{"paper":{"title":"On The MCMC Performance In Bernoulli Group Testing And The Random Max Set-Cover Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Ilias Zadik, Maxwell Lovig","submitted_at":"2024-10-11T20:08:54Z","abstract_excerpt":"The group testing problem is a canonical inference task where one seeks to identify $k$ infected individuals out of a population of $n$ people, based on the outcomes of $m$ group tests. Of particular interest is the case of Bernoulli group testing (BGT), where each individual participates in each test independently and with a fixed probability. BGT is known to be an \"information-theoretically\" optimal design, as there exists a decoder that can identify with high probability as $n$ grows the infected individuals using $m^*=\\log_2 \\binom{n}{k}$ BGT tests, which is the minimum required number of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.09231","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.09231/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"}