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The methodology is based on a combination of continuous mixtures of \u003ci\u003eg\u003c/i\u003e-priors for model parameters and a multiplicity-correction prior for the models themselves. We introduce our approach in the normal model and extend it to non-normal exponential families. A simulation study and an application with binary outcome is provided. An efficient implementation is available in the R-package “hypergsplines”.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/articles/dataset/Objective_Bayesian_Model_Selection_in_Generalised_Additive_Models_with_Penalised_Splines/1006465/1","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2016-01-18T23:15:21.000Z","registered":"2016-01-18T23:15:22.000Z","published":"2015","updated":"2020-09-04T23:37:32.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.1006465.v1","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}