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Lookup NU author(s): Dr Cristiano Villa
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.
Author(s): Villa C, Walker SG
Publication type: Article
Publication status: Published
Journal: Bayesian Analysis
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
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