Increasingly, researchers in many branches of science are coming into contact with Bayesian statistics or Bayesian probability theory. By encompassing both inductive and deductive logic, Bayesian analysis can improve model parameter estimates by many orders of magnitude. It provides a simple and unified approach to all data analysis problems, allowing the experimenter to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. 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 an introduction to Markov Chain Monte-Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian perspective. In addition, background material is provided in appendices and supporting Mathematica notebooks are available, providing an easy learning route for upper-undergraduates, graduate students, or any serious researcher in physical sciences or engineering.
• Introduces statistical inference in the larger context of scientific methods, and includes many worked examples and problem sets. • Presents Bayesian theory but also compares and contrasts with other existing ideas. • Mathematica support notebook is available for readers from www.cambridge.org/052184150X
Contents
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 Transform; Appendix C. Difference in two samples; Appendix D. Poisson ON/OFF details; Appendix E. Multivariate Gaussian from maximum entropy.
Reviews
'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
' … a clearly written guide to applied statistical analysis by using SPSS software. it is filled with examples and exercises that help readers to understand the types of problem that the techniques can address. If you are an SPSS enthusiast, a beginner or not, you will find this new edition a satisfying source of valuable infromation.' Journal of the RSS
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