[Statlist] Research Seminar in Statistics *FRIDAY 20 OCTOBER 2017* GSEM, University of Geneva

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Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you

Organizers :                                                                                   
E. Cantoni - D. La Vecchia - E. Ronchetti
S. Sperlich - F. Trojani - M.-P. Victoria-Feser 

FRIDAY 20 OCTOBER 2017 at 11:15am, Uni-Mail M 5220

Filtering Time-Evolving Dirichlet and Gamma Random Measures
Matteo RUGGIERO- Università degli Studi di Torino & Collegio Carlo Alberto, Italy

ABSTRACT:
After reviewing some recent results on filtering finite-dimensional diffusion processes via duality, we extend classic characterisations of posterior distributions under Dirichlet process and gamma random measures priors to a dynamic framework. We consider the problem of learning, from indirect observations, two families of measure-valued processes: a Fleming-Viot process, with data given by random samples from the process state at discrete times; and a Dawson-Watanabe process, with data collected according to a Poisson point process with intensity given by the process state at discrete times. Both processes are diffusions taking values in the space of discrete measures whose support varies with time, and are stationary and reversible with respect to Dirichlet and gamma priors respectively. A common methodology is developed to show that the time-marginal posteriors given past and present data belong to classes of finite mixtures of Dirichlet processes and gamma random measures respectively, yielding conjugacy of these classes to the type of data we consider. We provide explicit results on the parameters of the mixture components and on the mixing weights, which can be computed recursively, are time-varying and drive the mixtures towards the respective priors in absence of further data.


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