{"data":{"id":"10.6084/m9.figshare.976116.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.976116.v1","prefix":"10.6084","suffix":"m9.figshare.976116.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Abhra Sarkar","affiliation":[],"nameIdentifiers":[]},{"name":"Bani K. Mallick","affiliation":[],"nameIdentifiers":[]},{"name":"Staudenmayer, John","nameType":"Personal","givenName":"John","familyName":"Staudenmayer","affiliation":[],"nameIdentifiers":[]},{"name":"Debdeep Pati","affiliation":[],"nameIdentifiers":[]},{"name":"Carroll, Raymond J.","nameType":"Personal","givenName":"Raymond J.","familyName":"Carroll","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2014,"subjects":[{"subject":"Computational Biology"},{"subject":"110309 Infectious Diseases","subjectScheme":"FOR"},{"subject":"FOS: Health sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Health sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Information and Computing Sciences"},{"subject":"Biological Sciences"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Genetics"}],"contributors":[],"dates":[{"date":"2014-10-02","dateType":"Created"},{"date":"2016-01-18","dateType":"Updated"},{"date":"2014","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/10618600.2014.899237","relatedIdentifierType":"DOI"},{"relationType":"IsPreviousVersionOf","relatedIdentifier":"10.6084/m9.figshare.976116","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["0 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, e.g., normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. In particular, the models can adapt to asymmetry, heavy tails and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the data set and R programs implementing our methods are included as part of online supplemental materials.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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