Misspecified Bernstein-Von Mises theorem for hierarchical models
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913873154539520 |
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| author | Koers, Geerten Szabó, Botond van der Vaart, Aad |
| author_facet | Koers, Geerten Szabó, Botond van der Vaart, Aad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07803 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Misspecified Bernstein-Von Mises theorem for hierarchical models Koers, Geerten Szabó, Botond van der Vaart, Aad Statistics Theory 62F15 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. |
| title | Misspecified Bernstein-Von Mises theorem for hierarchical models |
| topic | Statistics Theory 62F15 |
| url | https://arxiv.org/abs/2308.07803 |