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2024 | Buch

Basic Bayesian Probabilities Kapitel lesen Erstes Kapitel lesen

Uncertainty Quantification with R

Bayesian Methods

verfasst von: Eduardo Souza de Cursi

Verlag: Springer Nature Switzerland

Buchreihe : International Series in Operations Research & Management Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book is a rigorous but practical presentation of the Bayesian techniques of uncertainty quantification, with applications in R. 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 Bayesian uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R 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 basic Bayesian probabilities, entropy, Bayesian estimation and decision, sequential Bayesian estimation, and numerical methods. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of Bayesian uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Basic Bayesian Probabilities
Abstract
This chapter contains a historical introduction and presents the basic elements of the Bayesian approach in probabilities, namely, the notions of exchangeability and De Finetti’s theorem. The combination of uncertainty quantification techniques and Bayesian procedures is introduced, namely, for the practical use of De Finetti’s theorem. Programs in R implement the elements introduced, namely, the representation of probability spaces and De Finetti’s theorem. Their use is exemplified.
Eduardo Souza de Cursi
Chapter 2. Beliefs
Abstract
This chapter presents the Dempster-Shafer theory of beliefs and plausibility, which can be seen as a formalism for the interpretation of probabilities in terms of degrees of belief. The basic notions are presented, with their implementation in R. It also explores the connections between beliefs and probabilities. Programs in R implement all the elements introduced, and their use is exemplified.
Eduardo Souza de Cursi
Chapter 3. Information and Entropy
Abstract
This chapter presents the notions connected to Shannon’s entropy and information, namely the joint, conditional, relative (Kullback–Leibler) entropies, and the mutual information, with their implementations in R. Applications to surprise quantification are shown, with their implementation in R. Examples show the use of the programs presented.
Eduardo Souza de Cursi
Chapter 4. Maximum Entropy
Abstract
This chapter presents the principle of maximum entropy, which furnishes a practical method for the generation of distributions. The representation of stochastic processes by Karhunen-Loève expansions is presented, including their combination with Hilbert’s approach of uncertainty quantification. Implementations in R are given, and their use is exemplified.
Eduardo Souza de Cursi
Chapter 5. Bayesian Inference
Abstract
This chapter presents the Bayesian approach for practical tasks, such as estimation, hypothesis testing, model or variable selection, and regression. The choice of priors is analyzed, by using Jeffreys approach and uncertainty quantification techniques. The Expectation-Maximization Algorithm is presented in this chapter. Implementations in R are given for all the topics, with examples of use.
Eduardo Souza de Cursi
Chapter 6. Sequential Bayesian Estimation
Abstract
This chapter presents Monte-Carlo Markov Chain methods and connected topics, namely Importance Sampling, Metropolis-Hastings Algorithm, Kalman Filtering, Particle Filtering, and Bayesian Optimization. The use of UQ for the determination of the distribution of the noise is presented. Programs in R implement all the topics introduced, with examples of use.
Eduardo Souza de Cursi
Backmatter
Metadaten
Titel
Uncertainty Quantification with R
verfasst von
Eduardo Souza de Cursi
Copyright-Jahr
2024
Electronic ISBN
978-3-031-48208-3
Print ISBN
978-3-031-48207-6
DOI
https://doi.org/10.1007/978-3-031-48208-3

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