Related papers: Uncertainty quantification for the horseshoe
Confidence intervals based on penalized maximum likelihood estimators such as the LASSO, adaptive LASSO, and hard-thresholding are analyzed. In the known-variance case, the finite-sample coverage properties of such intervals are determined…
Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…
For civil structures, structural damage due to severe loading events such as earthquakes, or due to long-term environmental degradation, usually occurs in localized areas of a structure. A new sparse Bayesian probabilistic framework for…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…
This paper develops a Hierarchical Bayesian Modeling (HBM) framework for uncertainty quantification of Finite Element (FE) models based on modal information. This framework uses an existing Fast Fourier Transform (FFT) approach to identify…
Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of…
Most NLP datasets are not annotated with protected attributes such as gender, making it difficult to measure classification bias using standard measures of fairness (e.g., equal opportunity). However, manually annotating a large dataset…
Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso,…
For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage…
Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds for the sparsity regimes where edge probabilities decrease as $O(\log(n)/n)$…
We study the asymptotic frequentist coverage of credible sets based on a novel Bayesian approach for a multiple linear regression model under variable selection. We initially ignore the issue of variable selection, which allows us to put a…
Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. The central challenge is to both mitigate…
In Bayesian statistics, horseshoe prior has attracted increasing attention as an approach to the sparse estimation. The estimation accuracy of compressed sensing with the horseshoe prior is evaluated by statistical mechanical method. It is…
We study pointwise estimation and uncertainty quantification for a sparse variational Gaussian process method with eigenvector inducing variables. For a rescaled Brownian motion prior, we derive theoretical guarantees and limitations for…
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…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…