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

Phil Gregory




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


Table of 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; D. Poisson ON/OFF details; Appendix E. Multivariate Gaussian from maximum entropy.





1. 概率理論在科學中的作用;2. 概率理論作為擴展邏輯;3. 貝葉斯推斷的實踐方法;4. 分配概率;5. 頻率主義統計推斷;6. 什麼是統計量?;7. 頻率主義假設檢驗;8. 最大熵概率;9. 貝葉斯推斷(高斯誤差);10. 線性模型擬合(高斯誤差);11. 非線性模型擬合;12. 馬爾可夫鏈蒙特卡羅;13. 貝葉斯頻譜分析;14. 貝葉斯推斷(泊松抽樣);附錄A. 奇異值分解;附錄B. 離散傅立葉變換;附錄C. 兩個樣本的差異;D. 泊松ON/OFF詳細信息;附錄E. 多變量高斯從最大熵。