Bayesian Probability Theory: Applications in the Physical Sciences
Cambridge University Press, 6/12/2014
EAN 9781107035904, ISBN10: 1107035902
Hardcover, 649 pages, 26.3 x 18 x 3.8 cm
Language: English
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.
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.