cubic die, minor posterior, kth bin, multinomial model, expectation value with respect, minor model, normalising factor, conditional measure, form invariant, multinomial theorem, geometric measure, multiplication function, first derivative vanishes, error interval, minor measures, invariant measure, complete fit, multinomial distribution New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Science does not prove anything. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
marginalisation paradox, incoherent alternative, commuting parameters, parameters commute, uninteresting parameters, silent parameter, form invariance, cubic die, minor posterior, kth bin, multinomial model, expectation value with respect, minor model, normalising factor, conditional measure, form invariant, multinomial theorem, geometric measure, multiplication function, first derivative vanishes, error interval, minor measures, invariant measure, complete fit, multinomial distribution New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 42
books:
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- Bayesian Inference (International Library of Critical Writings in Econometrics) by Nicholas G. Polson in Back Matter (1), and Back Matter (2)
- Maximum Entropy and Bayesian Methods (Fundamental Theories of Physics) by C.R. Smith in Back Matter (1), and Back Matter (2)
- Maximum Entropy and Bayesian Methods (Fundamental Theories of Physics) by John Skilling in Back Matter
- Bayes Theory (Springer Series in Statistics) by J. A. Hartigan in Back Matter
- Bayesian Analysis in Econometrics and Statistics: Essays in Honor of Harold Jeffreys by Arnold Zellner in Back Matter
See all 42 books this book cites
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