Bayesian predictive densities as an interpretation of a class of Skew--Student $t$ distributions with application to medical data

Abdolnasser Sadeghkhani

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arXiv · 1805.09468

Bayesian predictive densities as an interpretation of a class of Skew--Student $t$ distributions with application to medical data

Abdolnasser Sadeghkhani

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Abstract

This paper describes a new Bayesian interpretation of a class of skew--Student $t$ distributions. We consider a hierarchical normal model with unknown covariance matrix and show that by imposing different restrictions on the parameter space, corresponding Bayes predictive density estimators under Kullback-Leibler loss function embrace some well-known skew--Student $t$ distributions. We show that obtained estimators perform better in terms of frequentist risk function over regular Bayes predictive density estimators. We apply our proposed methods to estimate future densities of medical data: the leg-length discrepancy and effect of exercise on the age at which a child starts to walk.

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Abdolnasser Sadeghkhani. 2018-05-24. Bayesian predictive densities as an interpretation of a class of Skew--Student $t$ distributions with application to medical data. https://arxiv.org/abs/1805.09468

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