Related papers: Revisiting High Dimensional Bayesian Model Selecti…

Most of the consistency analyses of Bayesian procedures for variable selection in regression refer to pairwise consistency, that is, consistency of Bayes factors. However, variable selection in regression is carried out in a given class of…

In the class of normal regression models with a finite number of regressors, and for a wide class of prior distributions, a Bayesian model selection procedure based on the Bayes factor is consistent [Casella and Moreno J. Amer. Statist.…

Zellner's $g$-prior is a popular prior choice for the model selection problems in the context of normal regression models. Wang and Sun [J. Statist. Plann. Inference 147 (2014) 95-105] recently adopt this prior and put a special hyper-prior…

Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of…

The quality of a Bayes factor crucially depends on the number of regressors, the sample size and the prior on the regression parameters, and hence it has to be established in a case-by-case basis. In this paper we analyze the consistency of…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…

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…

This thesis responds to the challenges of using a large number, such as thousands, of features in regression and classification problems. There are two situations where such high dimensional features arise. One is when high dimensional…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…

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…

The paper addresses joint sparsity selection in the regression coefficient matrix and the error precision (inverse covariance) matrix for high-dimensional multivariate regression models in the Bayesian paradigm. The selected sparsity…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

In the Bayesian literature on model comparison, Bayes factors play the leading role. In the classical statistical literature, model selection criteria are often devised used cross-validation ideas. Amalgamating the ideas of Bayes factor and…

Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436--1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

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…

We consider the problem of variable selection in Bayesian multivariate linear regression models, involving multiple response and predictor variables, under multivariate normal errors. In the absence of a known covariance structure,…

Model selection is indispensable to high-dimensional sparse modeling in selecting the best set of covariates among a sequence of candidate models. Most existing work assumes implicitly that the model is correctly specified or of fixed…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…