Bayesian logical data analysis for the physical sciences : a comparative approach with Mathematica support / P.C. Gregory.

Format:

Book

Author/Creator:

Gregory, P. C. (Philip Christopher), 1941- author.

Language:

English

Subjects (All):

Mathematica (Computer file).

Bayesian statistical decision theory.

Physical sciences--Statistical methods.

Physical sciences.

Physical Description:

1 online resource (xvii, 468 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2005.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Title; Copyright; 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 with Gaussian errors; 10 Linear model fitting (Gaussian errors); 11 Nonlinear model fitting; 12 Markov chain Monte Carlo; 13 Bayesian revolution in spectral analysis; 14 Bayesian inference with Poisson sampling

Appendix A Singular value decompositionAppendix 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

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 455-460) and index.

ISBN:

1-107-14026-9

1-107-38600-4

1-280-41586-X

9786610415861

0-511-79127-5

0-511-17144-7

0-511-19717-9

0-511-08228-2

0-511-29855-2

0-511-08183-9

OCLC:

71365593