Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty Quantification for Bayesian CART   This work affords new insights into Bayesian CART in the context of
structured wavelet shrinkage. The main thrust is to develop a formal
inferential framework for Bayesian tree-based regression. We reframe Bayesian
CART as a g-type prior which departs from the typical wavelet product priors by
harnessing correlation induced by the tree topology. The practically used
Bayesian CART priors are shown to attain adaptive near rate-minimax posterior
concentration in the supremum norm in regression models. For the fundamental
goal of uncertainty quantification, we construct adaptive confidence bands for
the regression function with uniform coverage under self-similarity. In
addition, we show that tree-posteriors enable optimal inference in the form of
efficient confidence sets for smooth functionals of the regression function.

7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph