Related papers: Frequentist coverage of adaptive nonparametric Bay…

We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…

The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…

For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-\alpha)%$ Bayesian HPD credible set associated with priors which are truncations of…

This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…

We consider the nonparametric multivariate isotonic regression problem, where the regression function is assumed to be nondecreasing with respect to each predictor. Our goal is to construct a Bayesian credible interval for the function…

This article illustrates how indirect or prior information can be optimally used to construct a prediction region that maintains a target frequentist coverage rate. If the indirect information is accurate, the volume of the prediction…

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…

Rejoinder of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

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…

Uncertainty quantification for complex deep learning models is increasingly important as these techniques see growing use in high-stakes, real-world settings. Currently, the quality of a model's uncertainty is evaluated using…

In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

Bayesian composite likelihood estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed under Jeffrey's prior…

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…

We study Bayesian posterior consistency in parametric density models with proper priors, challenging the perception that the problem is settled. Classical results established consistency via MLE convergence under regularity and…

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…

A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics.

We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…

In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…