Cari colleghi,

nell’ambito del programma di Visiting Professors della Laurea Magistrale in Stochastics and Data Science dell’Università di Torino (il programma completo è consultabile alla pagina https://www.master-sds.unito.it/go/visiting), con piacere annunciamo il seguente corso:

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MARTA CATALANO (University of Warwick)

DEPENDENT NONPARAMETRIC PRIORS VIA COMPLETELY RANDOM MEASURES

Bayesian nonparametrics provides a natural framework for performing flexible inference with principled quantification of uncertainty. The main ingredients are discrete random measures, whose laws act as prior distribution for infinite-dimensional parameters and, combined with the data, provide their posterior distribution. Recent works use dependent random measures to perform simultaneous inference across multiple samples. The borrowing of strength across different samples is regulated by the dependence structure of the random measures, with complete dependence corresponding to maximal sharing of information and fully exchangeable observations. In these lectures we start from the notion of completely random measure and describe several ways of introducing dependence between them. Different models may still induce the same amount of borrowing of information, measured by an index of dependence. In the two sample case, this is often achieved by second order summaries of the joint distribution through linear correlation. In the multivariate scenario, we characterise dependence in terms of distance from exchangeability by relying on optimal transport. This allows for informed prior elicitations and provides a fair ground for model comparison.

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Il corso si svolgerà solo in presenza secondo il seguente calendario

Lez 1: mar 13/12: 14-16 - Aula 4 Lez 2: mer 14/12: 9.15-11.15 - Aula 4 Lez 3: mer 14/12: 14-16 - Aula 30 Lez 4: gio 15/12: 14-16 - Aula 11

Sede dei corsi: Corso Unione Sovietica 218/bis, 10134, Torino

Il corso è rivolto agli studenti della Laurea Magistrale ma la partecipazione è aperta a tutti gli interessati.

Cordiali saluti, Matteo Ruggiero

--- Matteo Ruggiero University of Torino and Collegio Carlo Alberto www.matteoruggiero.it