Related papers: Frequentist and Bayesian measures of confidence vi…

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…

In this paper we study the asymptotic properties of Bayesian multiple testing procedures for a large class of Gaussian scale mixture pri- ors. We study two types of multiple testing risks: a Bayesian risk proposed in Bogdan et al. (2011)…

Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…

This study focuses on finite-sample inference on the non-linear Bures-Wasserstein manifold and introduces a generalized bootstrap procedure for estimating Bures-Wasserstein barycenters. We provide non-asymptotic statistical guarantees for…

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

\citet{Rosenbaum83ps} introduced the notion of the propensity score and discussed its central role in causal inference with observational studies. Their paper, however, caused a fundamental incoherence with an early paper by…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…

In this article, we present data-subsetting algorithms that allow for the approximate and scalable implementation of the Bayesian bootstrap. They are analogous to two existing algorithms in the frequentist literature: the bag of little…

Conformal prediction has emerged as a cutting-edge methodology in statistics and machine learning, providing prediction intervals with finite-sample frequentist coverage guarantees. Yet, its interplay with Bayesian statistics, often…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of…

We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…

We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We…

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…

We propose a coupled bootstrap (CB) method for the test error of an arbitrary algorithm that estimates the mean in a Poisson sequence, often called the Poisson means problem. The idea behind our method is to generate two carefully-designed…

In this paper we present a frequentist-Bayesian hybrid method for estimating covariances of unfolded distributions using pseudo-experiments. The method is compared with other covariance estimation methods using the unbiased Rao-Cramer bound…

Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when…

Bayesian inference provides a framework to combine various model components with shared parameters, allowing joint uncertainty estimation and the use of all available data sources. Unfortunately, misspecification of any part of the model…