Dear all,

We are glad to announce the next DEMS webinar: Wednesday, 18th November 2020, time 13.00 (CET). link to attend: https://unimib.webex.com/unimib/onstage/g.php?MTID=eadc0aefcf2b20a4d5b65dfc1... The speaker is *François Caron*, Department of Statistics, University of Oxford (UK).

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*TITLE*. *A unified construction for series representations and finite approximations of completely random measures*

*ABSTRACT*. Infinite-activity completely random measures (CRMs) have become important building blocks of complex Bayesian nonparametric models. They have been successfully used in various applications such as clustering, density estimation, latent feature models, survival analysis or network science. Popular infinite-activity CRMs include the (generalized) gamma process and the (stable) beta process. However, except in some specific cases, exact simulation or scalable inference with these models is challenging and finite-dimensional approximations are often considered. In this work, we propose a general and unified framework to derive both series representations and finite-dimensional approximations of CRMs. Our framework can be seen as a generalization of constructions based on size-biased sampling of Poisson point process [Perman et al., 1992]. It includes as special cases several known series representations and finite approximations as well as novel ones. In particular, we show that one can get novel series representations for the generalized gamma process and the stable beta process. We show how these constructions can be used to derive novel algorithms for posterior inference, including a generalization of the slice sampler for normalized CRMs mixture models introduced by Griffin and Walker [2011]. We also provide some analysis of the truncation error.

Joint work with Juho Lee and Xenia Miscouridou https://arxiv.org/abs/1905.10733

*Details to attend the webinar.* Event number (access code): 174 366 0917 Event password: 18112020

Wednesday, November 18, 2020 1:00 pm, Europe Time (Rome, GMT+01:00)

Event address for attendees: https://unimib.webex.com/unimib/onstage/g.php?MTID=eadc0aefcf2b20a4d5b65dfc1...

******************************************************* The webinar is organized by the Department of Economics, Management and Statistics (DEMS) of the University of Milano - Bicocca.