Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica(r) Support

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.

"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

Increasingly, researchers in many branches of science are coming into contact with Bayesian statistics or Bayesian probability theory. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. The book also discusses numerical techniques for implementing the Bayesian calculations, including Markov Chain Monte-Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian pe rspective. Background material is provided in appendices and supporting Mathematica notebooks are available. Suitable for upper-undergraduates, graduate students, or any serious researcher in physical sciences or engineering.

A clear exposition of the underlying concepts, containing large numbers of worked examples and problem sets.

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

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.