Related papers: Asymptotics of Bayesian Uncertainty Estimation in …

This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$, their dimension $p$, and the dimension of feature space $N$ are all large and…

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…

In this expository note we describe a surprising phenomenon in overparameterized linear regression, where the dimension exceeds the number of samples: there is a regime where the test risk of the estimator found by gradient descent…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…

We consider three problems in high-dimensional Gaussian linear mixed models. Without any assumptions on the design for the fixed effects, we construct an asymptotic $F$-statistic for testing whether a collection of random effects is zero,…

To adopt neural networks in safety critical domains, knowing whether we can trust their predictions is crucial. Bayesian neural networks (BNNs) provide uncertainty estimates by averaging predictions with respect to the posterior weight…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of…

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density…

We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

Delattre et al. (2013) investigated asymptotic properties of the maximum likelihood estimator of the population parameters of the random effects associated with n independent stochastic differential equations (SDEs) assuming that the SDEs…

In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…

This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

The Bayesian formulation of inverse problems is attractive for three primary reasons: it provides a clear modelling framework; means for uncertainty quantification; and it allows for principled learning of hyperparameters. The posterior…

In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured,…