Partially Exchangeable Processes Indexed by the Vertices of a k-tree Constructed Via reinforcement

In this paper we introduced new stochastic processes indexed by the vertices of a k-tree. While these processes are of interest in their own right, there are statistical applications in Bayesian nonparametric problems. As such, the paper can be viewed as a natural extension of the papers of Muliere,Secchi and Walker from exchangeable to regression problems via consideration of partially exchangeable sequences. Reinforcement will again be the fundamental tool for constructing the processes. As a motivation fro our binary process we consider the bayesian nonparametric binary regression model.In this paper we have considered processes which are formed via dependent exchangeable sequences. The collection of these sequences wuold be termed partially exchangeable in the language of de Finetti. It is well known that partially exchamgeable sequences have applications in bayesian regression problems.