Full Description
This book is a rigorous but practical presentation of the techniques of uncertainty quantification, with applications in R and Python. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R and Python allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems.
The list of topics covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi-objective optimization, game theory, as well as linear algebraic equations, and probability and statistics. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.
Contents
1. Introduction.- 2. Some tips to use R and RStudio.- 3. Probabilities and Random Variables.- 4. Representation of random variables.- 5. Stochastic processes.- 6. Uncertain Algebraic Equations.- 7. Random Differential Equations.- 8. UQ in Game Theory.- 9. Optimization under uncertainty.- 10. Reliability.
