
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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Continuum Limit of Posteriors in Graph Bayesian Inverse Problems
We consider the problem of recovering a function input of a differential...
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Posterior Contraction Rates for Gaussian Cox Processes with Nonidentically Distributed Data
This paper considers the posterior contraction of nonparametric Bayesia...
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Consistent Inversion of Noisy NonAbelian XRay Transforms
For M a simple surface, the nonlinear and nonconvex statistical invers...
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Nonparametric Bayesian estimation of multivariate Hawkes processes
This paper studies nonparametric estimation of parameters of multivariat...
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Convergence rates for Penalised Least Squares Estimators in PDEconstrained regression problems
We consider PDE constrained nonparametric regression problems in which t...
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Posterior Consistency of Bayesian Inverse Regression and Inverse Reference Distributions
We consider Bayesian inference in inverse regression problems where the ...
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Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem
We consider the statistical nonlinear inverse problem of recovering the absorption term f>0 in the heat equation ∂_tu1/2Δ u+fu=0 on 𝒪×(0,T) u = g on ∂𝒪×(0,T) u(·,0)=u_0 on 𝒪, where 𝒪∈ℝ^d is a bounded domain, T<∞ is a fixed time, and g,u_0 are given sufficiently smooth functions describing boundary and initial values respectively. The data consists of N discrete noisy point evaluations of the solution u_f on 𝒪×(0,T). We study the statistical performance of Bayesian nonparametric procedures based on a large class of Gaussian process priors. We show that, as the number of measurements increases, the resulting posterior distributions concentrate around the true parameter generating the data, and derive a convergence rate for the reconstruction error of the associated posterior means. We also consider the optimality of the contraction rates and prove a lower bound for the minimax convergence rate for inferring f from the data, and show that optimal rates can be achieved with truncated Gaussian priors.
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