[Forum SIS] Avviso di mini-corso :: C.V.D. a DSS (Scienze Statistiche, Sapienza)

[Pierpaolo Brutti]

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 A v v i s o   d i   M i n i - C o r s o
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Venerdì 04 Aprile, ore 10:00-13:00
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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.

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Maggiori informazioni sui seminari presso il DSS sono
consultabili a quest'indirizzo: http://goo.gl/Y6OQYm

Saluti

Pierpaolo Brutti - Fulvio De Santis

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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.
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