Bayesian Logical Data Analysis for the Physical Sciences A Comparative Approach with Mathematica® Support

Description

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.

Reviews & endorsements

“All researchers and scientists who are interested in the Bayesian scientific paradigm can benefit greatly from the examples and illustrations here. It is a welcome addition to the vast literature on Bayesian inference.”
Sreenivasan Ravi, University of Mysore, Manasagangotri

Author

Phil Gregory, University of British Columbia, Vancouver
Phil Gregory is Professor Emeritus at the Department of Physics and Astronomy at the University of British Columbia.

Table of Contents

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.