Sequential Monte Carlo Methods for Bayesian Elliptic Inverse Problems

Beskos, Alex; Jasra, Ajay; Muzaffer, Ege; Stuart, Andrew M.

doi:10.48550/arxiv.1412.4459

Cited by 1 publication

(1 citation statement)

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“…The method is introduced for Bayesian inverse problems in [18] where it is used to study the problem of inferring the initial condition of the Navier-Stokes equations from data. In [4] the method is applied to the inverse problem of determining the coefficient of a divergence form elliptic PDE from linear functionals of the solution; furthermore the method is also proved to converge in the large particle limit J → ∞.…”

Section: The Enkf For Inverse Problemsmentioning

confidence: 99%

Analysis of the Ensemble Kalman Filter for Inverse Problems

Schillings¹,

Stuart²

2017

SIAM J. Numer. Anal.

195

358

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Abstract. The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous-time limit is derived and the long-time behavior of the resulting dynamical system is studied. Most of the rigorous analysis is confined to the linear forward problem, where we demonstrate that the continuous time limit of the EnKF corresponds to a set of gradient flows for the data misfit in each ensemble member, coupled through a common pre-conditioner which is the empirical covariance matrix of the ensemble. Numerical results demonstrate that the conclusions of the analysis extend beyond the linear inverse problem setting. Numerical experiments are also given which demonstrate the benefits of various extensions of the basic methodology.

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Section: The Enkf For Inverse Problemsmentioning

confidence: 99%