Bayesian inference : parameter estimation and decisions
著者
書誌事項
Bayesian inference : parameter estimation and decisions
（Advanced texts in physics）（Physics and astronomy online library）
Tokyo : Springer, 2003
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注記
Includes bibliographical references and index
"With 52 Figures, Numerous Examples, and 79 Problems with Solutions"
内容説明・目次
内容説明
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.
目次
1 Knowledge and Logic.- 2 Bayes' Theorem.- 3 Probable and Improbable Data.- 4 Description of Distributions I: Real x.- 5 Description of Distributions II: Natural x.- 6 Form Invariance I: Real x.- 7 Examples of Invariant Measures.- 8 A Linear Representation of Form Invariance.- 9 Beyond Form Invariance: The Geometric Prior.- 10 Inferring the Mean or Standard Deviation.- 11 Form Invariance II: Natural x.- 12 Independence of Parameters.- 13 The Art of Fitting I: Real x.- 14 Judging a Fit I: Real x.- 15 The Art of Fitting II: Natural x.- 16 Judging a Fit II: Natural x.- 17 Summary.- A Problems and Solutions.- A.1 Knowledge and Logic.- A.2 Bayes' Theorem.- A.3 Probable and Improbable Data.- A.7 Examples of Invariant Measures.- A.8 A Linear Representation of Form Invariance.- A.9 Beyond Form Invariance: The Geometric Prior.- A.10 Inferring the Mean or Standard Deviation.- A.12 Independence of Parameters.- B.1 The Correlation Matrix.- B.2 Calculation of a Jacobian.- B.4 The Beta Function.- C.1 The Multinomial Theorem.- D Form Invariance I: Probability Densities.- D.1 The Invariant Measure of a Group.- E Beyond Form Invariance: The Geometric Prior.- E.1 The Definition of the Fisher Matrix.- E.2 Evaluation of a Determinant.- E.3 Evaluation of a Fisher Matrix.- E.4 The Fisher Matrix of the Multinomial Model.- F Inferring the Mean or Standard Deviation.- G.1 Destruction and Creation Operators.- G.2 Unitary Operators.- G.3 The Probability Amplitude of the Histogram.- G.4 Form Invariance of the Histogram.- G.5 Quasi-Events in the Histogram.- G.6 Form Invariance of the Binomial Model.- G.7 Conservation of the Number of Events.- G.8 Normalising the Posterior of the Binomial Model.- G.9 Lack of Form Invariance of the Multinomial Model.- H Independence of Parameters.- H.1 On the Measure of a Factorising Group.- H.2 Marginal Distribution of the Posterior of the Multinomial Model.- H.3 A Minor Posterior of the Multinomial Model.- I.1 A Factorising Gaussian Model.- I.2 A Basis for Fourier Expansions.- J.2 The Deviation Between Two Distributions.- References.
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