Probabilistic Programming

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.

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