A simulation study to compare reference and other priors in the case of a standard univariate Student t-distribution

A. J. van der Merwe; M. J. von Maltitz; J. H. Meyer; P. C. N. Groenewald

doi:10.37920/sasj.2022.56.2.2

A. J. van der Merwe Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa
M. J. von Maltitz Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa
J. H. Meyer Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa
P. C. N. Groenewald Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa

DOI: https://doi.org/10.37920/sasj.2022.56.2.2

Keywords: Coverage percentages, Credibility intervals, Log-returns, Mean squared error, Probability-matching prior, Reference priors

Abstract

In this paper, reference and probability-matching priors are derived for the univariate Student t-distribution. These priors generally lead to procedures with properties frequentists can relate to while still retaining Bayes validity. The priors are tested by performing simulation studies. The focus is on the relative mean squared error from the posterior median and on the frequentist coverage of the 95% credibility intervals for a sample of size n = 30. Average interval lengths of the credibility intervals as well as the modes of the interval lengths based on 2 000 simulations are also considered. The performance of the priors is also tested on real data, namely daily logarithmic returns of IBM stocks.