Frieden Probability, Statistical Optics, and Data Testing

A Problem Solving Approach
Erscheinungsjahr 2012
ISBN: 978-3-642-96732-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 10, eBook

Reihe: Springer Series in Information Sciences

A basic skill in probability is practically demanded nowadays in many bran ches of optics, especially in image science. On the other hand, there is no text presently available that develops probability, and its companion fields stochastic processes and statistics, from the optical perspective. [Short of a book, a chapter was recently written for this purpose; see B. R. Frieden (ed. ): The Computer in Optical Research, Topics in Applied Physics, Vol. 41 (Springer, Berlin, Heidelberg, New York 1980) Chap. 3] Most standard texts either use illustrative examples and problems from electrical engineering or from the life sciences. The present book is meant to remedy this situation, by teaching probability with the specific needs of the optical researcher in mind. Virtually all the illustrative examples and applications of the theory are from image science and other fields of optics. One might say that photons have replaced electrons in nearly all considera tions here. We hope, in this manner, to make the learning of probability a pleasant and absorbing experience for optical workers. Some of the remaining applications are from information theory, a con cept which complements image science in particular. As will be seen, there are numerous tie-ins between the two concepts. Students will be adequately prepared for the material in this book if they have had a course in calculus, and know the basics of matrix manipulation.

Zielgruppe

Research

Autoren/Hrsg.

Frieden, B.R.

Inhaltsverzeichnis

1. Introduction.- 2. The Axiomatic Approach.- 3. Continuous Random Variables.- 4. Fourier Methods in Probability.- 5. Functions of Random Variables.- 6. Bernoulli Trials and its Limiting Cases.- 7. The Monte Carlo Calculation.- 8 Stochastic Processes.- 9. Introduction to Statistical Methods: Estimating the Mean, ian, Variance, S/N, and Simple Probability.- 10. Estimating a Probability Law.- 11. The Chi-Square Test of Significance.- 12. The Student f-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.- Appendix A. Error Function and its Derivative [4.12].- Appendix E. A Crib Sheet of Statistical Parameters and their Errors.- Appendix F Synopsis of Statistical Tests.- References.