Related papers: Uncertainty quantification for the horseshoe
We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…
One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian…
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…
Standard evaluations of Bayesian deep learning methods assume that metric estimates are reliable, but we show this assumption fails under data scarcity. Method rankings are not only unreliable at small $n$, but also dataset-dependent in…
Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying…
We investigate the frequentist coverage properties of Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To…
Quantifying uncertainty and updating reliability are essential for ensuring the safety and performance of engineering systems. This study develops a hierarchical Bayesian modeling (HBM) framework to quantify uncertainty and update…
We propose using a Bayes procedure with uniform improper prior to determine credible belts for the mean of a Poisson distribution in the presence of background and for the continuous problem of measuring a non-negative quantity $\theta$…
In a sparse stochastic block model with two communities of unequal sizes we derive two posterior concentration inequalities, that imply (1) posterior (almost-)exact recovery of the community structure under sparsity bounds comparable to…
We study the frequentist properties of Bayesian statistical inference for the stochastic block model, with an unknown number of classes of varying sizes. We equip the space of vertex labellings with a prior on the number of classes and,…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…
This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art…
Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
The horseshoe prior is known to possess many desirable properties for Bayesian estimation of sparse parameter vectors, yet its density function lacks an analytic form. As such, it is challenging to find a closed-form solution for the…
In the context of a vector autoregression (VAR) model, or any multivariate regression model, the number of relevant predictors may be small relative to the information set available from which to build a prediction equation. It is well…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…
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…