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dc.contributor.authorXu, Xiaojin
dc.contributor.authorMeng, Xiao-Li
dc.contributor.authorYu, Yaming
dc.date.accessioned2013-07-26T15:25:47Z
dc.date.issued2013
dc.identifier.citationXu, Xiaojin, Xiao-Li Meng, and Yaming Yu. Forthcoming. Thank God That Regressing Y on X is Not the Same as Regressing X on Y: Direct and Indirect Residual Augmentations. Journal of Computational and Graphical Statistics.en_US
dc.identifier.issn1061-8600en_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:10886850
dc.description.abstractWhat does regressing Y on X versus regressing X on Y have to do with MCMC? It turns out that many strategies for speeding up data-augmentation type algorithms can be understood as fostering independence or “de-correlation” between a regression function and the corresponding residual, thereby reducing or even eliminating dependence among MCMC iterates. There are two general classes of algorithms, those corresponding to regressing parameters on augmented data/auxiliary variables and those that operate the other way around. The interweaving strategy (Yu and Meng, 2011, JCGS) provides a general recipe to automatically take advantage of both, and it is the existence of two different types of residuals that makes the interweaving strategy seemingly magical in some cases and promising in general. The concept of residuals—which depends on actual data—also highlights the potential for substantial improvements when data augmentation schemes are allowed to depend on the observed data. At the same time, there is an intriguing phase transition type of phenomenon regarding choosing (partially) residual augmentation schemes, reminding us once more of the prevailing issue of trade-off between robustness and efficiency. This article reports on these latest theoretical investigations (using a class of normal/independence models) and empirical findings (using a posterior sampling for a Probit regression) in the search for effective residual augmentations—and ultimately more MCMC algorithms—that meet the 3-S criterion: simple, stable, and speedy.en_US
dc.description.sponsorshipStatisticsen_US
dc.language.isoen_USen_US
dc.publisherInforma UK (Taylor & Francis)en_US
dc.relation.isversionofdoi:10.1080/10618600.2013.794702en_US
dash.licenseOAP
dc.subjectAncillary-Sufficient Interweaving Strategy (ASIS)en_US
dc.subjectconditional augmentationen_US
dc.subjectMCMCen_US
dc.subjectmarginal augmentationen_US
dc.subjectphase transitionen_US
dc.subjectprobit regressionen_US
dc.subjectPX-DAen_US
dc.titleThank God That Regressing Y on X is Not the Same as Regressing X on Y: Direct and Indirect Residual Augmentationsen_US
dc.typeJournal Articleen_US
dc.description.versionAccepted Manuscripten_US
dc.relation.journalJournal of Computational and Graphical Statisticsen_US
dash.depositing.authorMeng, Xiao-Li
dc.date.available2013-07-26T15:25:47Z
dc.identifier.doi10.1080/10618600.2013.794702*
dash.contributor.affiliatedXu, Xiaojin
dash.contributor.affiliatedMeng, Xiao-li


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