Applied mathematical sciences (Springer-Verlag New York Inc.) ; Volume 215. [More in this series]
Applied mathematical sciences ; Volume 215
Summary note
The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider’s view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.
Bibliographic references
Includes bibliographical references and index.
Source of description
Description based on print version record.
Contents
Inverse problems and subjective computing
Linear algebra
Continuous and discrete multivariate distributions
Introduction to sampling
The praise of ignorance: randomness as lack of certainty
Enter subject: Construction of priors
Posterior densities, ill-conditioning, and classical regularization
Conditional Gaussian densities
Iterative linear solvers and priorconditioners
Hierarchical models and Bayesian sparsity
Sampling: the real thing
Dynamic methods and learning from the past
Bayesian filtering and Gaussian densities
.
ISBN
3-031-23824-9
Doi
10.1007/978-3-031-23824-6
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