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The proposed criterion uses a posterior covariance form and is computed by using only one Markov chain Monte Carlo run. Through numerical examples, we demonstrate how PCIC can apply in practice. Further, we show that PCIC is asymptotically unbiased to the quasi-Bayesian generalization error under mild conditions in weighted inference with both regular and singular statistical models.<\/jats:p>","DOI":"10.1162\/neco_a_01592","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T22:20:37Z","timestamp":1684189237000},"page":"1340-1361","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":4,"title":["Posterior Covariance Information Criterion for Weighted Inference"],"prefix":"10.1162","volume":"35","author":[{"given":"Yukito","family":"Iba","sequence":"first","affiliation":[{"name":"The Institute of Statistical Mathematics, Tokyo 190-8562, Japan iba@ism.ac.jp"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keisuke","family":"Yano","sequence":"additional","affiliation":[{"name":"The Institute of Statistical Mathematics, Tokyo 190-8562, Japan 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