Related papers: Semiparametric Bernstein-von Mises Theorem: Second…

The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…

Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…

We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of…

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we…

We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including…

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…

The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random variables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods…

We investigate the asymptotic behavior of parametric Bayes estimators under a broad class of loss functions that extend beyond the classical translation-invariant setting. To this end, we develop a unified theoretical framework for loss…

This work is concerned with nonparametric goodness-of-fit testing in the context of nonlinear inverse problems with random observations. Bayesian posterior distributions based upon a Gaussian process prior distribution are proven to…

Good large sample performance is typically a minimum requirement of any model selection criterion. This article focuses on the consistency property of the Bayes factor, a commonly used model comparison tool, which has experienced a recent…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

In Generalised Bayesian Inference (GBI), the learning rate and hyperparameters of the loss must be estimated. These inference-hyperparameters can't be estimated jointly with the other parameters, from the data, by giving them a prior.…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

The features in high dimensional biomedical prediction problems are often well described with lower dimensional manifolds. An example is genes that are organised in smaller functional networks. The outcome can then be described with the…

Given data from a Poisson point process with intensity $(x,y) \mapsto n \mathbf{1}(f(x)\leq y),$ frequentist properties for the Bayesian reconstruction of the support boundary function $f$ are derived. We mainly study compound Poisson…