Robust parameter estimation using the ensemble Kalman filter

TL;DR

This paper investigates the robustness of parameter estimation in stochastic differential equations using ensemble Kalman filters, highlighting limitations of traditional methods and exploring alternative robust techniques.

Contribution

It provides an elementary explanation for robustness issues and analyzes three robust estimation methods from a frequentist perspective.

Findings

Standard methods lack robustness to data perturbations.

Subsampling, rough path corrections, and data filtering improve robustness.

Numerical experiments demonstrate the effectiveness of these techniques.

Abstract

Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this observation in the context of continuous-time parameter estimation using an ensemble Kalman filter. We employ the frequentist perspective to shed new light on three robust estimation techniques; namely subsampling the data, rough path corrections, and data filtering. We illustrate our findings through a simple numerical experiment.