Probability, Statistical Optics, and Data Testing

1. Front Matter

   Pages I-XX

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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

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   Pages 99-133

7. Bernoulli Trials and Limiting Cases

   • B. Roy Frieden

   Pages 134-161

8. The Monte Carlo Calculation

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   Pages 162-176

9. Stochastic Processes

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   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

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    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 363-373

18. Introduction to Estimation Methods

    • B. Roy Frieden

    Pages 374-408

19. Back Matter

    Pages 409-443

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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.

• Likelihood
• Mathematical methods in physics
• Optical information
• Quantum optics
• Statistical optics
• Statistik
• Wahrscheinlichkeitsrechnung
• image formation and analysis
• optics
• probability theory

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)

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

  B. Roy Frieden

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