Related papers: Uncertainty quantification for the horseshoe

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…

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…

We consider the problem of setting confidence intervals on a parameter of interest from the maximum-likelihood fit of a physics model to a binned data set with a large number of bins, large event-counts per bin, and in the presence of…

We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…

We revisit the problem of simultaneously testing the means of $n$ independent normal observations under sparsity. We take a Bayesian approach to this problem by introducing a scale-mixture prior known as the normal-beta prime (NBP) prior.…

In this paper, we propose a new framework to construct confidence sets for a $d$-dimensional unknown sparse parameter $\theta$ under the normal mean model $X\sim N(\theta,\sigma^2I)$. A key feature of the proposed confidence set is its…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases,…

In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…

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 vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…

The issue of honesty in constructing confidence sets arises in nonparametric regression. While optimal rate in nonparametric estimation can be achieved and utilized to construct sharp confidence sets, severe degradation of confidence level…

Empirical Bayes methods can improve inference on unobservable individual effects by borrowing strength across units. This paper proposes nonparametric empirical Bayes confidence intervals (NP-EBCIs) for unobservable individual effects in a…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

The horseshoe prior, defined as a half Cauchy scale mixture of normal, provides a state of the art approach to Bayesian sparse signal recovery. We provide a new representation of the horseshoe density as a scale mixture of the Laplace…

We present a method for producing unbiased parameter estimates and valid confidence intervals under the constraints of differential privacy, a formal framework for limiting individual information leakage from sensitive data. Prior work in…

Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data generating processes when high-dimensional nuisance models are estimated by post-model-selection or…

We introduce a framework for uncertainty estimation that both describes and extends many existing methods. We consider typical hyperparameters involved in classical training as random variables and marginalise them out to capture various…