2011/08/12 by Suprateek Kundu, David B. Dunson, Kundu, Suprateek +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1108.2722
arxiv created 2011/08/12 · openalex publication_date 2011/08/12 · arxiv updated 2011/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 settings in which the number of candidate predictors (p) diverges with sample size (n). Our focus is on generalizing methods and asymptotic theory established for mixtures of g-priors to semiparametric linear regression models having unknown residual densities. Using a Dirichlet process location mixture for the residual density, we propose a semiparametric g-prior which incorporates an unknown matrix of cluster allocation indicators. For this class of priors, posterior computation can proceed via a straightforward stochastic search variable selection algorithm. In addition, Bayes factor and variable selection consistency is shown to result under various cases including proper and improper priors on g and p>n, with the models under comparison restricted to have model dimensions diverging at a rate less than n.