Natural (Non-)Informative Priors for Skew-symmetric Distributions


Dette, H; Ley, C; Rubio, F; (2017) Natural (Non-)Informative Priors for Skew-symmetric Distributions. Scandinavian Journal of Statistics. n/a-n/a. ISSN 1467-9469 DOI: https://doi.org/10.1111/sjos.12306

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[img] Text - Accepted Version
Restricted to Repository staff only until 10 October 2018.
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Abstract

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew-symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape 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 via a Monte Carlo simulation study that our non-informative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale-invariant 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.

Item Type: Article
Keywords: measure of skewness, prior elicitation, skew-symmetric distributions, total variation distance
Faculty and Department: Faculty of Epidemiology and Population Health > Dept of Non-Communicable Disease Epidemiology
URI: http://researchonline.lshtm.ac.uk/id/eprint/4646387

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