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07/16/2023
On posterior consistency of data assimilation with Gaussian process priors: the 2D Navier-Stokes equations
We consider a non-linear Bayesian data assimilation model for the period...
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10/24/2022
Inference for diffusions from low frequency measurements
Let (X_t) be a reflected diffusion process in a bounded convex domain in...
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09/05/2022
On free energy barriers in Gaussian priors and failure of MCMC for high-dimensional unimodal distributions
We exhibit examples of high-dimensional unimodal posterior distributions...
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07/20/2021
On some information-theoretic aspects of non-linear statistical inverse problems
Results by van der Vaart (1991) from semi-parametric statistics about th...
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05/17/2021
On log-concave approximations of high-dimensional posterior measures and stability properties in non-linear inverse problems
The problem of efficiently generating random samples from high-dimension...
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09/11/2020
On polynomial-time computation of high-dimensional posterior measures by Langevin-type algorithms
The problem of generating random samples of high-dimensional posterior d...
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07/31/2020
Statistical guarantees for Bayesian uncertainty quantification in non-linear inverse problems with Gaussian process priors
Bayesian inference and uncertainty quantification in a general class of ...
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10/16/2019
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 cons...
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06/08/2019
On statistical Calderón problems
For D a bounded domain in R^d, d > 3, with smooth boundary ∂ D, the non...
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05/02/2019
Consistent Inversion of Noisy Non-Abelian X-Ray Transforms
For M a simple surface, the non-linear and non-convex statistical invers...
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10/03/2018
Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions
The problem of determining a periodic Lipschitz vector field b=(b_1, ......
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09/24/2018