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Paper No. 10-22

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M Kolossiatis, JE Griffin and MFJ Steel

On Bayesian nonparametric modelling of two correlated distributions

Abstract: In this paper, we consider the problem of modelling a pair of related distributions using Bayesian nonparametric methods. A representation of the distributions as weighted sums of distributions is derived through normalisation. This allows us to define several classes of nonparametric priors. The properties of these distributions are explored and efficient Markov chain Monte Carlo methods are developed. The methodology is illustrated on simulated data and an example concerning hospital efficiency measurement.

Keywords: Hospital efficiencies, Markov chain Monte Carlo, Normalised Random Measures, P´olya urn