[Forum SIS] Seminar Ismael Castillo (Sorbonne Universisté) - Padova | February 14, 2020 | 12:30 a.m.

[Patrizia Piacentini - Dip]

The Department of Statistical Sciences, University of Padova, invites 
you to the Seminar:

TITLE
MULTISCALE ANALYSIS OF BAYESIAN CART

SPEAKER
ISMAEL CASTILLO
Laboratoire de Probabilités, Statistique et Modélisation
<http://www.lpsm.paris/>Sorbonne Université
**
WHEN
February 14, 2020 - 12.30 a.m.

WHERE
Room Benvenuti - Campus S. Caterina
Via C. Battisti, 241
Padova

ABSTRACT
This work affords new insights about Bayesian CART in the context of 
structured wavelet shrinkage. We show that practically used Bayesian 
CART priors lead to adaptive rate-minimax posterior concentration in the 
supremum norm in Gaussian white noise, performing optimally up to a 
logarithmic factor. To further explore the benefits of structured 
shrinkage, we propose the g-prior for trees, which departs from the 
typical wavelet product priors by harnessing correlation induced by the 
tree topology. Building on supremum norm adaptation, an adaptive 
nonparametric Bernstein–von Mises theorem for Bayesian CART is derived 
using multiscale techniques. For the fundamental goal of uncertainty 
quantification, we construct adaptive confidence bands with uniform 
coverage for the regression function under self-similarity. (Joint work 
with Veronika Rockova)

*Apologies for cross posting*

-- 
Patrizia Piacentini
Dipartimento di Scienze Statistiche
Via C. Battisti, 241
35121 Padova
tel 049 8274167
fax 049 8271524

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