The central assumption in the Bayesian approach to inductive reasoning is that there exists a random parameter that rules the distribution of the observations. The model is completed by choosing a prior distribution for the parameter, and inference consists in computing the conditional distribution of the parameter, given the sample. A different modeling strategy uses Ionescu-Tulcea theorem to define the law of the observation process from the sequence of predictive distributions. In this talk, we consider a class of predictive constructions based on measure-valued Pólya urn processes. These processes have been introduced in the probabilistic literature as an extension of k-colour urn models, but their implications for Bayesian statistics have yet to be explored.