This book provides a clear exposition of the underlying concepts of Bayesian analysis, with large numbers of worked examples and problem sets. It also discusses numerical techniques for implementing the Bayesian calculations, including an introduction to Markov chain Monte Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian perspective.
Background material is provided in appendices, and supporting Mathematica notebooks
are available from the publisher, providing an easy learning route for upper-undergraduates, graduate students, or any serious researcher in physical sciences or engineering.
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
Probability and Statistics