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arXiv · 2505.16275

Semiparametric Bernstein-von Mises theorems for reversible diffusions

Matteo Giordano·Kolyan Ray
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Abstract

We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals satisfying an approximate linearization condition, including several nonlinear functionals of the invariant measure. Our result is applied to Gaussian and Besov-Laplace priors, showing these can perform efficient semiparametric inference and thus justifying the corresponding Bayesian approach to uncertainty quantification. Our theoretical results are illustrated via numerical simulations.

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Matteo Giordano, Kolyan Ray. 2025-05-22. Semiparametric Bernstein-von Mises theorems for reversible diffusions. https://arxiv.org/abs/2505.16275

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