Related papers: Bayesian inverse problems with non-conjugate prior…

In this work, we analyze the regularizing property of the stochastic gradient descent for the efficient numerical solution of a class of nonlinear ill-posed inverse problems in Hilbert spaces. At each step of the iteration, the method…

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…

We derive the posterior contraction rate for non-parametric Bayesian estimation of the intensity function of a Poisson point process.

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study…

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and…

We study the problem of nonparametric regression when the regressor is endogenous, which is an important nonparametric instrumental variables (NPIV) regression in econometrics and a difficult ill-posed inverse problem with unknown operator…

Constrained learning is prevalent in many statistical tasks. Recent work proposes distance-to-set penalties to derive estimators under general constraints that can be specified as sets, but focuses on obtaining point estimates that do not…

Frequentist conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate the flexibility in criteria…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

In this article, we investigate posterior convergence of nonparametric binary and Poisson regression under possible model misspecification, assuming general stochastic process prior with appropriate properties. Our model setup and objective…

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…

The major goal of this paper is to study the second order frequentist properties of the marginal posterior distribution of the parametric component in semiparametric Bayesian models, in particular, a second order semiparametric…

In recent years, a series of convergence rates conditions for regularization methods has been developed. Mainly, the motivations for developing novel conditions came from the desire to carry over convergence rates results from the Hilbert…

We describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental result, the minimax rate on ellipsoids, is proved similarly to…

In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…

We study the posterior distribution of the Bayesian multiple change-point regression problem when the number and the locations of the change-points are unknown. While it is relatively easy to apply the general theory to obtain the…