Uncertainty Quantification for Bayesian CART
| Autor: | Ismaël Castillo, Veronika Ročková |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
010104 statistics & probability 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Statistics::Methodology 020206 networking & telecommunications Mathematics - Statistics Theory 02 engineering and technology Statistics Theory (math.ST) 0101 mathematics Statistics Probability and Uncertainty 01 natural sciences Statistics::Computation |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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