{"paper":{"title":"Beta-trees for testing multivariate goodness-of-fit and localizing deviations from a model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Guenther Walther, Valerie N.P. Ho","submitted_at":"2026-06-27T17:39:29Z","abstract_excerpt":"We introduce a novel goodness-of-fit (GOF) procedure based on Beta-tree partitions. A Beta-tree produces a data-adaptive partition of the sample space into regions and provides guaranteed finite sample confidence intervals for the probability contents of each region. The proposed test assesses whether the probabilities assigned by a null distribution $F_0$ fall within these intervals, thereby quantifying agreement between the model and the data. A key application is the selection of the number of components in a mixture model, where the null distribution is constructed via $k$-means clustering"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29021","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29021/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}