Nudging state-space models for Bayesian filtering under misspecified dynamics
File(s)
Published version
Author(s)
Gonzalez, Fabian
Akyildiz, O Deniz
Crisan, Dan
Miguez, Joaquin
Type
Journal Article
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.
Date Issued
2025-06-05
Date Acceptance
2025-05-20
Citation
Statistics and Computing, 2025, 35
ISSN
0960-3174
Publisher
Springer
Journal / Book Title
Statistics and Computing
Volume
35
Copyright Statement
© The Author(s) 2025 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s11222-025-10648-0
Subjects
Bayesian filtering
Nudging
Bayesian evidence
Marginal likelihood
Model mismatch
Misspecified dynamics
Publication Status
Published
Article Number
112
Date Publish Online
2025-06-05