Related papers: On Bayesian supremum norm contraction rates

Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…

We investigate Bayesian non-parametric inference of the $\Lambda$-measure of $\Lambda$-coalescent processes with recurrent mutation, parametrised by probability measures on the unit interval. We give verifiable criteria on the prior for…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a…

In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on $[0,1]$. We consider a parametrization of Beta distributions in terms of mean and scale parameters and…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

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 study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…

We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…

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…

The properties of black-hole and neutron-star binaries are extracted from gravitational-wave signals using Bayesian inference. This involves evaluating a multi-dimensional posterior probability function with stochastic sampling. The…

This paper studies quasi Bayesian estimation and uncertainty quantification for an unknown function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors.…

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…

We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…

In this paper, we study frequentist coverage errors of Bayesian credible sets for an approximately linear regression model with (moderately) high dimensional regressors, where the dimension of the regressors may increase with but is smaller…

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…

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to…

We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…

Approximate Bayesian Computation (ABC) is typically used when the likelihood is either unavailable or intractable but where data can be simulated under different parameter settings using a forward model. Despite the recent interest in ABC,…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…