Bayesian Inference
Subtitle: Parameter Estimation and Decisions
By: by Hanns L. Harney
Series: Advanced Texts in Physics; Advanced Texts in Physics
Publisher: Springer Berlin Heidelberg
Published: 2003
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 265
ISBN-13: 9783642055775; 9783662060063
Subjects: Quantum theory; Mathematics; Mathematical statistics; Physics; Computer science
Description: 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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Table of contents: title: Knowledge and Logic; title: Bayes' Theorem; title: Probable and improbable Data; title: Bayes' Theorem and the Truth; title: Description of Distributions I: Probability Densities; title: Description of Distributions II: Form Invariance I: Real x; title: Examples of Invariant Measures; title: A Linear Representation of Form Invariance; title: Beyond Form Invariance: The Geometric Prior; title: Econophysics; title: Inferring Mean or Standard Deviation; title: Form Invariance II: Natural x; title: Independence of Parameters; title: The Art of Fitting I: Real x; title: Judging a Fit I: Real x; title: The Art of Fitting II: Natural x; title: Judging a Fit II: Natural x; title: Summary; title: A Problems; title: B Form Invariance I: Probability Densities; title: C Beyond Form Invariance: The Geometric Prior; title: D Inferring Mean or Standard Deviation; title: E Form Invariance II: Natural x; title: F Independence of Parameters; title: G The Art of Fitting I: Real x; title: H Judging a Fit II: Natural x; title: Bibliography. .