Bayesian Inference: Data Evaluation and Decisions

✍ Scribed by Hanns Ludwig Harney (auth.)

Publisher: Springer International Publishing
Year: 2016
Tongue: English
Leaves: 245
Edition: 2
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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....Pages i-xiii
Knowledge and Logic....Pages 1-9
Bayes’ Theorem....Pages 11-25
Probable and Improbable Data....Pages 27-39
Description of Distributions I: Real x ....Pages 41-53
Description of Distributions II: Natural x ....Pages 55-61
Form Invariance I....Pages 63-80
Examples of Invariant Measures....Pages 81-90
A Linear Representation of Form Invariance....Pages 91-102
Going Beyond Form Invariance: The Geometric Prior....Pages 103-113
Inferring the Mean or the Standard Deviation....Pages 115-125
Form Invariance II: Natural x ....Pages 127-136
Item Response Theory....Pages 137-150
On the Art of Fitting....Pages 151-165
Summary....Pages 167-172
Back Matter....Pages 173-243

✦ Subjects

Mathematical Methods in Physics;Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences;Particle and Nuclear Physics;Probability Theory and Stochastic Processes;Medical and Radiation Physics;Computational

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