{"id":"W4409972846","doi":"10.1017/jpr.2025.4","title":"Weak convergence of adaptive Markov chain Monte Carlo","year":2025,"lang":"en","type":"article","venue":"Journal of Applied Probability","topic":"Markov Chains and Monte Carlo Methods","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Markov chain Monte Carlo; Markov chain; Monte Carlo method; Convergence (economics); Applied mathematics; Weak convergence; Chain (unit); Statistical physics; Markov chain mixing time; Mathematical optimization; Econometrics; Calculus (dental); Statistics; Variable-order Markov model; Markov model; Computer science","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":[0.01627978,0.001603372,0.002113025,0.00275273,0.001362549,0.002497739,0.003021406,0.002326722,0.005778172],"category_scores_gemma":[0.08469878,0.001082361,0.001954315,0.001002022,0.006278562,0.004704385,0.005945069,0.004609159,0.0008886462],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002634231,"about_ca_system_score_gemma":0.002886345,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003777405,"about_ca_topic_score_gemma":0.00209212,"domain_scores_codex":[0.9933714,0.003716602,0.0003371625,0.0008008813,0.001328831,0.00044519],"domain_scores_gemma":[0.9372839,0.04784352,0.00332289,0.002797837,0.006947006,0.0018047],"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":[0.00009371683,0.00004856849,0.001261034,0.0001592641,0.00008168408,0.0001383749,0.0001608256,0.2710675,0.002032568,0.7162847,0.001086062,0.007585633],"study_design_scores_gemma":[0.0000132046,0.00002680264,0.0001442186,0.00003532881,0.000007831588,0.00001995968,0.00001224188,0.8420234,0.0005193051,0.1566218,0.0005608787,0.00001510528],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01824033,0.0003131923,0.9751662,0.0006389985,0.0001048144,0.00009684237,0.00006474353,0.0001865148,0.005188386],"genre_scores_gemma":[0.7844935,0.001083712,0.196889,0.001046774,0.0003200539,0.001125955,0.0004354231,0.0005439546,0.01406157],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01627978,"threshold_uncertainty_score":0.0860967,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04321366215836191,"score_gpt":0.3184167514913435,"score_spread":0.2752030893329815,"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."}}