Probability, Statistical Optics, and Data Testing: A Problem Solving Approach

✍ Scribed by Professor B. Roy Frieden (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 507
• Series: Springer Series in Information Sciences 10
• Edition: 3
• Category: Library

✦ Synopsis

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 solution. This textbook develops these subjects within the context of optics using a problem-solving approach. All methods are explicitly derived and can be traced back to three simple axioms given at the outset. Students with some previous exposure to Fourier optics or linear theory will find the material particularly absorbing and easy to understand.
This third edition contains many new applications to optical and physical phenomena. This includes a method of estimating probability laws exactly, by regarding them as laws of physics to be determined using a new variational principle.

✦ Table of Contents

Front Matter....Pages I-XXIV
Introduction....Pages 1-6
The Axiomatic Approach....Pages 7-37
Continuous Random Variables....Pages 39-77
Fourier Methods in Probability....Pages 79-106
Functions of Random Variables....Pages 107-146
Bernoulli Trials and Limiting Cases....Pages 147-173
The Monte Carlo Calculation....Pages 175-190
Stochastic Processes....Pages 191-242
Introduction to Statistical Methods: Estimating the Mean, Median, Variance, S/N, and Simple Probability....Pages 243-276
Introduction to Estimating Probability Laws....Pages 277-305
The Chi-Square Test of Significance....Pages 307-320
The Student t -Test on the Mean....Pages 321-331
The F -Test on Variance....Pages 333-339
Least-Squares Curve Fitting — Regression Analysis....Pages 341-361
Principal Components Analysis....Pages 363-374
The Controversy Between Bayesians and Classicists....Pages 375-386
Introduction to Estimation Methods....Pages 387-450
Back Matter....Pages 451-493

✦ Subjects

Statistical Physics, Dynamical Systems and Complexity;Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences