
Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem
We consider the statistical nonlinear inverse problem of recovering the ...
read it

Consistent Inversion of Noisy NonAbelian XRay Transforms
For M a simple surface, the nonlinear and nonconvex statistical invers...
read it

On statistical Calderón problems
For D a bounded domain in R^d, d > 3, with smooth boundary ∂ D, the non...
read it

Posterior Consistency of Bayesian Inverse Regression and Inverse Reference Distributions
We consider Bayesian inference in inverse regression problems where the ...
read it

Continuum Limit of Posteriors in Graph Bayesian Inverse Problems
We consider the problem of recovering a function input of a differential...
read it

Efficient Bayesian shaperestricted function estimation with constrained Gaussian process priors
This article revisits the problem of Bayesian shaperestricted inference...
read it

Posterior inference unchained with EL_2O
Statistical inference of analytically nontractable posteriors is a diff...
read it
Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
For O a bounded domain in R^d and a given smooth function g:O→R, we consider the statistical nonlinear inverse problem of recovering the conductivity f>0 in the divergence form equation ∇·(f∇ u)=g on O, u=0 on ∂O, from N discrete noisy point evaluations of the solution u=u_f on O. We study the statistical performance of Bayesian nonparametric procedures based on a flexible class of Gaussian (or hierarchical Gaussian) process priors, whose implementation is feasible by MCMC methods. We show that, as the number N of measurements increases, the resulting posterior distributions concentrate around the true parameter generating the data, and derive a convergence rate N^λ, λ>0, for the reconstruction error of the associated posterior means, in L^2(O)distance.
READ FULL TEXT
Comments
There are no comments yet.