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

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

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By (author) Phil C. Gregory

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  • Publisher: CAMBRIDGE UNIVERSITY PRESS
  • Format: Paperback | 488 pages
  • Dimensions: 174mm x 246mm x 24mm | 962g
  • Publication date: 28 June 2010
  • Publication City/Country: Cambridge
  • ISBN 10: 0521150124
  • ISBN 13: 9780521150125
  • Edition: 1
  • Illustrations note: 132 b/w illus. 74 exercises
  • Sales rank: 333,696

Product description

Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica(R) notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.

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Author information

Phil Gregory is Professor Emeritus at the Department of Physics and Astronomy at the University of British Columbia.

Review quote

'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 'The examples are well integrated with the text and are enlightening.' Contemporary Physics 'The book can easily keep the readers amazed and attracted to its content throughout the read and make them want to return back to it recursively. It presents a perfect balance between theoretical inference and a practical know-how approach to Bayesian methods.' Stan Lipovetsky, Technometrics

Table of contents

Preface; Acknowledgements; 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 transforms; Appendix C. Difference in two samples; Appendix D. Poisson ON/OFF details; Appendix E. Multivariate Gaussian from maximum entropy; References; Index.