Related papers: Bernstein-von Mises theorems and uncertainty quant…

The paper develops Bernstein von Mises Theorem under hierarchical $g$ -priors for linear regression models. The results are obtained both when the error variance is known, and also when it is unknown. An inverse gamma prior is attached to…

We address the problem of uncertainty quantification for the deconvolution model \(Z = X + Y\), where \(X\) and \(Y\) are nonnegative random variables and the goal is to estimate the signal's distribution of \(X \sim F_0\) supported…

We study non-linear Bayesian inverse problems arising from semilinear partial differential equations (PDEs) that can be transformed into linear Bayesian inverse problems. We are then able to extend the early stopping for Ensemble…

I propose a semiparametric Bayesian inference framework for conditional moment equalities. The core idea is that these models deterministically map a conditional distribution of data to a structural parameter via the restriction that a…

The inferential model (IM) framework offers an alternative to the classical probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. A key distinction is that classical uncertainty quantification…

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

Few methods in Bayesian non-parametric statistics/ machine learning have received as much attention as Bayesian Additive Regression Trees (BART). While BART is now routinely performed for prediction tasks, its theoretical properties began…

We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…

This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…

We consider the inverse problem of recovering an unknown functional parameter $u$ in a separable Banach space, from a noisy observation $y$ of its image through a known possibly non-linear ill-posed map ${\mathcal G}$. The data $y$ is…

For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering the conductivity $f>0$ in the divergence form equation $$…

We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is…

In the recent Bayesian nonparametric literature, many examples have been reported in which Bayesian estimators and posterior distributions do not achieve the optimal convergence rate, indicating that the Bernstein-von Mises theorem does not…

We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain…

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…

The paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes formula and the well-posedness of the posterior measure are studied. The abstract…

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

When do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical…

In this paper we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…