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Probability, Statistical Optics, and Data Testing

A Problem Solving Approach

  • Textbook
  • © 1983

Overview

Authors:
  1. B. Roy Frieden

    1. Optical Sciences Center, The University of Arizona, Tucson, USA

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Part of the book series: Springer Series in Information Sciences (SSINF, volume 10)

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Introduction

    • B. Roy Frieden
    Pages 1-6

  3. The Axiomatic Approach

    • B. Roy Frieden
    Pages 7-36

  4. Continuous Random Variables

    • B. Roy Frieden
    Pages 37-69

  5. Fourier Methods in Probability

    • B. Roy Frieden
    Pages 70-98

  6. Functions of Random Variables

    • B. Roy Frieden
    Pages 99-133

  7. Bernoulli Trials and Its Limiting Cases

    • B. Roy Frieden
    Pages 134-161

  8. The Monte Carlo Calculation

    • B. Roy Frieden
    Pages 162-176

  9. Stochastic Processes

    • B. Roy Frieden
    Pages 177-232

  10. Introduction to Statistical Methods: Estimating the Mean, Median, Variance, S/N, and Simple Probability

    • B. Roy Frieden
    Pages 233-263

  11. Estimating a Probability Law

    • B. Roy Frieden
    Pages 264-293

  12. The Chi-Square Test of Significance

    • B. Roy Frieden
    Pages 294-306

  13. The Student t-Test on the Mean

    • B. Roy Frieden
    Pages 307-319

  14. The F-Test on Variance

    • B. Roy Frieden
    Pages 320-326

  15. Least-Squares Curve Fitting — Regression Analysis

    • B. Roy Frieden
    Pages 327-349

  16. Principal Components Analysis

    • B. Roy Frieden
    Pages 350-361

  17. The Controversy Between Bayesians and Classicists

    • B. Roy Frieden
    Pages 363-386

  18. Back Matter

    Pages 374-406
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Keywords

About this book

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.

Authors and Affiliations

  • Optical Sciences Center, The University of Arizona, Tucson, USA

    B. Roy Frieden

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