Researchers in many branches of science are increasingly 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. It 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 perspective.
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.
Review
"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
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