Diffusion bridge with misspecification: theory construction and application to high-resolution fish count data
Abstract
Stochastic processes of bridge types having pinned initial and terminal conditions have been widely used in applied research areas, but they all have a common drawback in that the model at hand is possibly misspecified owing to its stochastic nature; namely, parameter values and coefficients are distorted compared to the ground truth. We consider a pair of novel exactly-solvable optimization problems that provide both the lower and upper bounds of the performance index of a diffusion bridge. Our formulation is based on the Girsanov transformation, in which the model uncertainty is measured through relative entropy. We provide a sufficient condition under which these optimization problems are well-posed, and hence admit the corresponding maximizer/minimizer that achieves the worst-case lower and upper bounds given the ambiguity aversion or uncertainty size. We apply the proposed method to the latest 10-min, high-resolution fish count data of a migratory fish in a river and discuss the influence of model uncertainty on the estimation of the total fish count, which is an important problem in resource and environmental management.
Cite
@article{arxiv.2512.06216,
title = {Diffusion bridge with misspecification: theory construction and application to high-resolution fish count data},
author = {Hidekazu Yoshioka},
journal= {arXiv preprint arXiv:2512.06216},
year = {2025}
}