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Objective prior for the number of degrees of freedom of a t distribution.

Lookup NU author(s): Dr Cristiano VillaORCiD



This is the final published version of an article that has been published in its final definitive form by International Society for Bayesian Analysis, 2014.

For re-use rights please refer to the publisher's terms and conditions.


In 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 dom- inate 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.

Publication metadata

Author(s): Villa C, Walker SG

Publication type: Article

Publication status: Published

Journal: Bayesian Analysis

Year: 2014

Volume: 9

Issue: 1

Pages: 197-220

Print publication date: 01/03/2014

Online publication date: 01/01/2014

Acceptance date: 14/08/2013

Date deposited: 20/05/2020

ISSN (print): 1936-0975

ISSN (electronic): 1931-6690

Publisher: International Society for Bayesian Analysis


DOI: 10.1214/13-BA854


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