Minimum message length inference and mixture modelling of inverse gaussian distributions

Authors:
Daniel F. Schmidt;Enes Makalic
Affiliations:
Centre for MEGA Epidemiology, The University of Melbourne, Carlton, VIC, Australia;Centre for MEGA Epidemiology, The University of Melbourne, Carlton, VIC, Australia
Venue:
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
Year:
2012

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Abstract

This paper examines the problem of modelling continuous, positive data by finite mixtures of inverse Gaussian distributions using the minimum message length (MML) principle. We derive a message length expression for the inverse Gaussian distribution, and prove that the parameter estimator obtained by minimising this message length is superior to the regular maximum likelihood estimator in terms of Kullback---Leibler divergence. Experiments on real data demonstrate the potential benefits of using inverse Gaussian mixture models for modelling continuous, positive data, particularly when the data is concentrated close to the origin or exhibits a strong positive skew.