Bayesian Inference

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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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.

• Bayesian Decision Theory
• Commuting Parameters Physics
• Data Analysis Physics
• Factorizing Parameters Physics
• Fitting Experimental Data
• Fourier Expansion
• Geometric Prior Distribution
• Histogram Coherent Alternative
• Histogram Fitting
• Multinomial Distribution
• Partial Form Invariance
• Statistical Analysis Physics
• Statistical Testing and Model Choice
• Symmetry Group Physics

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

  Hanns Ludwig Harney

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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