Bayesian Inference: Parameter Estimation and Decisions

✍ Scribed by Prof. Hanns L. Harney (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 2003
Tongue: English
Leaves: 274
Series: Advanced Texts in Physics
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

The book provides a generalization of Gaussian error intervals to
situations where the data follow non-Gaussian distributions. This
usually occurs in frontier science, where the observed parameter is
just above background or the histogram of multiparametric data
contains empty bins. Then the validity of a theory
cannot be decided by the chi-squared-criterion, but this long-standing
problem is solved here. The book is based on Bayes' theorem, symmetry and
differential geometry. In addition to solutions of practical problems, the text
provides an epistemic insight: The logic of quantum mechanics is
obtained 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.

✦ Table of Contents

Front Matter....Pages I-XIII
Knowledge and Logic....Pages 1-7
Bayes’ Theorem....Pages 8-18
Probable and Improbable Data....Pages 19-28
Description of Distributions I: Real x ....Pages 29-39
Description of Distributions II: Natural x ....Pages 40-45
Form Invariance I: Real x ....Pages 46-56
Examples of Invariant Measures....Pages 57-64
A Linear Representation of Form Invariance....Pages 65-70
Beyond Form Invariance: The Geometric Prior....Pages 71-80
Inferring the Mean or Standard Deviation....Pages 81-94
Form Invariance II: Natural x ....Pages 95-108
Independence of Parameters....Pages 109-119
The Art of Fitting I: Real x ....Pages 120-129
Judging a Fit I: Real x ....Pages 130-136
The Art of Fitting II: Natural x ....Pages 137-152
Judging a Fit II: Natural x ....Pages 153-161
Summary....Pages 162-167
Back Matter....Pages 169-265

✦ Subjects

Quantum Information Technology, Spintronics;Quantum Physics;Statistical Physics, Dynamical Systems and Complexity;Statistical Theory and Methods;Computational Mathematics and Numerical Analysis

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