文章基本信息

标题：Objective Prior for the Number of Degrees of Freedom of a t Distribution
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作者：Cristiano Villa ; Stephen G. Walker
期刊名称：Bayesian Analysis
印刷版ISSN：1931-6690
电子版ISSN：1936-0975
出版年度：2014
卷号：9
期号：1
页码：197-220
DOI：10.1214/13-BA854
语种：English
出版社：International Society for Bayesian Analysis
摘要：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 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.