
Probabilistic Programming
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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
Parameters
Feasibility and Convexity
Kall's Theorem
Optimality and Convexity
Decision Regions for Optimality
Approximations
Inequalities
Probability Distributions
II. 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
Appendix
III. Chance Constraints
Quantile Rules
Joint Probability
Randomized Decisions
P-Model
Nonzero Order Rules
Conditional Quantiles
Appendix I
Linear Programming and Duality
Appendix II
Applications of Stochastic (Probabilistic) Programming in Various Fields (References)
References
Index
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