{"paper":{"title":"Convergence Analysis of the Data Augmentation Algorithm for Bayesian Linear Regression with Non-Gaussian Errors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"James P. Hobert, Kshitij Khare, Qian Qin, Yeun Ji Jung","submitted_at":"2015-06-09T21:50:14Z","abstract_excerpt":"Gaussian errors are sometimes inappropriate in a multivariate linear regression setting because, for example, the data contain outliers. In such situations, it is often assumed that the error density is a scale mixture of multivariate normal densities that takes the form $f(\\varepsilon) = \\int_0^\\infty |\\Sigma|^{-\\frac{1}{2}} u^{\\frac{d}{2}} \\, \\phi_d \\big( \\Sigma^{-\\frac{1}{2}} \\sqrt{u} \\, \\varepsilon \\big) \\, h(u) \\, du$, where $d$ is the dimension of the response, $\\phi_d(\\cdot)$ is the standard $d$-variate normal density, $\\Sigma$ is an unknown $d \\times d$ positive definite scale matrix, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03113","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}