Titlebook: Stochastic Methods for Modeling and Predicting Complex Dynamical Systems; Uncertainty Quantifi Nan Chen Textbook 2023 The Editor(s) (if app

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Conditional Gaussian Nonlinear Systems,s of nonlinear models, where the joint and marginal distributions can both be highly non-Gaussian, but the conditional distributions of certain variables are Gaussian. The conditional Gaussianity allows using closed analytic formulae to solve nonlinear data assimilation problems that significantly f

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Parameter Estimation with Uncertainty Quantification, applied to estimate model parameters utilizing the Metropolis-Hastings algorithm. Next, the expectation-maximization (EM) algorithm is described, aiming to estimate model parameters with partial observations. The EM algorithm alternates between estimating the parameters via maximum likelihood estim

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Combining Stochastic Models with Machine Learning,t combine stochastic models with machine learning to advance the understanding and forecast of many complex dynamical systems. Machine learning can serve as the surrogate forecast model in data assimilation to improve the efficiency and accuracy of the ensemble forecast. Reciprocally, data assimilat

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Data Assimilation,and applications of these methods are discussed. The continuous version of the Kalman filter, namely the Kalman-Bucy filter, and other data assimilation techniques, such as the smoother, and their applications are briefly studied at the end of this chapter.

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978-3-031-22251-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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