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Bayesian scientific computing

Calvetti, Daniela.

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Bayesian scientific computing

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bayesian scientific computing/ by Daniela Calvetti, Erkki Somersalo.
Author:	Calvetti, Daniela.
other author:	Somersalo, Erkki.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xvii, 286 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Inverse problems (Differential equations) - Numerical solutions. -
Online resource:	https://doi.org/10.1007/978-3-031-23824-6
ISBN:	9783031238246

Bayesian scientific computing
Calvetti, Daniela.

Bayesian scientific computing[electronic resource] /by Daniela Calvetti, Erkki Somersalo. - Cham :Springer International Publishing :2023. - xvii, 286 p. :ill. (some col.), digital ;24 cm. - Applied mathematical sciences,v. 2152196-968X ;. - Applied mathematical sciences ;v. 215..

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.

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.

ISBN: 9783031238246

Standard No.: 10.1007/978-3-031-23824-6doiSubjects--Topical Terms:

555563
Inverse problems (Differential equations)
--Numerical solutions.

LC Class. No.: QA371

Dewey Class. No.: 515.357

Bayesian scientific computing
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245 1 0 $a Bayesian scientific computing $h [electronic resource] / $c by Daniela Calvetti, Erkki Somersalo.
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300 $a xvii, 286 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 2196-968X ; $v v. 215
505 0 $a 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.
520 $a 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.
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650 0 $a Bayesian statistical decision theory. $3 551404
650 1 4 $a Computational Science and Engineering. $3 893018
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
650 2 4 $a Linear Algebra. $3 3338825
650 2 4 $a Mathematics of Computing. $3 891213
700 1 $a Somersalo, Erkki. $3 752080
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950 $a Mathematics and Statistics (SpringerNature-11649)