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

Villa, Cristiano, Walker, Stephen (2014) Objective prior for the number of degrees of freedom of a t distribution. Bayesian Analysis, 9 (1). pp. 197-220. ISSN 1936-0975. (doi:10.1214/13-BA854)

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http://dx.doi.org/10.1214/13-BA854

## Abstract

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.

Item Type: Article 10.1214/13-BA854 Q ScienceQ Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Statistics Cristiano Villa 18 Oct 2014 22:26 UTC 29 May 2019 13:13 UTC https://kar.kent.ac.uk/id/eprint/43475 (The current URI for this page, for reference purposes)