A Monte Carlo Method for Computing the HPD Interval for Ratio of Two Multivariate Normal Generalized Variances

摘要

In this article, we develop a method for computing a Bayesian HPD (highest probability density) interval for a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval are intractable and thus a Bayesian HPD interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao (1999). Necessary theory involved in the method and computation is provided.