{"paper":{"title":"The Two-Sample Problem Via Relative Belief Ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Luai Al-Labadi","submitted_at":"2018-05-17T06:49:01Z","abstract_excerpt":"This paper deals with a new Bayesian approach to the two-sample problem. More specifically, let $x=(x_1,\\ldots,x_{n_1})$ and $y=(y_1,\\ldots,y_{n_2})$ be two independent samples coming from unknown distributions $F$ and $G$, respectively. The goal is to test the null hypothesis $\\mathcal{H}_0:~F=G$ against all possible alternatives. First, a Dirichlet process prior for $F$ and $G$ is considered. Then the change of their Cram\\'{e}r-von Mises distance from a priori to a posteriori is compared through the relative belief ratio. Many theoretical properties of the procedure have been developed and s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07238","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"}