Related papers: A Better (Bayesian) Interval Estimate for Within-S…

Following the critical review of Seaman et al. (2012), we reflect on what is presumably the most essential aspect of Bayesian statistics, namely the selection of a prior density. In some cases, Bayesian inference remains fairly stable under…

Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…

Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…

Notions of depth in regression have been introduced and studied in the literature. Regression depth (RD) of Rousseeuw and Hubert (1999), the most famous one, is a direct extension of Tukey location depth (Tukey (1975)) to regression. Like…

We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…

This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…

Bayesian highest posterior density (HPD) intervals can be estimated directly from simulations via empirical shortest intervals. Unfortunately, these can be noisy (that is, have a high Monte Carlo error). We derive an optimal weighting…

In recent years, neural networks have revolutionized various domains, yet challenges such as hyperparameter tuning and overfitting remain significant hurdles. Bayesian neural networks offer a framework to address these challenges by…

We consider maximin and Bayesian $D$-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes…

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…

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate…

We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences…

Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to…

This paper introduces two methods for estimating reliable prediction intervals for local linear least-squares regressions, named Bounded Oscillation Prediction Intervals (BOPI). It also proposes a new measure for comparing interval…

Using normal approximation (NA) to construct a kernel-smoother-based confidence interval faces a fundamental challenge: the normalization makes a small estimation bias become a non-negligible inferential bias. This paper takes a different…

We study the problem of learning individualized dose intervals using observational data. There are very few previous works for policy learning with continuous treatment, and all of them focused on recommending an optimal dose rather than an…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…

We consider the problem of constructing differentially private nonparametric confidence intervals (CIs) for an arbitrary quantity using resampling. A growing body of work has adapted resampling ideas to the private setting, including…