Related papers: Consistency of Bayes factor for nonnested model se…

Mixtures of Zellner's g-priors have been studied extensively in linear models and have been shown to have numerous desirable properties for Bayesian variable selection and model averaging. Several extensions of g-priors to Generalized…

Testing the (in)equality of variances is an important problem in many statistical applications. We develop default Bayes factor tests to assess the (in)equality of two or more population variances, as well as a test for whether the…

As AI systems develop in complexity it is becoming increasingly hard to ensure non-discrimination on the basis of protected attributes such as gender, age, and race. Many recent methods have been developed for dealing with this issue as…

Informally, "Information Inconsistency" is the property that has been observed in many Bayesian hypothesis testing and model selection procedures whereby the Bayesian conclusion does not become definitive when the data seems to become…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the…

We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…

We describe Bayes factors based on z, t, $\chi^2$, and F statistics when non-local moment prior distributions are used to define alternative hypotheses. The non-local alternative prior distributions are centered on standardized effects. The…

In this paper we introduce objective proper prior distributions for hypothesis testing and model selection based on measures of divergence between the competing models; we call them divergence based (DB) priors. DB priors have simple forms…

We study high-dimensional Bayesian linear regression with product priors. Using the nascent theory of non-linear large deviations (Chatterjee and Dembo,2016), we derive sufficient conditions for the leading-order correctness of the naive…

This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…

In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously produce a minimally-informative…

The power-expected-posterior (PEP) prior is an objective prior for Gaussian linear models, which leads to consistent model selection inference, under the M-closed scenario, and tends to favor parsimonious models. Recently, two new forms of…

The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…

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…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

We develop a Bayesian variable selection method, called SVEN, based on a hierarchical Gaussian linear model with priors placed on the regression coefficients as well as on the model space. Sparsity is achieved by using degenerate spike…