Computational Probability

Algorithms and Applications in the Mathematical Sciences

  • John H. Drew
  • Diane L. Evans
  • Andrew G. Glen
  • Lawrence M. Leemis

Part of the In Operations Research & Management Science book series (ISOR, volume 117)

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Pages 13-29
  3. Algorithms for Continuous Random Variables

  4. Algorithms for Discrete Random Variables

  5. Applications

  6. Back Matter
    Pages 207-221

About this book

Introduction

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.

Keywords

APPL Maple Random variable Simulation Survival analysis Transformation algorithm algorithms calculus computational probability computer algebra computer algebra system modeling statistics univariate random variables

Authors and affiliations

  • John H. Drew
    • 1
  • Diane L. Evans
    • 2
  • Andrew G. Glen
    • 3
  • Lawrence M. Leemis
    1. 1.College of William and MaryWilliamsburgUSA
    2. 2.Rose-Hulman Institute of TechnologyTerre HauteUSA
    3. 3.United States Military AcademyWest PointUSA

    Bibliographic information

    • DOI https://doi.org/10.1007/978-0-387-74676-0
    • Copyright Information Springer US 2008
    • Publisher Name Springer, Boston, MA
    • eBook Packages Mathematics and Statistics
    • Print ISBN 978-0-387-74675-3
    • Online ISBN 978-0-387-74676-0
    • Series Print ISSN 0884-8289
    • About this book