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Bayesian Inference

Data Evaluation and Decisions

  • Book
  • © 2016

Overview

Authors:
  1. Hanns Ludwig Harney

    1. Max-Planck-Institute for Nuclear Ph , Heidelberg, Germany

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  • 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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Knowledge and Logic

    • Hanns Ludwig Harney
    Pages 1-9

  3. Bayes’ Theorem

    • Hanns Ludwig Harney
    Pages 11-25

  4. Probable and Improbable Data

    • Hanns Ludwig Harney
    Pages 27-39

  5. Description of Distributions I: Real x

    • Hanns Ludwig Harney
    Pages 41-53

  6. Description of Distributions II: Natural x

    • Hanns Ludwig Harney
    Pages 55-61

  7. Form Invariance I

    • Hanns Ludwig Harney
    Pages 63-80

  8. Examples of Invariant Measures

    • Hanns Ludwig Harney
    Pages 81-90

  9. A Linear Representation of Form Invariance

    • Hanns Ludwig Harney
    Pages 91-102

  10. Going Beyond Form Invariance: The Geometric Prior

    • Hanns Ludwig Harney
    Pages 103-113

  11. Inferring the Mean or the Standard Deviation

    • Hanns Ludwig Harney
    Pages 115-125

  12. Form Invariance II: Natural x

    • Hanns Ludwig Harney
    Pages 127-136

  13. Item Response Theory

    • Hanns Ludwig Harney
    Pages 137-150

  14. On the Art of Fitting

    • Hanns Ludwig Harney
    Pages 151-165

  15. Summary

    • Hanns Ludwig Harney
    Pages 167-172

  16. Back Matter

    Pages 173-243
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Keywords

About this book

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.

Authors and Affiliations

  • Max-Planck-Institute for Nuclear Ph , Heidelberg, Germany

    Hanns Ludwig Harney

About the author

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.

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