2013/10/03 by Rajesh Talluri, Talluri, Rajesh, Veerabhadran Baladandayuthapani +3 · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1310.1127
openalex publication_date 2013/10/03 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
We propose Bayesian methods for Gaussian graphical models that lead to sparse\nand adaptively shrunk estimators of the precision (inverse covariance) matrix.\nOur methods are based on lasso-type regularization priors leading to\nparsimonious parameterization of the precision matrix, which is essential in\nseveral applications involving learning relationships among the variables. In\nthis context, we introduce a novel type of selection prior that develops a\nsparse structure on the precision matrix by making most of the elements exactly\nzero, in addition to ensuring positive definiteness -- thus conducting model\nselection and estimation simultaneously. We extend these methods to finite and\ninfinite mixtures of Gaussian graphical models for clustered data using\nDirichlet process priors. We discuss appropriate posterior simulation schemes\nto implement posterior inference in the proposed models, including the\nevaluation of normalizing constants that are functions of parameters of\ninterest which result from the restrictions on the correlation matrix. We\nevaluate the operating characteristics of our method via several simulations\nand in application to real data sets.\n