Nudging state-space models for Bayesian filtering under misspecified dynamics Articles uri icon

publication date

  • June 2025

start page

  • 112-1

end page

  • 112-25

volume

  • 35

International Standard Serial Number (ISSN)

  • 0960-3174

Electronic International Standard Serial Number (EISSN)

  • 1573-1375

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.

subjects

  • Telecommunications

keywords

  • nudging; bayesian filter; misspecified dynamics