# Laplace priors and spatial inhomogeneity in Bayesian inverse problems

@inproceedings{Agapiou2021LaplacePA, title={Laplace priors and spatial inhomogeneity in Bayesian inverse problems}, author={Sergios Agapiou and Sven Wang}, year={2021} }

Spatially inhomogeneous functions, which may be smooth in some regions and rough in other regions, are modelled naturally in a Bayesian manner using so-called Besov priors which are given by random wavelet expansions with Laplace-distributed coefficients. This paper studies theoretical guarantees for such prior measures – specifically, we examine their frequentist posterior contraction rates in the setting of non-linear inverse problems with Gaussian white noise. Our results are first derived…

## 2 Citations

On the inability of Gaussian process regression to optimally learn compositional functions

- Computer Science, Mathematics
- 2022

We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower…

Nonparametric Bayesian inference for reversible multi-dimensional diffusions

- MathematicsArXiv
- 2020

Nonparametric Bayesian modelling of reversible multi-dimensional diffusions with periodic drift is studied to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure.

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