A Course in Computational Probability and Statistics

ISBN-13: 9780387900292 / Angielski / Miękka / 1977 / 156 str.

Walter F. Freiberger; Ulf Grenander

Opis

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 Scien- tific 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 Stockholm 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.

Spis treści

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. Stochastic Processes.- 4.1 General Properties.- 4.2 An Investment Example.- 4.3 Stationary Stochastic Processes.- 4.4 Markov Chains.- Appendix 4: Figures.- 5. Particular Stochastic 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 Stochastic 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.