Computational Probability: Algorithms and Applications in the Mathematical Sciences

✍ Scribed by John H. Drew, Diane L. Evans, Andrew G. Glen, Lawrence M. Leemis (auth.)

• Publisher: Springer US
• Year: 2008
• Tongue: English
• Leaves: 215
• Series: In Operations Research & Management Science 117
• Edition: 1
• Category: Library

✦ Synopsis

Computational probability encompasses data structures and algorithms that have emerged over the past decade that allow researchers and students to focus on a new class of stochastic problems. COMPUTATIONAL PROBABILITY is the first book that examines and presents these computational methods in a systematic manner. The techniques described here address problems that require exact probability calculations, many of which have been considered intractable in the past. The first chapter introduces computational probability analysis, followed by a chapter on the Maple computer algebra system. The third chapter begins the description of APPL, the probability modeling language created by the authors. The book ends with three applications-based chapters that emphasize applications in survival analysis and stochastic simulation.

The algorithmic material associated with continuous random variables is presented separately from the material for discrete random variables. Four sample algorithms, which are implemented in APPL, are presented in detail: transformations of continuous random variables, products of independent continuous random variables, sums of independent discrete random variables, and order statistics drawn from discrete populations.

The APPL computational modeling language gives the field of probability a strong software resource to use for non-trivial problems and is available at no cost from the authors. APPL is currently being used in applications as wide-ranging as electric power revenue forecasting, analyzing cortical spike trains, and studying the supersonic expansion of hydrogen molecules. Requests for the software have come from fields as diverse as market research, pathology, neurophysiology, statistics, engineering, psychology, physics, medicine, and chemistry.

✦ Table of Contents

Front Matter....Pages i-x
Computational Probability....Pages 3-11
Maple for APPL....Pages 13-29
Data Structures and Simple Algorithms....Pages 33-44
Transformations of Random Variables....Pages 45-54
Products of Random Variables....Pages 55-68
Data Structures and Simple Algorithms....Pages 71-90
Sums of Independent Random Variables....Pages 91-118
Order Statistics....Pages 119-131
Reliability and Survival Analysis....Pages 135-151
Stochastic Simulation....Pages 153-183
Other Applications....Pages 185-205
Back Matter....Pages 207-221

✦ Subjects

Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Appl.Mathematics/Computational Methods of Engineering; Computational Mathematics and Numerical Analysis; Statistics for Engineering, Physics, Computer Scien