62 – Recent Advances in Bayesian Nonparametric Methods
On the Transition Function of Some Time-Dependent Dirichlet and Gamma Processes
Antonio Lijoi
University of Pavia
Matteo Ruggiero
University of Torino and Collegio Carlo Alberto
Dario Span`o
University of Warwick
We highlight a Bayesian interpretation of the transition functions of two classes of measure val- ued diffusions widely used in population genetics, given by Fleming-Viot and Dawson-Watanabe models, which describe time evolving random measures in the Dirichlet and gamma families re- spectively. We review some recent results on temporal conjugacy of these classes under certain assumptions on the data collection at discrete times, and discuss their interpretation in terms of dimensionality reduction of the transition function and of the associated forward propagation of the marginal measure of the process.