{"id":"W2248636914","doi":"10.1007/0-8176-4487-3_8","title":"Range of Correlation Matrices for Dependent Random Variables with Given Marginal Distributions","year":2007,"lang":"en","type":"book-chapter","venue":"Birkhäuser Boston eBooks","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Random variable; Range (aeronautics); Combinatorics; Matrix (chemical analysis); Correlation; Marginal distribution; Random matrix; Distribution (mathematics); Positive-definite matrix; Set (abstract data type); Conditional probability distribution; Scale (ratio); Discrete mathematics; Statistics; Mathematical analysis; Physics; Geometry","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002811455,0.0008593025,0.0006606628,0.001612201,0.0004819641,0.002259793,0.001172506,0.000927662,0.004141287],"category_scores_gemma":[0.01315498,0.0005631923,0.0008807179,0.001286383,0.00180181,0.002575201,0.002073117,0.002050857,0.0009891858],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008415362,"about_ca_system_score_gemma":0.0004586833,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004920158,"about_ca_topic_score_gemma":0.0003912036,"domain_scores_codex":[0.9982026,0.0005991813,0.00009613048,0.000394401,0.0005570721,0.0001506613],"domain_scores_gemma":[0.9932716,0.005157326,0.000408902,0.0004787513,0.0004550151,0.0002284288],"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":[0.00009418197,0.00003347731,0.001237672,0.000152048,0.00003705116,0.0002844122,0.0002617551,0.04730492,0.005149642,0.919315,0.002124239,0.02400561],"study_design_scores_gemma":[0.00002285394,0.0000839007,0.00105328,0.0000794365,0.00002275121,0.0005825902,0.00007855844,0.19229,0.00339075,0.7948092,0.007543032,0.00004368072],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05508188,0.002463942,0.9021659,0.0005696396,0.00003843074,0.0000548512,0.000411005,0.0002910857,0.03892321],"genre_scores_gemma":[0.7881892,0.003755792,0.1949489,0.0004011325,0.0002055015,0.0003980944,0.001030024,0.0002285776,0.01084289],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004141287,"threshold_uncertainty_score":0.01486862,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06443512843431935,"score_gpt":0.2969955204649542,"score_spread":0.2325603920306348,"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."}}