{"id":"W2569664619","doi":"10.1137/15m100866x","title":"Lower Bounds on the Probability of a Finite Union of Events","year":2016,"lang":"en","type":"article","venue":"SIAM Journal on Discrete Mathematics","topic":"Risk and Portfolio Optimization","field":"Decision Sciences","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Upper and lower bounds; Event (particle physics); Discrete mathematics; Pairwise comparison; Finite set; Class (philosophy); Statistics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.005105176,0.0001324028,0.0003160716,0.000167298,0.0001091617,0.00005111276,0.0006002738,0.00006370448,0.0004082434],"category_scores_gemma":[0.004752088,0.00005056275,0.0002235507,0.0003996752,0.000147304,0.0001725319,0.00005486572,0.0001396129,0.00006561067],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003277687,"about_ca_system_score_gemma":0.00007665793,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.106862e-7,"about_ca_topic_score_gemma":0.000001909221,"domain_scores_codex":[0.9967749,0.0003336745,0.001077241,0.0001546204,0.00149785,0.0001617552],"domain_scores_gemma":[0.9950798,0.002535401,0.001228382,0.0006598331,0.0004167194,0.00007986704],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.002037087,0.006141834,0.03776876,0.0002278527,0.000610591,0.00004182952,0.01911307,0.02618741,0.005842379,0.7178348,0.02775451,0.1564398],"study_design_scores_gemma":[0.0006864398,0.001009758,0.004020186,0.0007196613,0.00003324285,0.00002124009,0.0005165722,0.003011656,0.003349239,0.9830708,0.003387036,0.0001741607],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9189737,0.00002642964,0.06532007,0.003372655,0.0004281093,0.0003212013,0.00003774785,0.000009715045,0.0115104],"genre_scores_gemma":[0.9958283,0.0001589484,0.002543058,0.00005080297,0.00004354024,0.000002547256,4.031092e-7,0.00001112632,0.001361313],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.265236,"threshold_uncertainty_score":0.5689037,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07988994126648957,"score_gpt":0.3476467137898471,"score_spread":0.2677567725233576,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}