{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T09:47:18Z","timestamp":1777974438095,"version":"3.51.4"},"reference-count":31,"publisher":"Wiley","issue":"14","license":[{"start":{"date-parts":[[2017,3,12]],"date-time":"2017-03-12T00:00:00Z","timestamp":1489276800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2017,3,12]],"date-time":"2017-03-12T00:00:00Z","timestamp":1489276800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1"},{"start":{"date-parts":[[2017,3,12]],"date-time":"2017-03-12T00:00:00Z","timestamp":1489276800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Canadian Foundation for Innovation"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2017,6,30]]},"abstract":"<jats:p>An important statistical task in disease mapping problems is to identify divergent regions with unusually high or low risk of disease. Leave\u2010one\u2010out cross\u2010validatory (LOOCV) model assessment is the gold standard for estimating predictive p\u2010values that can flag such divergent regions. However, actual LOOCV is time\u2010consuming because one needs to rerun a Markov chain Monte Carlo analysis for each posterior distribution in which an observation is held out as a test case. This paper introduces a new method, called integrated importance sampling (iIS), for estimating LOOCV predictive <jats:italic>p<\/jats:italic>\u2010values with only Markov chain samples drawn from the posterior based on a full data set. The key step in iIS is that we integrate away the latent variables associated the test observation with respect to their conditional distribution <jats:italic>without<\/jats:italic> reference to the actual observation. By following the general theory for importance sampling, the formula used by iIS can be proved to be equivalent to the LOOCV predictive p\u2010value. We compare iIS and other three existing methods in the literature with two disease mapping datasets. Our empirical results show that the predictive <jats:italic>p<\/jats:italic>\u2010values estimated with iIS are almost identical to the predictive <jats:italic>p<\/jats:italic>\u2010values estimated with actual LOOCV and outperform those given by the existing three methods, namely, the posterior predictive checking, the ordinary importance sampling, and the ghosting method by Marshall and Spiegelhalter (2003). Copyright \u00a9 2017 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.7278","type":"journal-article","created":{"date-parts":[[2017,3,13]],"date-time":"2017-03-13T00:47:13Z","timestamp":1489366033000},"page":"2220-2236","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Estimating cross\u2010validatory predictive <i>p<\/i>\u2010values with integrated importance sampling for disease mapping models"],"prefix":"10.1002","volume":"36","author":[{"given":"Longhai","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics University of Saskatchewan  106 Wiggins Rd Saskatoon S7N5E6 SK Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4030-7413","authenticated-orcid":false,"given":"Cindy X.","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Public Health University of Saskatchewan  104 Clinic Place Saskatoon S7N5E5 SK Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shi","family":"Qiu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics University of Saskatchewan  106 Wiggins Rd Saskatoon S7N5E6 SK Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2017,3,12]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00116466"},{"key":"e_1_2_9_3_1","volume-title":"Bayesian Methods for Mapping Disease Risk. Geographical and Environmental Epidemiology: Methods for Small\u2010area Studies","author":"Clayton DG","year":"1992"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0258(20000915\/30)19:17\/18<2217::AID-SIM565>3.0.CO;2-E"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1191\/0962280205sm388oa"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/1390802"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0258(20000915\/30)19:17\/18<2377::AID-SIM576>3.0.CO;2-1"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1214\/07-BA218"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/13-EJS854"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1403"},{"key":"e_1_2_9_11_1","first-page":"733","article-title":"Posterior predictive assessment of model fitness via realized discrepancies","volume":"6","author":"Gelman A","year":"1996","journal-title":"Statistica Sinica"},{"key":"e_1_2_9_12_1","first-page":"147","article-title":"Model determination using predictive distributions with implementation via sampling\u2010based methods (with discussion)","volume":"4","author":"Gelfand AE","year":"1992","journal-title":"Bayesian Statistics"},{"issue":"437","key":"e_1_2_9_13_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/01621459.1997.10473617","article-title":"On the variability of case\u2010deletion importance sampling weights in the Bayesian linear model","volume":"92","author":"Peruggia M","year":"1997","journal-title":"Journal of American Statistical Association"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1214\/08-EJS259"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1162\/08997660260293292"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-015-9577-2"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2532003"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1214\/06-BA117A"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1198\/073500103288619430"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2006.07.015"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511790942"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.2307\/1913710"},{"key":"e_1_2_9_23_1","unstructured":"NealRM.Probabilistic inference using Markov Chain Monte Carlo methods Dept. of Computer Science University of Toronto Toronto Canada 1993\u00a0http:\/\/www.utstat.utoronto.ca\/~radford\/sta4503\/review.pdf."},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1028905934"},{"key":"e_1_2_9_25_1","volume-title":"Monte Carlo Strategies in Scientific Computing","author":"Liu JS","year":"2001"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1162\/08997660260293292"},{"key":"e_1_2_9_27_1","article-title":"Pareto smoothed importance sampling","author":"Vehtari A","year":"2015","journal-title":"arXiv:1507.02646 [stat]"},{"key":"e_1_2_9_28_1","volume-title":"Atlas of Cancer Mortality in the Federal Republic of Germany","author":"Becker N","year":"1997"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1191\/0962280205sm389oa"},{"key":"e_1_2_9_30_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780203492024"},{"key":"e_1_2_9_31_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10474012"},{"key":"e_1_2_9_32_1","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2009.0018"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.7278","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.7278","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T02:13:36Z","timestamp":1696472016000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.7278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,12]]},"references-count":31,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2017,6,30]]}},"alternative-id":["10.1002\/sim.7278"],"URL":"https:\/\/doi.org\/10.1002\/sim.7278","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,12]]}}}