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DESCRIPTION:\n	\n		\n			\n				\n					TITLE / TITRE\n					Adaptive Bayesian predictive inference
 \n					\n					ABSTRACT /RÉSUMÉ\n\n				Bayesian predictive inference provides a coherent 
 description of entire predictive uncertainty through predictive distributi
 ons. We examine several widely used sparsity priors from the predictive (a
 s opposed to estimation) inference viewpoint. Our context is estimating a 
 predictive distribution of a high-dimensional Gaussian observation with a 
 known variance but an unknown sparse mean under the Kullback–Leibler loss.
  First\, we show that LASSO (Laplace) priors are incapable of achieving ra
 te-optimal performance. This new result contributes to the literature on n
 egative findings about Bayesian LASSO posteriors. However\, deploying the 
 Laplace prior inside the Spike-and-Slab framework (for example with the Sp
 ike-and-Slab LASSO prior)\, rate-minimax performance can be attained with 
 properly tuned parameters (depending on the sparsity level sn). We highlig
 ht the discrepancy be- tween prior calibration for the purpose of predicti
 on and estimation. Going further\, we investigate popular hierarchical pri
 ors which are known to attain adaptive rate-minimax performance for estima
 tion. Whether or not they are rate-minimax also for predictive inference h
 as\, until now\, been unclear. We answer affirmatively by showing that hie
 rarchical Spike-and-Slab priors are adaptive and attain the minimax rate w
 ithout the knowledge of sn. This is the first rate-adaptive result in the 
 literature on predictive density estimation in sparse setups. This finding
  celebrates benefits of a fully Bayesian inference.\n\n				PLACE / LIEU \n					En l
 igne / Online\n					\n					ZOOM\n					https://hecmontreal.zoom.us/j/87251454048?pwd=MHBzL
 2VXbStQaTIxRmNKZnhobld6Zz09\n					ID: 872 5145 4048 / CODE: csmqV\n					\n					ORGANIZERS
  /ORGANISATEURS \n					Léo Belzile (Université de Montréal)\n					Joel Kamnitzer (Mc
 Gill University)\n					Giovanni Rosso (Concordia University)\n					Alina Stancu (Con
 cordia University)\n			\n		\n	\n\n
DTSTART:20240223T203000Z
DTEND:20240223T213000Z
SUMMARY:Veronika Ročková (University of Chicago)
URL:/mathstat/channels/event/veronika-rockova-universi
 ty-chicago-355501
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