Bayesian Logical Data Analysis for the Physical Sciences

A Comparative Approach with Mathematica Support

Phil Gregory

468 pages, parution le 06/04/2005

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Résumé

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.

Sommaire

Preface
Acknowledgments
Role of probability theory in science
Probability theory as extended logic
The how-to of Bayesian inference
Assigning probabilities
Frequentist statistical inference
What is a statistic?
Frequentist hypothesis testing
Maximum entropy probabilities
Bayesian inference (Gaussian errors)
Linear model fitting (Gaussian errors)
Nonlinear model fitting
Markov Chain Monte Carlo
Bayesian spectral analysis
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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Phil Gregory
Parution	06/04/2005
Nb. de pages	468
Format	18 x 25
Couverture	Relié
Poids	1141g
Intérieur	Noir et Blanc
EAN13	9780521841504
ISBN13	978-0-521-84150-4