Bollettino settimanale
Settimana 05/12/2022 - 09/12/2022
Seminari
Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
Gruppo U.M.I. PR.I.S.M.A. (PRobability In Statistics, Mathematics and Applications)
Date: Monday 5th December, 2022
Schedule: 16:00 - Rome Time
Where: On-line talk (see below the streaming link)
Speaker: Antonio Lijoi (Università Bocconi)
Title: "Discrete random structures and Bayesian nonparametric modeling"
Abstract:
Discrete random structures, such as random partitions and discrete random measures, have emerged as effective tools for Bayesian modeling and have fueled exciting advances in density estimation, clustering, prediction, feature allocation and survival analysis. The Dirichlet process (DP) has undoubtedly emerged as a reference model, mostly due to its analytical tractability. Nonetheless, the DP shares also some well-known limitations that have spurred a very lively area of research aiming at the proposal and the investigation of more general and flexible discrete nonparametric priors. The talk will provide a broad overview of such classes of priors and will specifically focus on those obtained as normalization of completely random measures. Characterizations of the induced random partitions and predictive rules will be illustrated and their role in designing computational algorithms for the approximation of Bayesian inferences of interest will be highlighted, both in exchangeable and non-exchangeable settings.
Speaker: Federico Camerlenghi (Milano Bicocca)
Title: Normalized random measures with atoms' interaction
Abstract:
The seminal work of Ferguson (1973), who introduced the Dirichlet
process, has spurred the definition and investigation of more general
classes of Bayesian nonparametric priors, with the aim at increasing
flexibility while maintaining analytical tractability. Among the
numerous generalizations, a fundamental class of random probability
measures has been introduced by Regazzini et al. (2003): this is the
class of normalized random measures with independent increments (NRMIs).
NRMIs are random probability measures with almost surely discrete
realizations, defined through the specifications of two ingredients: i)
a sequence of unnormalized weights, which are the jumps of a Levy
process on the positive real line; ii) a sequence of i.i.d. random atoms
from a common base measure. The proposed construction is appealing from
a mathematical standpoint, because analytical tractability is preserved,
however NRMIs do not allow interaction among atoms, which are supposed
to be independent and identically distributed. In some applied
frameworks, the i.i.d. assumption could be too restrictive, for
instance, in model-based clustering, when they are used as mixing
measures in mixture models. To overcome this limitation, we propose a
new class of normalized random measures with atoms' interaction. In our
construction the atoms come from a finite point process, which is marked
with i.i.d. positive weights. Thus, a new class of random probability
measures is obtained by normalization. The desired interaction among
atoms is then induced by a suitable choice of the law of the point
process, which can create a repulsive or attractive behaviour. By means
of Palm calculus, we are able to characterize marginal, predictive and
posterior distributions for the proposed model. We specialize all our
results for several choices of the finite point process, i.e., in the
Determinantal, Gibbs and Shot-Noise Cox case.
(Based on a joint work with Raffaele Argiento, Mario Beraha and Alessandra Guglielmi.)
Further Info: Click here for PR.I.S.M.A. Page and Click here for PR.I.S.M.A. calendar of scientific meetings 2022/24 Page
Streaming Link (MS Teams): Click here
Università degli Studi Roma Tor Vergata
Dipartimento di Matematica
DIFFERENTIAL EQUATIONS SEMINAR
Date: December 6th 2022
Schedule: 16:00 - Rome Time
Where: Conference Room 1201 "R. Dal Passo"
Speaker: Marco Ghimenti (Università di Pisa)
Title: " Compactness and blow up for Yamabe boundary problem "
Abstract: In 1992 Escobar extended the well known Yamabe problem to manifolds with boundary. The case of the scalar flat target manifold is particularly interesting since it also represents a generalization
to Riemann mapping theorem to higher dimensions. In this talk we discuss when the solutions of the Yamabe boundary problem are a compact set, or when they form a blowing up sequence, underlining the affinities and the differences with the classical Yamabe problem.
Nota: Questo seminario fa parte delle attività finanziate dal progetto MIUR Dipartimento d'eccellenza MATH@TOV CUP E83C18000100006
Organizing Committee:
Riccardo Molle (mail to contact)
Alfonso Sorrentino (mail to contact)
Further Info and Program: Click here for DIFFERENTIAL EQUATIONS SEMINAR Page
Streaming Link (MS Teams): This seminar will be held in person
Eventi
Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica
Corso di Dottorato
INTRODUCTION TO LOEWNER THEORY IN ONE COMPLEX VARIABLE (PRELIMINARY PROGRAMME OF THE COURSE)
Where: Conference Room 1200 and Online
Speaker: Prof. Pavel Gumenyuk (Politecnico di Milano)
Period: 22.08.11 - 22.20.12
Schedule:
| Day | Time and Room |
|---|---|
| 2022.08.11 | 14:00 - 16:00 Conference Room 1200 |
| 2022.10.11 | 14:00 - 16:00 OnLine |
| 2022.22.11 | 14:00 - 16:00 OnLine |
| 2022.24.11 | 14:00 - 16:00 OnLine |
| 2022.29.11 | 14:00 - 16:00 OnLine |
| 2022.05.12 | 14:00 - 16:00 OnLine |
| 2022.06.12 | 14:00 - 16:00 OnLine |
| 2022.13.12 | 14:00 - 16:00 OnLine |
| 2022.15.12 | 14:00 - 16:00 OnLine |
| 2022.20.12 | 14:00 - 16:00 OnLine |
Organizing Committee: Fillippo Bracci (Contatto E-Mail)
Title: INTRODUCTION TO LOEWNER THEORY IN ONE COMPLEX VARIABLE
Title: INTRODUCTION TO LOEWNER THEORY IN ONE COMPLEX VARIABLE
Abstract: Topics of the course belong to Complex Analysis in one complex variable and are mainly related to problems in Conformal Mapping. At the same time, although it is not discussed in the course, the modern Loewner Theory has natural extension to several complex variables. Loewner Theory combines deep results from Complex Analysis with fundamental ideas from Dynamics and Lie Group Theory. It includes, as a special case, the theory of one-parameter semigroups, which is classically known to have important applications to time-homogeneous Markov processes. The course would be primarily useful for those students who are interested in Complex Anal- ysis (one and/or several variables) or whose who wish to refresh and deepen his/hers knowledge in one complex variable. Furthermore, the course is advisable for students in Probabilities, espe- cially for those who are interested in applications of Complex Analysis to Stochastic Processes. Finally, the course would be enjoyable for everybody who is curious to see how ideas and meth- ods from different parts of Analysis can work together in the unit disk of the complex plane.