Efficient Metropolis–Hastings Proposal Mechanisms for Bayesian Regression Tree Models

Efficient Bayesian Multivariate Surface Regression

Functional Models for Regression Tree Leaves

This paper presents a study about functional models for regression tree leaves. We evaluate experimentally several alternatives to the averages commonly used in regression trees. We have implemented a regression tree learner (HTL) that is able to use several alternative models in the tree leaves. We study the effect on accuracy and the computational cost of these alternatives. The experiments c...

Regression tree models for designed experiments

Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter situations, regression tree models can provide simpler and more intuitive interpretations of interaction effects as differences between conditional main effects. We...

Bayesian Model Averaging for Linear Regression Models

We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferenc...

Bayesian quantile regression for single-index models

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the...