Nudging state-space models for Bayesian filtering under misspecified dynamics
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...
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Zusammenfassung: | 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
model. 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 (SSMs) 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 SSMs to obtain robust models under
misspecified dynamics. To demonstrate the use of nudging, we provide numerical
experiments on linear Gaussian SSMs and a stochastic Lorenz 63 model with
misspecified dynamics and show that nudging offers a robust filtering strategy
for these cases. |
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DOI: | 10.48550/arxiv.2411.00218 |