Redesigning the ensemble Kalman filter with a dedicated model of epistemic uncertainty
Chatchuea Kimchaiwong, Jeremie Houssineau, Adam M. Johansen
TL;DR
The paper tackles sequential state estimation when epistemic uncertainty dominates, proposing a possibilistic ensemble Kalman filter (p-EnKF) grounded in possibility theory. By representing uncertainty with Gaussian possibility functions and using an ensemble of weighted particles, the method derives a Kalman-like prediction and an update that mirror the SqrtEnKF, while naturally incorporating inflation and localisation through constrained optimization on the ensemble. The authors develop a rigorous approach to fitting a Gaussian possibility function to an ensemble, leverage transport maps for deterministic prediction, and show that the p-EnKF can outperform standard EnKF variants in small-sample regimes while remaining robust under nonlinearity and partial observation. The results on linear and Lorenz-96–type models demonstrate strong uncertainty quantification, with practical benefits for data assimilation where epistemic uncertainty is prominent, and point to scalable extensions via sparse precision structures and direct precision-matrix updates.
Abstract
The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering techniques. However, in many real-world problems, some (or all) of the uncertainty is epistemic, arising from a lack of knowledge, and is difficult to model probabilistically. This paper introduces a possibilistic ensemble Kalman filter designed for this setting and characterizes some of its properties. Using possibility theory to describe epistemic uncertainty is appealing from a philosophical perspective, and it is easy to justify certain heuristics often employed in standard ensemble Kalman filters as principled approaches to capturing uncertainty within it. The possibilistic approach motivates a robust mechanism for characterizing uncertainty which shows good performance with small sample sizes, and can outperform standard ensemble Kalman filters at given sample size, even when dealing with genuinely aleatoric uncertainty.