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

Phil Gregory, 2005, Cambridge University Press, 468 pp., hardcover

ISBN: 052184150X

The underlying concepts of Bayesian analysis, with large numbers of worked examples and problem sets, are covered here in great detail. The text also discusses numerical techniques for implementing Bayesian calculations, with an introduction to Markov chain Monte Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian perspective.

Contents
Role of Probability Theory in Science | Probability Theory as Extended Logic | The How-To of Bayesian Inference | Assigning Probabilities | Frequentist Statistical Inference | What Is a Statistic? | Frequentist Hypothesis Testing | Maximum Entropy Probabilities | Bayesian Inference with Gaussian Errors | Linear Model Fitting (Gaussian Errors) | Nonlinear Model Fitting | Markov Chain Monte Carlo | Bayesian Revolution in Spectral Analysis | Bayesian Inference with 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

This book is available in the Wolfram Research bookstore.