Abstract:
This paper presents two types of symmetric scale mixture probability distributions which include the normal, Student t, Pearson Type VII, variance gamma, exponential power, uniform power and generalised t (GT) distributions. Expressing a symmetric distirbution into a scale mixture for enables efficient Bayersian Markov chain Monte Carlo (MCMC) algorithms in the implementation of complicated statistical models. Moreover, the mixing parameters, a by-product of the scale mixtures representation, can be used to identify possible outliers. this paper also proposes a uniform scale mixture representation for the GT density and demonstrates how this density representation alleviates the computational burden of the Gibbs sampler.
