{"id":"W2152104303","doi":"10.1239/jap/1053003548","title":"On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials","year":2003,"lang":"en","type":"article","venue":"Journal of Applied Probability","topic":"Reliability and Maintenance Optimization","field":"Engineering","cited_by":40,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto; University of Manitoba","funders":"","keywords":"Mathematics; Markov chain; Sequence (biology); Applied mathematics; Variable-order Markov model; Markov process; Markov model; Markov chain mixing time; Distribution (mathematics); Statistics; Mathematical analysis","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":[0.01227056,0.001264336,0.001902091,0.002007123,0.000646641,0.002036928,0.00299057,0.001697861,0.003253521],"category_scores_gemma":[0.05901421,0.0007849722,0.001115644,0.002144452,0.004119883,0.006030752,0.002410373,0.003317325,0.0007386031],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002592133,"about_ca_system_score_gemma":0.001965757,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002794908,"about_ca_topic_score_gemma":0.002061821,"domain_scores_codex":[0.9974022,0.001247067,0.0001080639,0.0003665411,0.0006449333,0.0002312494],"domain_scores_gemma":[0.9505975,0.04153136,0.002448359,0.002303678,0.002361198,0.0007578652],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001216776,0.00005627944,0.001433578,0.0001721576,0.00005028722,0.0001925052,0.0002121452,0.7002268,0.0009656546,0.2819937,0.0009374842,0.01363763],"study_design_scores_gemma":[0.000009917199,0.00001478672,0.0001683576,0.00002992366,0.000005996128,0.00003614497,0.00001907562,0.9357439,0.0002952123,0.06339148,0.0002676665,0.00001760487],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.0247392,0.0008072782,0.9713845,0.0003063795,0.00004461076,0.00005116063,0.00009387974,0.0001958565,0.0023772],"genre_scores_gemma":[0.7312905,0.002752042,0.2583687,0.0003420219,0.0002154761,0.0006791805,0.0006887729,0.0004312061,0.005232191],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.01227056,"threshold_uncertainty_score":0.06489366,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02223120450416083,"score_gpt":0.2545740882627782,"score_spread":0.2323428837586173,"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."}}