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1st Edition - January 28, 1972
Author: S. Vajda
Editors: Z. W. Birnbaum, E. Lukacs
9 7 8 - 1 - 4 8 3 2 - 6 8 3 7 - 8
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… Read more
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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.
IntroductionI. Stochastic Programming Parameters Feasibility and Convexity Kall's Theorem Optimality and Convexity Decision Regions for Optimality Approximations Inequalities Probability DistributionsII. Decision Problems A Decision Problem The Active Approach Two-Stage Programming Under Uncertainty The Complete Problem Examples Discrete Values of bi The General Case, b Stochastic Feasibility Optimality The General Case, A and b Stochastic The General Case, b, A, and B Stochastic Inequalities AppendixIII. Chance Constraints Quantile Rules Joint Probability Randomized Decisions P-Model Nonzero Order Rules Conditional QuantilesAppendix I Linear Programming and DualityAppendix II Applications of Stochastic (Probabilistic) Programming in Various Fields (References)ReferencesIndex
No. of pages: 140
Published: January 28, 1972
Imprint: Academic Press
eBook ISBN: 9781483268378
Affiliations and expertise
Bowling Green State University
Steven Vajda, Visiting Professor at Sussex University, formerly Professor of Operational Research, Department of Engineering Production, University of Birmingham.