Bayesian Inference

This new edition offers a comprehensive introduction to the analysis of data using Bayes rule. It generalizes Gaussian error intervals to situations in which the data follow distributions other than Gaussian. This is particularly useful when the observed parameter is barely above the background or the histogram of multiparametric data contains many empty bins, so that the determination of the validity of a theory cannot be based on the chi-squared-criterion. In addition to the solutions of practical problems, this approach provides an epistemic insight: the logic of quantum mechanics is obtained as the logic of unbiased inference from counting data. New sections feature factorizing parameters, commuting parameters, observables in quantum mechanics, the art of fitting with coherent and with incoherent alternatives and fitting with multinomial distribution. Additional problems and examples help deepen the knowledge. Requiring no knowledge of quantum mechanics, the book is written on introductory level, with many examples and exercises, for advanced undergraduate and graduate students in the physical sciences, planning to, or working in, fields such as medical physics, nuclear physics, quantum mechanics, and chaos.

Teaches application of statistical analysis methods to indedepent of the software package used Contains numerous examples and illustrations, often taken from physics research Comprehensive and suitably balanced between theory and examples Requires no detailed knowledge of quantum mechanics Includes new sections on the art of fitting Contains many new problems and solutions

Auteur
Hanns Ludwig Harney, born in 1939, professor at the University of Heidelberg. He has contributed to experimental and theoretical physics within the Max-Planck Institute for Nuclear Physics at Heidelberg. His interest is focused on symmetries, such as isospin and its violation, as well as chaos, observed as reproducible fluctuations. Since the 1990's, the symmetry properties of common probability distributions lead him to a reformulation of Bayesian inference.

Contenu
Knowledge an Logic.- Bayes' Theorem.- Probable and Improbable Data.- Descriptions of Distributions I: Real x.- Description of Distributions II: Natural x .- Form Invariance I.- Examples of Invariant Measures.- A Linear Representation of Form Invariance.- Going Beyond Form Invariance: The Geometric Prior.- Inferring the Mean or Standard Deviation.- Form Invariance II: Natural x .- Item Response Theory.- On the Art of Fitting .- Problems and Solutions.- Description of Distributions I.- Real x.- Form Invariance I.- Beyond Form Invariance: The Geometric Prior.- Inferring Mean or Standard Deviation.- Form Invariance II: Natural x .- Item Response Theory.- On the Art of Fitting.