Size-biased sampling and discrete nonparametric Bayesian inference

In this paper, we establish the connection between two different topics, i.e. size-biased sampling schemes and Bayesian updating mechanisms for a general class P of discrete nonparametric priors. By exploiting this connection, we are able to use size-biased sampling theory to find representations of the class particularly suitable for applications to inference problems and to derive new general results about its posterior and predictive distributions and about the properties of a sample from P. Potential of the approach is illustrated via an application to the Dirichlet process and an investigation of a new class of symmetric priors.