Abstract
We obtain rates of contraction of posterior distributions in inverse problems with discrete observations. In a general setting of smoothness scales we derive abstract results for general priors, with contraction rates determined by discrete Galerkin approximation. The rate depends on the amount of prior concentration near the true function and the prior mass of functions with inferior Galerkin approximation. We apply the general result to non-conjugate series priors, showing that these priors give near optimal and adaptive recovery in some generality, Gaussian priors, and mixtures of Gaussian priors, where the latter are also shown to be near optimal and adaptive.
| Original language | English |
|---|---|
| Number of pages | 27 |
| Journal | Sankhya A |
| DOIs | |
| Publication status | Published - 2024 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Keywords
- 35R30
- 62G20
- Adaptive estimation
- Fixed design
- Galerkin
- Gaussian prior
- Hilbert scale
- Interpolation
- Linear inverse problem
- Nonparametric Bayesian estimation
- Posterior contraction rate
- Random series prior
- Regression
- Regularity scale