A0804
Title: Generalized measure-valued Polya sequences
Authors: Hristo Sariev - Sofia University (Bulgaria) [presenting]
Abstract: Measure-valued Polya urn sequences (MVPS) are a generalization of the observation processes generated by k-color Polya urn models, where the space of colors is unbounded and urn composition is modeled by finite measures. An extension of MVPSs is investigated via a randomization of the law of the reinforcement, called generalized measure-valued Polya urn sequences (GMVPS). Using that, the urn composition process is a measure-valued Markov chain, showing that GVMPSs can be represented as mixtures of MVPSs. The focus is then on the class of generalized randomly reinforced Polya sequences (GRRPS), which are GMVPSs whose reinforcement is a weighted Dirac measure. It follows from the form of their predictive distributions that the dynamics of GRRPSs are driven by the interaction between weights and observations. Under the additional assumption that the weights are marginally exchangeable, it is proven that the joint process tracking weights and observations is partially conditionally identically distributed, from which its asymptotic properties are derived.
