----------------------------------------------------------------------------- A v v i s o d i M i n i - C o r s o ----------------------------------------------------------------------------- Venerdì 04 Aprile, ore 10:00-13:00 ----------------------------------------------------------------------------- Aula VI (quarto piano) Dipartimento di Scienze Statistiche Sapienza Università di Roma C.LAUDIO DURASTANTI V.ALENTINA CAMMAROTA D.OMENICO MARINUCCI (Dip. di Matematica, Università degli Studi di Roma Tor Vergata) terranno un mini-corso dal titolo STEIN-MALLIAVIN APPROXIMATIONS IN STATISTICS & PROBABILITY tutti gli interessati sono invitati a partecipare. ----------------------------------------------------------------------------- Maggiori informazioni sui seminari presso il DSS sono consultabili a quest'indirizzo: http://goo.gl/Y6OQYm Saluti Pierpaolo Brutti - Fulvio De Santis --- P R O G R A M Part I: The Geometry of Needlets Excursion Sets Domenico Marinucci In this talk, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on wavelet/needlet components of spherical random fields. For such fields, we consider smoothed polynomial transforms, such as those arising from local estimates of angular power spectra and bispectra; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. Our main technical tools are recent results on Malliavin calculus and Total Variation bounds for Gaussian subordinated fields by Nourdin and Peccati, and the Gaussian Kinematic Formula by Adler and Taylor, which we shall review briefly in the talk. We put particular emphasis on the analysis of Euler-Poincaré characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the statistical investigation of asymmetries and anisotropies in Cosmic Microwave Background radiation (CMB) data. Based on joint work with Sreekar Vadlamani Part II: Stein-Malliavin Approximations for Needlets Polyspectra Valentina Cammarota We provide quantitative Central Limit Theorems, in the high frequency limit, for nonlinear transforms of spherical wavelets/needlets random fields, which are of immediate interest for spherical data analysis. In particular, we focus on so-called needlets polyspectra, which are popular tools for nonGaussianity analysis in the cosmological community, and on the area of excursion sets. Our results are based on Stein-Maliavin approximations for nonlinear transforms of Gaussian fields, and on an explicit derivation on the high-frequency limit of the fields' variances, which may have some independent interest. Based on joint work with Domenico Marinucci Part III: Normal Approximations for Linear and U-Statistics on Spherical Poisson Fields Claudio Durastanti We review a recent stream of research on Normal approximations for linear and U-statistics of wavelets/needlets coefficients evaluated on a homogeneous spherical Poisson fi...eld. We show how exploting results from Peccati and Zheng (2011), based on Malliavin calculus and Stein''s methods, it is possible to assess the rate of convergence to Gaussianity for a triangular array of statistics with growing dimensions. These results can be exploited in a number of statistical applications, such as spherical density estimations, searching for point sources, estimation of variance and the spherical two-sample problem. Based on joint work with Solesne Bourguin, Domenico Marinucci and Giovanni Peccati.