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Standard leave-one-out cross-validation (LOO-CV) requires that the observation model can be factorized into simple terms, but a lot of important models in temporal and spatial statistics do not have this property or are inefficient or unstable when forced into a factorized form. We derive how to efficiently compute and validate both exact and approximate LOO-CV for any Bayesian non-factorized model with a multivariate normal or Student-<jats:inline-formula><jats:alternatives><jats:tex-math>$$t$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>t<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>distribution on the outcome values. We demonstrate the method using lagged simultaneously autoregressive (SAR) models as a case study.<\/jats:p>","DOI":"10.1007\/s00180-020-01045-4","type":"journal-article","created":{"date-parts":[[2020,11,20]],"date-time":"2020-11-20T22:03:04Z","timestamp":1605909784000},"page":"1243-1261","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5765-8995","authenticated-orcid":false,"given":"Paul-Christian","family":"B\u00fcrkner","sequence":"first","affiliation":[]},{"given":"Jonah","family":"Gabry","sequence":"additional","affiliation":[]},{"given":"Aki","family":"Vehtari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,20]]},"reference":[{"issue":"4","key":"1045_CR1","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1016\/j.ijforecast.2009.08.001","volume":"26","author":"T Ando","year":"2010","unstructured":"Ando T, Tsay R (2010) Predictive likelihood for Bayesian model selection and averaging. 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