Format:
Online-Ressource (XIII, 265 p)
,
digital
Edition:
Reproduktion Springer eBook Collection. Physics and Astronomy
ISBN:
9783662060063
Series Statement:
Advanced Texts in Physics
Content:
The book provides a generalization of Gaussian error intervals tosituations where the data follow non-Gaussian distributions. Thisusually occurs in frontier science, where the observed parameter isjust above background or the histogram of multiparametric datacontains empty bins. Then the validity of a theorycannot be decided by the chi-squared-criterion, but this long-standingproblem is solved here. The book is based on Bayes' theorem, symmetry anddifferential geometry. In addition to solutions of practical problems, the textprovides an epistemic insight: The logic of quantum mechanics isobtained 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
Note:
Knowledge and Logic -- Bayes' Theorem.- Probable and improbable Data -- Bayes' Theorem and the Truth.- Description of Distributions I: Probability Densities -- Description of Distributions II: Form Invariance I: Real x -- Examples of Invariant Measures.- A Linear Representation of Form Invariance.- Beyond Form Invariance: The Geometric Prior -- Econophysics -- Inferring Mean or Standard Deviation.- Form Invariance II: Natural x -- Independence of Parameters -- The Art of Fitting I: Real x -- Judging a Fit I: Real x -- The Art of Fitting II: Natural x.- Judging a Fit II: Natural x.- Summary -- A Problems -- B Form Invariance I: Probability Densities -- C Beyond Form Invariance: The Geometric Prior -- D Inferring Mean or Standard Deviation -- E Form Invariance II: Natural x -- F Independence of Parameters -- G The Art of Fitting I: Real x -- H Judging a Fit II: Natural x -- Bibliography. .
Additional Edition:
ISBN 9783642055775
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783642055775
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783540003977
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9783662060070
Language:
English
Keywords:
Bayes-Entscheidungstheorie
;
Bayes-Inferenz
