Abstract
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger’s boundary value problem for stochastic processes in particular.
Highlights
This survey focuses on sequential data assimilation techniques for state and parameter estimation in the context of discrete- and continuous-time stochastic diffusion processes
In addition to surveying recent developments for discrete- and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we provide a unifying framework from the perspective of coupling of measures, and Schrodinger’s boundary value problem for stochastic processes in particular
We find that M ≥ Meff ≥ 1 an√d the accuracy of a data assimilation step decreases with √decreasing Meff, that is, the convergence rate 1/ M of a standard Monte Carlo method is replaced by 1/ Meff (Agapiou, Papaspipliopoulos, Sanz-Alonso and Stuart 2017)
Summary
This survey focuses on sequential data assimilation techniques for state and parameter estimation in the context of discrete- and continuous-time stochastic diffusion processes. We will view such interacting particle systems in this review from the perspective of approximating a certain boundary value problem in the space of probability measures, where the boundary conditions are provided by the underlying stochastic process, the data, and Bayes’ theorem This point of view leads naturally to optimal transportation (Villani 2003, Reich and Cotter 2015) and, more importantly for this review, to Schrodinger’s problem (Follmer and Gantert 1997, Leonard 2014, Chen, Georgiou and Pavon 2014), as formulated first by Erwin Schrodinger in the form of a boundary value problem for Brownian motion (Schrodinger 1931). M , is generally assumed to be small to moderate relative to the number of variables of interest, we will focus on robust but generally biased particle methods
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