We introduce a stochastic process based on nonhomogeneous Poisson processes and urn processes which can be reinforced to produce a mixture of semi-Markov processes. By working with the notion of exchangeable blocks within the process, we present a Bayesian nonparametric framework for handling...

We define a reinforced stochastic process of random variables indexed by the vertices of a k-tree and with values in a Polish space. The work presents a natural extension from an exchangeable to a partially exchangeable setting of previous work done by the authors.