{"paper":{"title":"Monte Carlo simulation on the Stiefel manifold via polar expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.CO","authors_text":"David B. Dunson, Michael Jauch, Peter D. Hoff","submitted_at":"2019-06-18T16:55:42Z","abstract_excerpt":"Motivated by applications to Bayesian inference for statistical models with orthogonal matrix parameters, we present $\\textit{polar expansion},$ a general approach to Monte Carlo simulation from probability distributions on the Stiefel manifold. To bypass many of the well-established challenges of simulating from the distribution of a random orthogonal matrix $\\boldsymbol{Q},$ we construct a distribution for an unconstrained random matrix $\\boldsymbol{X}$ such that $\\boldsymbol{Q}_X,$ the orthogonal component of the polar decomposition of $\\boldsymbol{X},$ is equal in distribution to $\\boldsym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07684","kind":"arxiv","version":1},"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"}