Titlebook: Data Assimilation; A Mathematical Intro Kody Law,Andrew Stuart,Konstantinos Zygalakis Textbook 2015 Springer International Publishing Switz

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Candy Arquiett,Mark Gerke,Irene Datskoue subject that is potentially rather technical, a fact that can obscure the structure manifest in the continuous-time formulation. In order to avoid technicalities that can obfuscate the derivations, and in order to create space to highlight the structure present in the continuous-time models, we pr

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Managing & Protecting Our Water Resourceslies in the case of linear dynamics when the initial conditions and the observational noise are Gaussian; the explicit Kalman–Bucy formulas are useful for the building of intuition. In Section?7.2, we discuss MCMC methods to sample from the smoothing distributions of interest. However, as in the dis

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Advanced Technologies in Water TreatmentThe formulation of the data-assimilation problem described in the previous chapter is probabilistic, and its computational resolution requires the probing of a posterior probability distribution on signal-given data.

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Discrete Time: Formulation,In this chapter, we introduce the mathematical framework for discrete-time data assimilation. Section?2.1 describes the mathematical models we use for the underlying signal, which we wish to recover, and for the data, which we use for the recovery.

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Mathematical Background,ata assimilation. In particular, we touch on the subjects of probability, dynamical systems, probability metrics, and dynamical systems for probability measures, in Sections?1.1,?1.2,?1.3, and?1.4 respectively. Our treatment is necessarily terse and very selective, and the bibliography section?1.5 provides references to the literature.

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