2021/07/30 by Dirk Blömker, Claudia Schillings, Blömker, Dirk +5 · 1 citation
Computer Science · Environmental Science · Mathematics · #62F15 #65C30 #65N21 #65N75 #90C56 #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Numerical Analysis (math.NA) #Soil Geostatistics and Mapping #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.2107.14508
openalex publication_date 2021/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively applies the ensemble Kalman update to evolve (the approximation of the) prior into the posterior measure. For the convergence analysis of the EKI it is common practice to derive a continuous version, replacing the iteration with a stochastic differential equation. In this paper we validate this approach by showing that the stochastic EKI iteration converges to paths of the continuous-time stochastic differential equation by considering both the nonlinear and linear setting, and we prove convergence in probability for the former, and convergence in moments for the latter. The methods employed can also be applied to the analysis of more general numerical schemes for stochastic differential equations in general.