Vajda / Birnbaum / Lukacs Probabilistic Programming

1. Auflage 2014
ISBN: 978-1-4832-6837-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 140 Seiten, Web PDF

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.

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

Autoren/Hrsg.

Vajda, S.

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Probabilistic Programming;4
3;Copyright Page;5
4;Table of Contents;6
5;Introduction;8
6;Chapter I. Stochastic Programming;14
6.1;Parameters;14
6.2;Feasibility and Convexity;15
6.3;Kall's Theorem;18
6.4;Optimality and Convexity;21
6.5;Decision Regions for Optimality;25
6.6;Approximations;27
6.7;Inequalities;30
6.8;Probability Distributions;31
7;Chapter II. Decision Problems;36
7.1;A Decision Problem;36
7.2;The Active Approach;37
7.3;Two-Stage Programming under Uncertainty;40
7.4;The Complete Problem;42
7.5;Examples;48
7.6;Discrete Values of bi;55
7.7;The General Case, b Stochastic;57
7.8;Feasibility;58
7.9;Optimality;61
7.10;The General Case, A and b Stochastic;64
7.11;The General Case, b, A, and B Stochastic;67
7.12;Inequalities;69
7.13;Appendix;84
8;Chapter III. Chance Constraints;88
8.1;Quantile Rules;91
8.2;Joint Probability;101
8.3;Randomized Decisions;103
8.4;P-Model;105
8.5;Nonzero Order Rules;111
8.6;Conditional Quantiles;114
9;Appendix I: Linear Programming and Duality;118
10;Appendix II: Applications of Stochastic (Probabilistic) Programming in Various Fields (References);128
11;References;131
12;Index;138