Bayesian Probability Theory

Wolfgang von der Linden is Professor for Theoretical and Computational Physics at the Graz University of Technology. His research area is statistical physics with focus on strongly correlated quantum-many-body physics, based on computational techniques. Volker Dose is a former Director of the surface physics division of the Max Planck Institute for plasma physics. He has contributed to Bayesian methods in physics, astronomy and climate research. Udo von Toussaint is a Senior Scientist in the material research division of the Max Planck Institute for plasma physics, where he works on Bayesian experimental design, data fusion, molecular dynamics and inverse problems in the field of plasma-wall interactions.

• Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer–Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.