{"id":"W4312510636","doi":"10.1007/978-3-030-95864-0_4","title":"Chapter 4: The Matrix-Variate Gaussian Distribution","year":2022,"lang":"en","type":"book-chapter","venue":"","topic":"Statistical and numerical algorithms","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University; McGill University","funders":"","keywords":"Random variate; Gaussian; Mathematics; Multivariate normal distribution; Statistical physics; Matrix (chemical analysis); Applied mathematics; Multivariate statistics; Statistics; Random variable; Physics; Quantum mechanics","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":[0.0007433089,0.000806082,0.000545716,0.0009852899,0.0006979696,0.002415445,0.0007853751,0.001038017,0.02456846],"category_scores_gemma":[0.002364119,0.0004146706,0.0005569533,0.001279882,0.001464692,0.002190765,0.001083313,0.002681263,0.01089747],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001236758,"about_ca_system_score_gemma":0.0009612766,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001658835,"about_ca_topic_score_gemma":0.001482007,"domain_scores_codex":[0.9994726,0.0001004781,0.00001699222,0.0001116643,0.0002674467,0.00003077527],"domain_scores_gemma":[0.9994573,0.0002600122,0.00002486327,0.00008070418,0.0001583851,0.00001878444],"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":[0.00000842313,0.00001185256,0.00009146419,0.000117478,0.000008915803,0.00006381406,0.0001282705,0.003772434,0.0007414491,0.9143664,0.0407749,0.03991453],"study_design_scores_gemma":[0.000002636265,0.0000106504,0.0003195333,0.0001766406,0.000009423567,0.0002466911,0.00004098833,0.01336417,0.001097473,0.6219574,0.3627566,0.00001770429],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.003636618,0.02443244,0.6305019,0.004526024,0.003287693,0.00009232401,0.0009847124,0.0008735491,0.3316648],"genre_scores_gemma":[0.137296,0.05856776,0.2372823,0.003994923,0.006353694,0.000321603,0.001742511,0.00225707,0.5521842],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.02456846,"threshold_uncertainty_score":0.08218974,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04257325894935809,"score_gpt":0.2981115138530593,"score_spread":0.2555382549037012,"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."}}