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DTSTAMP:20250719T042402Z
DESCRIPTION:TITLE / TITRE\n\nSkew-symmetric approximations of posterior dis
 tributions\n	\n	ABSTRACT / RÉSUMÉ\n\nA broad class of regression models that
  routinely appear in several fields of application can be expressed as par
 tially or fully discretized Gaussian linear regressions. Besides incorpora
 ting the classical Gaussian response setting\, this class crucially encomp
 asses probit\, multinomial probit and tobit models\, among others. The rel
 evance of these representations has motivated decades of active research w
 ithin the Bayesian field. A main reason for this constant interest is that
 \, unlike for the Gaussian response setting\, the posterior distributions 
 induced by these models do not seem to belong to a known and tractable cla
 ss\, under the commonly-assumed Gaussian priors. In this seminar\, I will 
 review\, unify and extend recent advances in Bayesian inference and comput
 ation for such a class of models\, proving that unified skew-normal (SUN) 
 distributions (which include Gaussians as a special case) are conjugate to
  the general form of the likelihood induced by these formulations. This re
 sult opens new avenues for improved sampling-based methods and more accura
 te and scalable deterministic approximations from variational Bayes. These
  results are further extended via a general and provably-optimal strategy 
 to improve\, via a simple perturbation\, the accuracy of any symmetric app
 roximation of a generic posterior distribution. Crucially\, such a novel p
 erturbation is derived without additional optimization steps and yields a 
 similarly-tractable approximation within the class of skew-symmetric densi
 ties that provably enhances the finite-sample accuracy of the original sym
 metric approximation. Theoretical support is provided\, in asymptotic sett
 ings\, via a refined version of the Bernstein–von Mises theorem that relie
 s on skew-symmetric limiting densities.\n\nPLACE /LIEU\n	Webinar\n	\n	ZOOM\n	h
 ttps://us06web.zoom.us/j/84226701306?pwd=UEZ5NVpZaUlldW5qNU8vZzIvbEJXQT09
 \n
DTSTART:20240315T150000Z
DTEND:20240315T160000Z
SUMMARY:Daniele Durante (Bocconi University)
URL:/mathstat/channels/event/daniele-durante-bocconi-u
 niversity-355996
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