Probability, Statistical Optics, and Data Testing

Professor Emeritus - B. Roy Frieden: B.S., M.S., Ph.D., Professor of Optical Sciences, Univ. of Arizona.

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. Introduction to Estimating Probability Laws.- 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.- Appendix B.- Appendix C.- Appendix D.- Appendix E.- Appendix F.- Appendix G.- References.

From the reviews of the third edition:

"Scientists in optics are increasingly confronted with problems that are of a random nature and that require a working knowledge of probability and statistics for their solutions. This textbook develops these subjects within the context of optics using a problem-solving approach. ... The book is exclusively wealthy in contents. The author generously shares his reflections and assumptions with the reader and puts the unsolved problems yet, what makes this book an especially interesting one." (Dmitry Ostrouchov, Zentralblatt MATH, Vol. 978, 2002)