Bayesian Logical Data Analysis for the Physical Sciences

A Comparative Approach with Mathematica Support
Erscheinungsjahr 2011
ISBN: 978-0-521-15012-5
Verlag: Cambridge University Press

Buch, Englisch, 486 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 834 g

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.

Autoren/Hrsg.

Gregory, P. C.

Gregory, Phil

Fachgebiete

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

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.