A Course in Computational Probability and Statistics

by Walter Freiberger, Ulf Grenander

Overview

This book arose out of a number of different contexts, and numerous persons have contributed to its conception and development. It had its origin in a project initiated jointly with the IBM Cambridge Scientific Center, particularly with Dr. Rhett Tsao, then of that Center. We are grateful to Mr. Norman Rasmussen, Manager of the IBM Scientific Center Complex, for his initial support. The work is being carried on at Brown University with generous support from the Office of Computing Activities of the National Science Foundation (grants GJ-174 and GJ-7l0); we are grateful to Dr. John Lehmann of this Office for his interest and encouragement. Professors Donald McClure and Richard Vitale of the Division of Applied Mathematics at Brown University contributed greatly to the project and taught courses in its spirit. We are indebted to them and to Dr. Tore Dalenius of the University of Skholm for helpful criticisms of the manuscript. The final stimulus to the book's completion came from an invLtation to teach a course at the IBM European Systems Research Institute at Geneva. We are grateful to Dr. J.F. Blackburn, Director of the Institute, for his invitation, and to him and his wife Beverley for their hospitality. We are greatly indebted to Mrs. Katrina Avery for her splendid secretarial and editorial work on the manuscript.

Product Details

ISBN-13:	9780387900292
Publisher:	Springer New York
Publication date:	07/12/1977
Series:	Applied Mathematical Sciences , #6
Edition description:	1st ed. 1971. Rev. 2nd printing
Pages:	156
Product dimensions:	7.01(w) x 10.00(h) x 0.01(d)

Table of Contents

1. Randomness.- 1.1 Fundamentals.- 1.2 Random Number Generation.- Appendix 1: Figures.- 2. Simulation.- 2.1 Simple Monte Carlo.- 2.2 Assignments.- 2.3 Randomness and Monte Carlo.- 2.4 Improved Monte Carlo.- 2.5 Quadrature.- 2.6 Conclusions.- 3. Limit Theorems.- 3.1 Limits of Convolutions.- 3.2 An Insurance Model.- 3.3 Approximation.- Appendix 3: Figures.- 4. Shastic Processes.- 4.1 General Properties.- 4.2 An Investment Example.- 4.3 Stationary Shastic Processes.- 4.4 Markov Chains.- Appendix 4: Figures.- 5. Particular Shastic Processes.- 5.1 A Growth Model.- 5.2 The Random Phase Model.- 5.3 Renewal Processes.- Appendix 5: Figures.- 6. Decision Problems.- 6.1 Generalities.- 6.2 A Shastic Approximation Problem.- 6.3 An Insurance Game.- 6.4 Design of Experiments.- 6.5 A Search Problem.- Appendix 6: Figures.- 7. A Computational Approach to Statistics.- 7.1 Statistical Computing.- 7.2 Analysis of Variance.- 7.3 Non-Standard Situations.- 7.4 Bayesian Estimation.- Appendix 7: Figures.- 8. Time-Series Analysis.- 8.1 Estimation of the Spectral Density.- 8.2 The Fast Fourier Transform.- 8.3 Regression Analysis of Time Series.- 8.4 Signal Detection.- Appendix 8: Figures.- References.