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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.
This book targets the use of R, which is a GNU project to develop a tool for language and environment for statistical computing and graphics. An IDE is proposed by RStudio. The popularity of R and RStudio make that the reader will find on the web many sites and information about it. A wide literature can also be found about this software. The community of the users of R proposes a large choice of packages to extend the possibilities of R.
The book contains many programs. If you are an expert in R, you will find certainly a large number of improvements to the programs presented. Analogously, the community of the users of R proposes many packages to solve a large number of practical problems and implementing the methods considered in this book. We cite many of them, but – probably, even certainly – not all the existing contributions. The author apologizes in advance to any forgotten contributors, whose works are not cited in the book, but who have made the effort and been kind enough to make their work product available to the community. As mentioned above, we recommend that R users search software repositories such as cran.r-project.org.
In the book Uncertainty Quantification with R, we tried to illustrate the practical use of UQ techniques under R. In this book, the philosophy is the same: we focus on practical aspects, and the theoretical arguments are reduced to the strictly minimal amount necessary to the understanding of the practical methods introduced. We ask for your indulgence on this point – as indicated, we are more concerned with the practical aspects and do not deal with the theoretical aspects in this book – the reader should refer to the texts in the literature to study the mathematical arguments underlying the methods discussed.
Basic Bayesian Probabilities
Beliefs
Information and Entropy
Maximum Entropy
Bayesian Inference
Sequential Bayesian Estimation