Scale mixtures distributions in statistical modelling

Blackwell Publishing Ltd
Publication Type:
Journal Article
Australian & New Zealand Journal of Statistics, 2008, 50 (2), pp. 135 - 146
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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.
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