Bayesian Probability Theory
Bayesian Probability Theory
Applications in the Physical Sciences
Wolfgang von der Linden, Technische Universität Graz, Austria
Volker Dose, Max-Planck-Institut für Plasmaphysik, Garching, Germany
Udo von Toussaint, Max-Planck-Institut für Plasmaphysik, Garching, Germany
Volker Dose, Max-Planck-Institut für Plasmaphysik, Garching, Germany
Udo von Toussaint, Max-Planck-Institut für Plasmaphysik, Garching, Germany
August 2014
Hardback
9781107035904
$113.00
USDHardback
USD
eBook
From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.
- Uses many real-world applications to show how to perform the numerical evaluations
- Contains numerical techniques required to solve demanding probabilistic problems numerically
Product details
August 2014Hardback
9781107035904
649 pages
263 × 180 × 38 mm
1.3kg
128 b/w illus.
Available
Table of Contents
- 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.
