Related papers: Bayesian linear inverse problems in regularity sca…

We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many'…

We consider a Bayesian hierarchical version of the normal theory general linear model which is practically relevant in the sense that it is general enough to have many applications and it is not straightforward to sample directly from the…

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…

We construct optimal low-rank approximations for the Gaussian posterior distribution in linear Gaussian inverse problems with possibly infinite-dimensional separable Hilbert parameter spaces and finite-dimensional data spaces. We first…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…

We consider the Bayesian inverse homogenization problem of recovering the locally periodic two scale coefficient of a two scale elliptic equation, given limited noisy information on the solution. We consider both the uniform and the…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score…

Piecewise constant priors are routinely used in the Bayesian Cox proportional hazards model for survival analysis. Despite its popularity, large sample properties of this Bayesian method are not yet well understood. This work provides a…

Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data…

We present a new class of prior measures in connection to $\ell_p$ regularization techniques when $p \in(0,1)$ which is based on the generalized Gamma distribution. We show that the resulting prior measure is heavy-tailed, non-convex and…

We develop a fully intrinsic Bayesian framework for nonparametric regression on the unit sphere based on isotropic Gaussian field priors and the harmonic structure induced by the Laplace-Beltrami operator. Under uniform random design, the…

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and…

We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…