Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-16

August 1998

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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