Probabilistic Programming

Probabilistic Programming

1st Edition - January 28, 1972

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  • Author: S. Vajda
  • eBook ISBN: 9781483268378

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Probabilistic Programming discusses a high-level language known as probabilistic programming. This book consists of three chapters. Chapter I deals with “wait-and-see” problems that require waiting until an observation is made on the random elements, while Chapter II contains the analysis of decision problems, particularly of so-called two-stage problems. The last chapter focuses on “chance constraints,” such as constraints that are not expected to be always satisfied, but only in a proportion of cases or “with given probabilities.” This text specifically deliberates the decision regions for optimality, probability distributions, Kall's Theorem, and two-stage programming under uncertainty. The complete problem, active approach, quantile rules, randomized decisions, and nonzero order rules are also covered. This publication is suitable for developers aiming to define and automatically solve probability models.

Table of Contents

  • Introduction

    I. Stochastic Programming


    Feasibility and Convexity

    Kall's Theorem

    Optimality and Convexity

    Decision Regions for Optimality



    Probability Distributions

    II. Decision Problems

    A Decision Problem

    The Active Approach

    Two-Stage Programming Under Uncertainty

    The Complete Problem


    Discrete Values of bi

    The General Case, b Stochastic



    The General Case, A and b Stochastic

    The General Case, b, A, and B Stochastic



    III. Chance Constraints

    Quantile Rules

    Joint Probability

    Randomized Decisions


    Nonzero Order Rules

    Conditional Quantiles

    Appendix I

    Linear Programming and Duality

    Appendix II

    Applications of Stochastic (Probabilistic) Programming in Various Fields (References)



Product details

  • No. of pages: 140
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: January 28, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9781483268378

About the Author

S. Vajda

Steven Vajda, Visiting Professor at Sussex University, formerly Professor of Operational Research, Department of Engineering Production, University of Birmingham.

Affiliations and Expertise

Mount Sinai School of Medicine, New York, NY, USA

About the Editors

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University

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