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Paper No. 10-24

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JE Griffin, M Kolossiatis and MFJ Steel

Comparing Distributions Using Dependent Normalized Random Measure Mixtures

Date: December 2010

Abstract: A methodology for the simultaneous Bayesian nonparametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in some detail. Efficient slice sampling methods are developed for inference. Various posterior summaries are introduced which allow better understanding of the differences between distributions. The methods are illustrated on simulated data and examples from survival analysis and stochastic frontier analysis.

Keywords: Bayesian nonparametrics; Dependent distributions; Dirichlet process; Normalized Generalized Gamma process; Slice sampling; Utility function.