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We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…

Berger et al. (2001) and Ren et al. (2012) derived noninformative priors for Gaussian process models of spatially correlated data using the reference prior approach (Berger, Bernardo, 1991). The priors have good statistical properties and…

We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…

A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…

Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we…

Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…

Estimating unknown parameters subject to prior constraints is important in statistical inference, particularly in fields such as reliability analysis, survival studies, and engineering, where prior structural information about the…

We develop a Bayesian approach to estimate weight matrices in spatial autoregressive (or spatial lag) models. Datasets in regional economic literature are typically characterized by a limited number of time periods T relative to spatial…

This paper presents a Bayesian model for unsupervised learning of verb selectional preferences. For each verb the model creates a Bayesian network whose architecture is determined by the lexical hierarchy of Wordnet and whose parameters are…

This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

Although Bayesian inference is an immensely popular paradigm among a large segment of scientists including statisticians, most applications consider objective priors and need critical investigations (Efron, 2013, Science). While it has…

Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…

Noninformative uniform priors are staples of Bayesian inference, especially in Bayesian machine learning. This study challenges the assumption that they are optimal and their use in Bayesian inference yields optimal outcomes. Instead of…

We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…

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…

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 propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to…