Objective Prior for the Number of Degrees of Freedom of a T Distribution

dc.contributor.utaustinauthorWalker, Stephen G.en_US
dc.creatorVilla, Cristianoen_US
dc.creatorWalker, Stephen G.en_US
dc.date.accessioned2016-10-28T19:52:50Z
dc.date.available2016-10-28T19:52:50Z
dc.date.issued2014en_US
dc.description.abstractIn this paper, we construct an objective prior for the degrees of freedom of a t distribution, when the parameter is taken to be discrete. This parameter is typically problematic to estimate and a problem in objective Bayesian inference since improper priors lead to improper posteriors, whilst proper priors may dominate the data likelihood. We find an objective criterion, based on loss functions, instead of trying to define objective probabilities directly. Truncating the prior on the degrees of freedom is necessary, as the t distribution, above a certain number of degrees of freedom, becomes the normal distribution. The defined prior is tested in simulation scenarios, including linear regression with t-distributed errors, and on real data: the daily returns of the closing Dow Jones index over a period of 98 days.en_US
dc.description.departmentMathematicsen_US
dc.description.sponsorshipen_US
dc.identifierdoi:10.15781/T29Z90F6N
dc.identifier.citationVilla, Cristiano, and Stephen G. Walker. "Objective Prior for the Number of Degrees of Freedom of at Distribution." Bayesian Analysis, Vol. 9, No. 1 (2014): 197-220.en_US
dc.identifier.doi10.1214/13-ba854en_US
dc.identifier.issn1931-6690en_US
dc.identifier.urihttp://hdl.handle.net/2152/43313
dc.language.isoEnglishen_US
dc.relation.ispartofen_US
dc.relation.ispartofserialBayesian Analysisen_US
dc.rightsAdministrative deposit of works to Texas ScholarWorks: This works author(s) is or was a University faculty member, student or staff member; this article is already available through open access or the publisher allows a PDF version of the article to be freely posted online. The library makes the deposit as a matter of fair use (for scholarly, educational, and research purposes), and to preserve the work and further secure public access to the works of the University.en_US
dc.rights.restrictionOpenen_US
dc.subjectobjective prioren_US
dc.subjectt distributionen_US
dc.subjectkullback-leibler divergenceen_US
dc.subjectlinearen_US
dc.subjectregressionen_US
dc.subjectself-information loss functionen_US
dc.subjectrobust analysisen_US
dc.subjectfinancialen_US
dc.subjectreturnen_US
dc.subjectbayesian-analysisen_US
dc.subjectlinear-regressionen_US
dc.subjectmodelsen_US
dc.subjecterrorsen_US
dc.subjectmathematics, interdisciplinary applicationsen_US
dc.subjectstatistics & probabilityen_US
dc.titleObjective Prior for the Number of Degrees of Freedom of a T Distributionen_US
dc.typeArticleen_US

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