{"data":{"id":"10.6084/m9.figshare.1627948","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1627948","prefix":"10.6084","suffix":"m9.figshare.1627948","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Rossell, David","givenName":"David","familyName":"Rossell","affiliation":[],"nameIdentifiers":[]},{"name":"Telesca, Donatello","givenName":"Donatello","familyName":"Telesca","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Nonlocal Priors for High-Dimensional Estimation"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2021,"subjects":[{"subject":"Medicine"},{"subject":"Biotechnology"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"69999 Biological Sciences not elsewhere classified","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subjectScheme":"FOR"},{"subject":"80699 Information Systems not elsewhere classified","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subjectScheme":"FOR"},{"subject":"FOS: Computer and information sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","schemeUri":"http://www.abs.gov.au/ausstats/abs@.nsf/0/6BB427AB9696C225CA2574180004463E","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Inorganic Chemistry"},{"subject":"FOS: Chemical sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2021-09-29","dateType":"Created"},{"date":"2021-09-29","dateType":"Updated"},{"date":"2021","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1080/01621459.2015.1130634","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["9020269 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":"Jointly achieving parsimony and good predictive power in high dimensions is a main challenge in statistics. Nonlocal priors (NLPs) possess appealing properties for model choice, but their use for estimation has not been studied in detail. We show that for regular models NLP-based Bayesian model averaging (BMA) shrink spurious parameters either at fast polynomial or quasi-exponential rates as the sample size \u003ci\u003en\u003c/i\u003e increases, while nonspurious parameter estimates are not shrunk. We extend some results to linear models with dimension \u003ci\u003ep\u003c/i\u003e growing with \u003ci\u003en\u003c/i\u003e. Coupled with our theoretical investigations, we outline the constructive representation of NLPs as mixtures of truncated distributions that enables simple posterior sampling and extending NLPs beyond previous proposals. Our results show notable high-dimensional estimation for linear models with \u003ci\u003ep\u003c/i\u003e \u0026gt; \u0026gt;\u003ci\u003en\u003c/i\u003e at low computational cost. NLPs provided lower estimation error than benchmark and hyper-g priors, SCAD and LASSO in simulations, and in gene expression data achieved higher cross-validated \u003ci\u003eR\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e with less predictors. Remarkably, these results were obtained without prescreening variables. Our findings contribute to the debate of whether different priors should be used for estimation and model selection, showing that selection priors may actually be desirable for high-dimensional estimation. Supplementary materials for this article are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0iVVRGLTgiPz4KPHJlc291cmNlIHhtbG5zPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCIgeG1sbnM6eHNpPSJodHRwOi8vd3d3LnczLm9yZy8yMDAxL1hNTFNjaGVtYS1pbnN0YW5jZSIgeHNpOnNjaGVtYUxvY2F0aW9uPSJodHRwOi8vZGF0YWNpdGUub3JnL3NjaGVtYS9rZXJuZWwtNCBodHRwOi8vc2NoZW1hLmRhdGFjaXRlLm9yZy9tZXRhL2tlcm5lbC00LjEvbWV0YWRhdGEueHNkIj4KICA8aWRlbnRpZmllciBpZGVudGlmaWVyVHlwZT0iRE9JIj4xMC42MDg0L005LkZJR1NIQVJFLjE2Mjc5NDg8L2lkZW50aWZpZXI+CiAgPGNyZWF0b3JzPgogICAgPGNyZWF0b3I+CiAgICAgIDxjcmVhdG9yTmFtZT5EYXZpZCBSb3NzZWxsPC9jcmVhdG9yTmFtZT4KICAgICAgPGdpdmVuTmFtZT5EYXZpZDwvZ2l2ZW5OYW1lPgogICAgICA8ZmFtaWx5TmFtZT5Sb3NzZWxsPC9mYW1pbHlOYW1lPgogICAgPC9jcmVhdG9yPgogICAgPGNyZWF0b3I+CiAgICAgIDxjcmVhdG9yTmFtZT5Eb25hdGVsbG8gVGVsZXNjYTwvY3JlYXRvck5hbWU+CiAgICAgIDxnaXZlbk5hbWU+RG9uYXRlbGxvPC9naXZlbk5hbWU+CiAgICAgIDxmYW1pbHlOYW1lPlRlbGVzY2E8L2ZhbWlseU5hbWU+CiAgICA8L2NyZWF0b3I+CiAgPC9jcmVhdG9ycz4KICA8dGl0bGVzPgogICAgPHRpdGxlPk5vbmxvY2FsIFByaW9ycyBmb3IgSGlnaC1EaW1lbnNpb25hbCBFc3RpbWF0aW9uPC90aXRsZT4KICA8L3RpdGxlcz4KICA8ZGVzY3JpcHRpb25zPgogICAgPGRlc2NyaXB0aW9uIGRlc2NyaXB0aW9uVHlwZT0iQWJzdHJhY3QiPiZsdDtwJmd0O0pvaW50bHkgYWNoaWV2aW5nIHBhcnNpbW9ueSBhbmQgZ29vZCBwcmVkaWN0aXZlIHBvd2VyIGluIGhpZ2ggZGltZW5zaW9ucyBpcyBhIG1haW4gY2hhbGxlbmdlIGluIHN0YXRpc3RpY3MuIE5vbmxvY2FsIHByaW9ycyAoTkxQcykgcG9zc2VzcyBhcHBlYWxpbmcgcHJvcGVydGllcyBmb3IgbW9kZWwgY2hvaWNlLCBidXQgdGhlaXIgdXNlIGZvciBlc3RpbWF0aW9uIGhhcyBub3QgYmVlbiBzdHVkaWVkIGluIGRldGFpbC4gV2Ugc2hvdyB0aGF0IGZvciByZWd1bGFyIG1vZGVscyBOTFAtYmFzZWQgQmF5ZXNpYW4gbW9kZWwgYXZlcmFnaW5nIChCTUEpIHNocmluayBzcHVyaW91cyBwYXJhbWV0ZXJzIGVpdGhlciBhdCBmYXN0IHBvbHlub21pYWwgb3IgcXVhc2ktZXhwb25lbnRpYWwgcmF0ZXMgYXMgdGhlIHNhbXBsZSBzaXplICZsdDtpJmd0O24mbHQ7L2kmZ3Q7IGluY3JlYXNlcywgd2hpbGUgbm9uc3B1cmlvdXMgcGFyYW1ldGVyIGVzdGltYXRlcyBhcmUgbm90IHNocnVuay4gV2UgZXh0ZW5kIHNvbWUgcmVzdWx0cyB0byBsaW5lYXIgbW9kZWxzIHdpdGggZGltZW5zaW9uICZsdDtpJmd0O3AmbHQ7L2kmZ3Q7IGdyb3dpbmcgd2l0aCAmbHQ7aSZndDtuJmx0Oy9pJmd0Oy4gQ291cGxlZCB3aXRoIG91ciB0aGVvcmV0aWNhbCBpbnZlc3RpZ2F0aW9ucywgd2Ugb3V0bGluZSB0aGUgY29uc3RydWN0aXZlIHJlcHJlc2VudGF0aW9uIG9mIE5MUHMgYXMgbWl4dHVyZXMgb2YgdHJ1bmNhdGVkIGRpc3RyaWJ1dGlvbnMgdGhhdCBlbmFibGVzIHNpbXBsZSBwb3N0ZXJpb3Igc2FtcGxpbmcgYW5kIGV4dGVuZGluZyBOTFBzIGJleW9uZCBwcmV2aW91cyBwcm9wb3NhbHMuIE91ciByZXN1bHRzIHNob3cgbm90YWJsZSBoaWdoLWRpbWVuc2lvbmFsIGVzdGltYXRpb24gZm9yIGxpbmVhciBtb2RlbHMgd2l0aCAmbHQ7aSZndDtwJmx0Oy9pJmd0OyAmZ3Q7ICZndDsmbHQ7aSZndDtuJmx0Oy9pJmd0OyBhdCBsb3cgY29tcHV0YXRpb25hbCBjb3N0LiBOTFBzIHByb3ZpZGVkIGxvd2VyIGVzdGltYXRpb24gZXJyb3IgdGhhbiBiZW5jaG1hcmsgYW5kIGh5cGVyLWcgcHJpb3JzLCBTQ0FEIGFuZCBMQVNTTyBpbiBzaW11bGF0aW9ucywgYW5kIGluIGdlbmUgZXhwcmVzc2lvbiBkYXRhIGFjaGlldmVkIGhpZ2hlciBjcm9zcy12YWxpZGF0ZWQgJmx0O2kmZ3Q7UiZsdDsvaSZndDsmbHQ7c3VwJmd0OzImbHQ7L3N1cCZndDsgd2l0aCBsZXNzIHByZWRpY3RvcnMuIFJlbWFya2FibHksIHRoZXNlIHJlc3VsdHMgd2VyZSBvYnRhaW5lZCB3aXRob3V0IHByZXNjcmVlbmluZyB2YXJpYWJsZXMuIE91ciBmaW5kaW5ncyBjb250cmlidXRlIHRvIHRoZSBkZWJhdGUgb2Ygd2hldGhlciBkaWZmZXJlbnQgcHJpb3JzIHNob3VsZCBiZSB1c2VkIGZvciBlc3RpbWF0aW9uIGFuZCBtb2RlbCBzZWxlY3Rpb24sIHNob3dpbmcgdGhhdCBzZWxlY3Rpb24gcHJpb3JzIG1heSBhY3R1YWxseSBiZSBkZXNpcmFibGUgZm9yIGhpZ2gtZGltZW5zaW9uYWwgZXN0aW1hdGlvbi4gU3VwcGxlbWVudGFyeSBtYXRlcmlhbHMgZm9yIHRoaXMgYXJ0aWNsZSBhcmUgYXZhaWxhYmxlIG9ubGluZS4mbHQ7L3AmZ3Q7PC9kZXNjcmlwdGlvbj4KICA8L2Rlc2NyaXB0aW9ucz4KICA8c3ViamVjdHM+CiAgICA8c3ViamVjdD5NZWRpY2luZTwvc3ViamVjdD4KICAgIDxzdWJqZWN0PkJpb3RlY2hub2xvZ3k8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5FY29sb2d5PC9zdWJqZWN0PgogICAgPHN1YmplY3Qgc2NoZW1lVVJJPSJodHRwOi8vd3d3LmFicy5nb3YuYXUvYXVzc3RhdHMvYWJzQC5uc2YvMC82QkI0MjdBQjk2OTZDMjI1Q0EyNTc0MTgwMDA0NDYzRSIgc3ViamVjdFNjaGVtZT0iRk9SIj42OTk5OSBCaW9sb2dpY2FsIFNjaWVuY2VzIG5vdCBlbHNld2hlcmUgY2xhc3NpZmllZDwvc3ViamVjdD4KICAgIDxzdWJqZWN0IHNjaGVtZVVSST0iaHR0cDovL3d3dy5hYnMuZ292LmF1L2F1c3N0YXRzL2Fic0AubnNmLzAvNkJCNDI3QUI5Njk2QzIyNUNBMjU3NDE4MDAwNDQ2M0UiIHN1YmplY3RTY2hlbWU9IkZPUiI+ODA2OTkgSW5mb3JtYXRpb24gU3lzdGVtcyBub3QgZWxzZXdoZXJlIGNsYXNzaWZpZWQ8L3N1YmplY3Q+CiAgICA8c3ViamVjdCBzY2hlbWVVUkk9Imh0dHA6Ly93d3cuYWJzLmdvdi5hdS9hdXNzdGF0cy9hYnNALm5zZi8wLzZCQjQyN0FCOTY5NkMyMjVDQTI1NzQxODAwMDQ0NjNFIiBzdWJqZWN0U2NoZW1lPSJGT1IiPjE5OTk5IE1hdGhlbWF0aWNhbCBTY2llbmNlcyBub3QgZWxzZXdoZXJlIGNsYXNzaWZpZWQ8L3N1YmplY3Q+CiAgICA8c3ViamVjdD5Jbm9yZ2FuaWMgQ2hlbWlzdHJ5PC9zdWJqZWN0PgogIDwvc3ViamVjdHM+CiAgPHB1Ymxpc2hlcj5UYXlsb3IgJmFtcDsgRnJhbmNpczwvcHVibGlzaGVyPgogIDxwdWJsaWNhdGlvblllYXI+MjAyMTwvcHVibGljYXRpb25ZZWFyPgogIDxkYXRlcz4KICAgIDxkYXRlIGRhdGVUeXBlPSJDcmVhdGVkIj4yMDIxLTA5LTI5PC9kYXRlPgogICAgPGRhdGUgZGF0ZVR5cGU9IlVwZGF0ZWQiPjIwMjEtMDktMjk8L2RhdGU+CiAgPC9kYXRlcz4KICA8cmVzb3VyY2VUeXBlIHJlc291cmNlVHlwZUdlbmVyYWw9IkRhdGFzZXQiPkRhdGFzZXQ8L3Jlc291cmNlVHlwZT4KICA8c2l6ZXM+CiAgICA8c2l6ZT45MDIwMjY5IEJ5dGVzPC9zaXplPgogIDwvc2l6ZXM+CiAgPHJlbGF0ZWRJZGVudGlmaWVycz4KICAgIDxyZWxhdGVkSWRlbnRpZmllciByZWxhdGVkSWRlbnRpZmllclR5cGU9IkRPSSIgcmVsYXRpb25UeXBlPSJJc1N1cHBsZW1lbnRUbyI+MTAuMTA4MC8wMTYyMTQ1OS4yMDE1LjExMzA2MzQ8L3JlbGF0ZWRJZGVudGlmaWVyPgogIDwvcmVsYXRlZElkZW50aWZpZXJzPgogIDxyaWdodHNMaXN0PgogICAgPHJpZ2h0cyByaWdodHNVUkk9Imh0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