Nudging state-space models for Bayesian filtering under misspecified dynamics

TL;DR

This paper shows that nudging techniques can improve Bayesian filtering by implicitly creating more robust state-space models that better handle misspecified dynamics, with theoretical and empirical support.

Contribution

It introduces a theoretical framework linking nudging to likelihood improvement and demonstrates its effectiveness in robust filtering under model misspecification.

Findings

Nudging increases the marginal likelihood of observations.

Nudging provides robustness in filtering with misspecified models.

Numerical experiments confirm improved performance with nudging.

Abstract

Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that general nudging techniques can also tackle another crucial statistical problem in filtering, namely the misspecification of the transition kernel. Specifically, we rely on the formulation of nudging as a general operation increasing the likelihood and prove analytically that, when applied carefully, nudging techniques implicitly define state-space models that have higher marginal likelihoods for a given (fixed) sequence of observations. This provides a theoretical justification of nudging techniques as data-informed algorithmic modifications of state-space models to obtain robust models under misspecified dynamics. To demonstrate the use of nudging, we provide numerical experiments on linear Gaussian state-space models and a stochastic Lorenz 63 model with misspecified dynamics and show that nudging offers a robust filtering strategy for these cases.