Misspecified Bernstein–von Mises theorem for hierarchical models
Abstract
We derive a Bernstein von-Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrized by a finite-dimensional parameter of interest. We apply our results to hierarchical models containing non-linear operators, including the squared integral operator, and PDE-constrained inverse problems. More specifically, we consider the elliptic, time-independent Schrödinger equation with parametric boundary condition and general parabolic PDEs with parametric potential and boundary constraints. Our theoretical results are complemented with numerical analysis on synthetic data sets, considering both the square integral operator and the Schrödinger equation.
Fields of Study & Subjects
Numerical methods in inverse problems
Statistical Mechanics and Entropy
Model Reduction and Neural Networks
Publication details
- Journal / source
- Bernoulli
- Publisher
- Bernoulli Society for Mathematical Statistics and Probability
- Volume
- 32
- Issue
- 3
- Pages
- 1975-2000
- Publication date
- 29 April 2026
- Language
- EN