Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support
Cambridge University Press, 5/20/2010
EAN 9780521150125, ISBN10: 0521150124
Paperback, 488 pages, 24.4 x 17 x 2.8 cm
Language: English
Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.
Preface
Acknowledgements
1. Role of probability theory in science
2. Probability theory as extended logic
3. The how-to of Bayesian inference
4. Assigning probabilities
5. Frequentist statistical inference
6. What is a statistic?
7. Frequentist hypothesis testing
8. Maximum entropy probabilities
9. Bayesian inference (Gaussian errors)
10. Linear model fitting (Gaussian errors)
11. Nonlinear model fitting
12. Markov Chain Monte Carlo
13. Bayesian spectral analysis
14. Bayesian inference (Poisson sampling)
Appendix A. Singular value decomposition
Appendix B. Discrete Fourier transforms
Appendix C. Difference in two samples
Appendix D. Poisson ON/OFF details
Appendix E. Multivariate Gaussian from maximum entropy
References
Index.
'As well as the usual topics to be found in a text on Bayesian inference, chapters are included on frequentist inference (for contrast), non-linear model fitting, spectral analysis and Poisson sampling.' Zentralblatt MATH