Bayesian Inference: Data Evaluation and Decisions, 2nd Edition

Authors: Hanns Ludwig Harney



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

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.

Table of contents

Front Matter

Knowledge and Logic

Bayes’ Theorem

Probable and Improbable Data

Description 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 the Standard Deviation

Form Invariance II: Natural x

Item Response Theory

On the Art of Fitting

Summary

Back Matter

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