Natural (non-)informative priors for skew-symmetric distributions
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Date
2016
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Abstract
In this paper, we present an innovative method for constructing proper priors for the
skewness parameter in the skew-symmetric family of distributions. The proposed method is
based on assigning a prior distribution on the perturbation effect of the skewness parameter,
which is quantified in terms of the Total Variation distance. We discuss strategies to translate
prior beliefs about the asymmetry of the data into an informative prior distribution of this
class. We show that our priors induce posterior distributions with good frequentist properties
via a Monte Carlo simulation study. We also propose a scale- and location-invariant prior
structure for models with unknown location and scale parameters and provide sufficient
conditions for the propriety of the corresponding posterior distribution. Illustrative examples
are presented using simulated and real data.
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Keywords
measure of skewness, Wasserstein metric, total variation distance, skew-symmetric distributions, prior elicitation