Probability, Statistical Optics, and Data Testing

A Problem Solving Approach
3rd Auflage 2001
ISBN: 978-3-540-41708-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 10, 496 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1600 g

Reihe: Springer Series in Information Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Frieden, Roy

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Angewandte Optik
• Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
• Naturwissenschaften Physik Elektromagnetismus Optik
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

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 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.