MPS-RR 1998-16
August 1998

Nonparametric Bayes inference for concave distribution functions

Martin Bøgsted Hansen

Steffen L. Lauritzen

Abstract

A way of making Bayesian inference for concave distribution functions is introduced. This is done by uniquely transforming a mixture of Dirichlet processes on the space of distribution functions to the space of concave distribution functions. The approach also gives a way of making Bayesian analysis of multiplicatively censored data. We give a method for sampling from the posterior distribution by use of a Polya urn scheme in combination with at Markov chain Monte Carlo algorithm. The methods are extended to estimation of concave distribution functions for incompletely observed data. Finally, consistency issues are touched upon.

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