Bayesian Logical Data Analysis for the Physical Sciences

A Comparative Approach with Mathematica Support
Erscheinungsjahr 2011
ISBN: 978-0-521-84150-4
Verlag: Cambridge University Press

Buch, Englisch, 488 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 1104 g

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® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.

Autoren/Hrsg.

Gregory, P. C.

Gregory, Phil

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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.

Über Autor(innen)

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