{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T12:07:36Z","timestamp":1791806856062,"version":"4.3.4"},"reference-count":24,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2019,12,24]],"date-time":"2019-12-24T00:00:00Z","timestamp":1577145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,3,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without relying on asymptotic approximations. However, sharply constrained priors are not necessary in some settings and tend to limit modelling scope to a narrow set of distributions that are tractable computationally. We propose to replace the sharp indicator function of the constraint with an exponential kernel, thereby creating a close-to-constrained neighbourhood within the Euclidean space in which the constrained subspace is embedded. This kernel decays with distance from the constrained space at a rate depending on a relaxation hyperparameter. By avoiding the sharp constraint, we enable use of off-the-shelf posterior sampling algorithms, such as Hamiltonian Monte Carlo, facilitating automatic computation in a broad range of models. We study the constrained and relaxed distributions under multiple settings and theoretically quantify their differences. Application of the method is illustrated through several novel modelling examples.<\/jats:p>","DOI":"10.1093\/biomet\/asz069","type":"journal-article","created":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T07:09:53Z","timestamp":1573628993000},"page":"191-204","source":"Crossref","is-referenced-by-count":10,"title":["Bayesian constraint relaxation"],"prefix":"10.1093","volume":"107","author":[{"given":"Leo L","family":"Duan","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Florida, 101C Griffin-Floyd Hall, P.O. Box 118545, Gainesville, Florida 32611, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander L","family":"Young","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, Duke University, Box 90251, Durham, North Carolina 27708, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Akihiko","family":"Nishimura","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Los Angeles, 8125 Math Sciences Building, Los Angeles, California 90095, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David B","family":"Dunson","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Florida, 101C Griffin-Floyd Hall, P.O. 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