عنوان

Probability, Statistical Optics, and Data Testing :

3642972896

9783642972898

b576670

Probability, Statistical Optics, and Data Testing :

[Book]

a Problem Solving Approach

by B. Roy Frieden.

Second edition

Berlin, Heidelberg

Springer Berlin Heidelberg

1991

(xx, 443 pages 110 illustrations)

Springer series in information sciences, 10.

1. Introduction --; 2. The Axiomatic Approach --; 3. Continuous Random Variables --; 4. Fourier Methods in Probability --; 5. Functions of Random Variables --; 6. Bernoulli Trials and Limiting Cases --; 7. The Monte Carlo Calculation --; 8. Stochastic Processes --; 9. Introduction to Statistical Methods: Estimating the Mean, Median, Variance, S/N, and Simple Probability --; 10. Estimating a Probability Law --; 11. The Chi-Square Test of Significance --; 12. The Student t-Test on the Mean --; 13. The F-Test on Variance --; 14. Least-Squares Curve Fitting --; Regression Analysis --; 15. Principal Components Analysis --; 16. The Controversy Between Bayesians and Classicists --; 17. Introduction to Estimation Methods --; Appendix A. Error Function and Its Derivative --; Appendix E.A Crib Sheet of Statistical Parameters and Their Errors --; Appendix F. Synopsis of Statistical Tests --; References.

This new edition incorporates corrections of all known typographical errors in the first edition, as well as some more substantive changes. Chief among the latter is the addition of Chap. 17, on methods of estimation. As with the rest of the text, most applications and examples cited in the new chapter are from the optical perspective. The intention behind this new chapter is to empower the optical researcher with a yet broader range of research tools. Certainly a basic knowledge of estimation methods should be among these. In particular, the sections on likelihood theory and Fisher information prepare readers for the problems of optical parameter estimation and probability law estimation. Physicists and optical scientists might find this material particularly useful, since the subject of Fisher information is generally not covered in standard physical science curricula. Since the words "statistical optics" are prominent in the title of this book, their meaning needs to be clarified. There is a general tendency to overly emphasize the statistics of photons as the sine qua non of statistical optics. In view is taken, which equally emphasizes the random medium this text a wider that surrounds the photon, be it a photographic emulsion, the turbulent atmo­ sphere, a vibrating lens holder, etc. Also included are random interpretations of ostensibly deterministic phenomena, such as the Hurter-Driffield (H and D) curve of photography. Such a "random interpretation" sometimes breaks new ground, as in Chap.

Mathematical physics.

Physics.

by B. Roy Frieden.

B Roy Frieden

[Book]

Y