LEADER 04295nam 2200601 450 001 9910682585103321 005 20231106111745.0 010 $a3-031-23824-9 024 7 $a10.1007/978-3-031-23824-6 035 $a(MiAaPQ)EBC7211997 035 $a(Au-PeEL)EBL7211997 035 $a(CKB)26257781900041 035 $a(DE-He213)978-3-031-23824-6 035 $a(PPN)269093354 035 $a(EXLCZ)9926257781900041 100 $a20230530d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBayesian scientific computing /$fDaniela Calvetti, Erkki Somersalo 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (295 pages) 225 1 $aApplied mathematical sciences ;$vVolume 215 311 08$aPrint version: Calvetti, Daniela Bayesian Scientific Computing Cham : Springer International Publishing AG,c2023 9783031238239 320 $aIncludes bibliographical references and index. 327 $aInverse 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 -- . 330 $aThe once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider?s view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas. 410 0$aApplied mathematical sciences (Springer-Verlag New York Inc.) ;$vVolume 215. 606 $aBayesian statistical decision theory 606 $aInverse problems (Differential equations)$xNumerical solutions 606 $aEstadística bayesiana$2thub 606 $aProblemes inversos (Equacions diferencials)$2thub 606 $aSolucions numèriques$2thub 608 $aLlibres electrònics$2thub 615 0$aBayesian statistical decision theory. 615 0$aInverse problems (Differential equations)$xNumerical solutions. 615 7$aEstadística bayesiana 615 7$aProblemes inversos (Equacions diferencials) 615 7$aSolucions numèriques 676 $a519.542 700 $aCalvetti$b Daniela$0524724 702 $aSomersalo$b Erkki 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910682585103321 996 $aBayesian scientific computing$93291891 997 $aUNINA