Related papers: Bayesian Regression Using a Prior on the Model Fit…

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…

Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…

Neural networks are the cornerstone of modern machine learning, yet can be difficult to interpret, give overconfident predictions and are vulnerable to adversarial attacks. Bayesian neural networks (BNNs) provide some alleviation of these…

The choice of the prior distribution is a key aspect of Bayesian analysis. For the spatial regression setting a subjective prior choice for the parameters may not be trivial, from this perspective, using the objective Bayesian analysis…

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies, there are rather few theoretically optimal Bayes methods…

We study central limit theorems for linear statistics in high-dimensional Bayesian linear regression with product priors. Unlike the existing literature where the focus is on posterior contraction, we work under a non-contracting regime…

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

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…

We consider the specification of prior distributions for Bayesian model comparison, focusing on regression-type models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior…

Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve also as building blocks in more complex formulations, such as density regression, nonparametric…

Researchers and managers model ecological communities to infer the biotic and abiotic variables that shape species' ranges, habitat use, and co-occurrence which, in turn, are used to support management decisions and test ecological…

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are…

In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of…

We study high-dimensional Bayesian linear regression with a general beta prime distribution for the scale parameter. Under the assumption of sparsity, we show that appropriate selection of the hyperparameters in the beta prime prior leads…

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

Two-component mixture priors provide a traditional way to induce sparsity in high-dimensional Bayes models. However, several aspects of such a prior, including computational complexities in high-dimensions, interpretation of exact zeros and…

We propose a variational Bayesian (VB) procedure for high-dimensional linear model inferences with heavy tail shrinkage priors, such as student-t prior. Theoretically, we establish the consistency of the proposed VB method and prove that…

We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy…

We consider deep neural networks in a Bayesian framework with a prior distribution sampling the network weights at random. Following a recent idea of Agapiou and Castillo (2023), who show that heavy-tailed prior distributions achieve…

We develop a modeling framework for dynamic function-on-scalars regression, in which a time series of functional data is regressed on a time series of scalar predictors. The regression coefficient function for each predictor is allowed to…