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Titlebook: Bayesian Scientific Computing; Daniela Calvetti,Erkki Somersalo Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive

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发表于 2025-3-21 19:01:48 | 显示全部楼层 |阅读模式
期刊全称Bayesian Scientific Computing
影响因子2023Daniela Calvetti,Erkki Somersalo
视频video
发行地址Provides accessible exposition.Presents work of internationally known authors.Includes supplementary material
学科分类Applied Mathematical Sciences
图书封面Titlebook: Bayesian Scientific Computing;  Daniela Calvetti,Erkki Somersalo Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive
影响因子.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 ti
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发表于 2025-3-21 22:16:14 | 显示全部楼层
Linear Algebra,or dealing with multidimensional phenomena, including multivariate statistics that without this language would become awkward and cumbersome. Instead of collecting all the linear algebra definitions and results that will be needed in a comprehensive primer, we introduce them gradually throughout the
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The Praise of Ignorance: Randomnessas Lack of Certainty,tion and indirect observations. We adopt here the Bayesian point of view: Any quantity that is not known exactly, in the sense that a value can be attached to it with no uncertainty, is modeled as a random variable. In this sense, randomness means lack of certainty. The subjective part of this appro
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Posterior Densities, Ill-Conditioning,and Classical Regularization,er in the Bayesian play of inverse problems, the posterior distribution, and in particular, the posterior density. Bayes’ formula is the way in which prior and likelihood combine into the posterior density. In this chapter, we show through some examples how to explore and analyze posterior distribut
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Sampling: The Real Thing,d to calculate estimates of integrals via Monte Carlo integration. It was also indicated that sampling from a non-Gaussian probability density may be a challenging task. In this section we further develop the topic and introduce Markov chain Monte Carlo (MCMC) sampling.
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Dynamic Methods and Learning from the Past,an essay on Bayes’ work, in which he asked how to assign a subjective probability to the sunrise, given that the sun had been observed to rise a given number of times before. Price’s idea is that we learn from earlier experiences, and update our expectations based on them. The question was revisited
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