{"data":{"id":"10.6084/m9.figshare.c.2062916","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2062916","prefix":"10.6084","suffix":"m9.figshare.c.2062916","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"D. Fouskakis","affiliation":[],"nameIdentifiers":[]},{"name":"I. Ntzoufras","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Power-Conditional-Expected Priors: Using \u003ci\u003eg\u003c/i\u003e-priors with Random Imaginary Data for Variable Selection"}],"publisher":"Figshare","container":{},"publicationYear":2015,"subjects":[{"subject":"Biochemistry"},{"subject":"Genetics"},{"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":"Physiology"},{"subject":"Pharmacology"},{"subject":"Biotechnology"},{"subject":"Evolutionary Biology"},{"subject":"Ecology"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"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":"Infectious Diseases"},{"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)"}],"contributors":[],"dates":[{"date":"2015-12-05","dateType":"Created"},{"date":"2016-06-07","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/10618600.2015.1036996","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"http://creativecommons.org/licenses/by/3.0/us"}],"descriptions":[{"description":"The Zellner's \u003ci\u003eg\u003c/i\u003e-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed as power-priors with fixed set of imaginary data. In this paper, we borrow ideas from the power-expected-posterior (PEP) priors in order to introduce, under the \u003ci\u003eg\u003c/i\u003e-prior approach, an extra hierarchical level that accounts for the imaginary data uncertainty. For normal regression variable selection problems, the resulting power-conditional-expected-posterior (PCEP) prior is a conjugate normal-inverse gamma prior which provides a consistent variable selection procedure and gives support to more parsimonious models than the ones supported using the \u003ci\u003eg\u003c/i\u003e-prior and the hyper-\u003ci\u003eg\u003c/i\u003e prior for finite samples. Detailed illustrations and comparisons of the variable selection procedures using the proposed method, the \u003ci\u003eg\u003c/i\u003e-prior and the hyper-\u003ci\u003eg\u003c/i\u003e prior are provided using both simulated and real data examples.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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