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Conditional Independence in Applied Probability

  • Paul E. Pfeiffer

Table of contents

  1. Front Matter
    Pages N1-ix
  2. Paul E. Pfeiffer
    Pages 1-17
  3. Paul E. Pfeiffer
    Pages 19-43
  4. Paul E. Pfeiffer
    Pages 45-77
  5. Paul E. Pfeiffer
    Pages 79-112
  6. Paul E. Pfeiffer
    Pages 113-138
  7. Back Matter
    Pages 142-157

About this book

Introduction

It would be difficult to overestimate the importance of stochastic independence in both the theoretical development and the practical appli­ cations of mathematical probability. The concept is grounded in the idea that one event does not "condition" another, in the sense that occurrence of one does not affect the likelihood of the occurrence of the other. This leads to a formulation of the independence condition in terms of a simple "product rule," which is amazingly successful in capturing the essential ideas of independence. However, there are many patterns of "conditioning" encountered in practice which give rise to quasi independence conditions. Explicit and precise incorporation of these into the theory is needed in order to make the most effective use of probability as a model for behavioral and physical systems. We examine two concepts of conditional independence. The first concept is quite simple, utilizing very elementary aspects of probability theory. Only algebraic operations are required to obtain quite important and useful new results, and to clear up many ambiguities and obscurities in the literature.

Keywords

calculus probability probability space probability theory

Authors and affiliations

  • Paul E. Pfeiffer
    • 1
  1. 1.Department of Mathematical SciencesRice UniversityHoustonUSA

Bibliographic information