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We study asymptotic frequentist behavior of the posterior in this model. Specifically, we show that when the true conditional density has a certain smoothness level, then the posterior contraction rate around the truth is equal up to a log factor to the frequentist minimax rate of estimation. An extension to the case when the covariate space is unbounded is also established. As our result holds without a priori knowledge of the smoothness level of the true density, the established posterior contraction rates are adaptive. Moreover, we show that the rate is not affected by inclusion of irrelevant covariates in the model. In Monte Carlo simulations, a version of the model compares favorably to a cross-validated kernel conditional density estimator.<\/jats:p>","DOI":"10.1017\/s0266466616000220","type":"journal-article","created":{"date-parts":[[2016,7,13]],"date-time":"2016-07-13T09:26:30Z","timestamp":1468401990000},"page":"980-1012","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":23,"title":["ADAPTIVE BAYESIAN ESTIMATION OF CONDITIONAL DENSITIES"],"prefix":"10.1017","volume":"33","author":[{"given":"Andriy","family":"Norets","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Debdeep","family":"Pati","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,7,13]]},"reference":[{"key":"S0266466616000220_ref23","volume-title":"Nonparametric Econometrics: Theory and Practice","author":"Li","year":"2007"},{"key":"S0266466616000220_ref18","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1991.3.1.79"},{"key":"S0266466616000220_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1016218228"},{"key":"S0266466616000220_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/13-AOS1192"},{"key":"S0266466616000220_ref20","doi-asserted-by":"publisher","DOI":"10.1002\/hec.1777"},{"key":"S0266466616000220_ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2013.01.011"},{"key":"S0266466616000220_ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.04.031"},{"key":"S0266466616000220_ref1","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1214\/aos\/1018031206","article-title":"The consistency of posterior distributions in nonparametric problems","volume":"27","author":"Barron","year":"1999","journal-title":"The Annals of Statistics"},{"key":"S0266466616000220_ref41","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1289"},{"key":"S0266466616000220_ref25","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS765"},{"key":"S0266466616000220_ref14","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000727"},{"key":"S0266466616000220_ref30","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476965"},{"key":"S0266466616000220_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/10-EJS584"},{"key":"S0266466616000220_ref35","doi-asserted-by":"publisher","DOI":"10.1214\/10-BA605"},{"key":"S0266466616000220_ref16","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v027.i05"},{"key":"S0266466616000220_ref13","doi-asserted-by":"publisher","DOI":"10.1214\/009053606000001271"},{"key":"S0266466616000220_ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S026646661300042X"},{"key":"S0266466616000220_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2006.05.022"},{"key":"S0266466616000220_ref33","doi-asserted-by":"publisher","DOI":"10.3150\/14-BEJ663"},{"key":"S0266466616000220_ref4","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000000205"},{"key":"S0266466616000220_ref7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2007.00582.x"},{"key":"S0266466616000220_ref6","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asn012"},{"key":"S0266466616000220_ref31","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS703"},{"key":"S0266466616000220_ref37","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2009.05.004"},{"key":"S0266466616000220_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOS811"},{"key":"S0266466616000220_ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2012.06.012"},{"key":"S0266466616000220_ref34","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/ast015"},{"key":"S0266466616000220_ref36","doi-asserted-by":"publisher","DOI":"10.1214\/08-AOS678"},{"key":"S0266466616000220_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000000490"},{"key":"S0266466616000220_ref40","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/89.3.513"},{"key":"S0266466616000220_ref8","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000253"},{"key":"S0266466616000220_ref26","unstructured":"Norets A . 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