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.
From: Matteo Giordano [view email]
[v1]
Thu, 22 May 2025 06:21:29 UTC (579 KB)
[v2]
Thu, 2 Jul 2026 14:50:58 UTC (1,210 KB)
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