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Robert McCulloch

Publications and source records attributed to Robert McCulloch.

4 recordsLinked to original sources
arXiv2018

Heteroscedastic BART Using Multiplicative Regression Trees

BART (Bayesian Additive Regression Trees) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear response surfaces, its advantages include a matrix-free formulation and the lack of a requirement to prespecify a confining regression basis. Although flexible in fitting the mean, BART has been limited by its reliance on a constant variance error model. This homoscedastic assumption is unrealistic in many applications. Alleviating this limitation, we propose HBART, a nonparametric heteroscedastic elaboration of BART. In BART, the mean function is modeled with a sum of trees, each of which determines an additive contribution to the mean. In HBART, the variance function is further modeled with a product of trees, each of which determines a multiplicative contribution to the variance. Like the mean model, this flexible, multidimensional variance model is entirely nonparametric with no need for the prespecification of a confining basis. Moreover, with this enhancement, HBART can provide insights into the potential relationships of the predictors with both the mean and the variance. Practical implementations of HBART with revealing new diagnostic plots are demonstrated with simulated and real data on used car prices, fishing catch production and alcohol consumption.

stat.ME↗
arXiv2018

Fully Nonparametric Bayesian Additive Regression Trees

Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian quantification of the uncertainty through the posterior. However, BART assumes IID normal errors. This strong parametric assumption can lead to misleading inference and uncertainty quantification. In this paper, we use the classic Dirichlet process mixture (DPM) mechanism to nonparametrically model the error distribution. A key strength of BART is that default prior settings work reasonably well in a variety of problems. The challenge in extending BART is to choose the parameters of the DPM so that the strengths of the standard BART approach is not lost when the errors are close to normal, but the DPM has the ability to adapt to non-normal errors.

stat.ML↗
arXiv2013

Parallel Bayesian Additive Regression Trees

Bayesian Additive Regression Trees (BART) is a Bayesian approach to flexible non-linear regression which has been shown to be competitive with the best modern predictive methods such as those based on bagging and boosting. BART offers some advantages. For example, the stochastic search Markov Chain Monte Carlo (MCMC) algorithm can provide a more complete search of the model space and variation across MCMC draws can capture the level of uncertainty in the usual Bayesian way. The BART prior is robust in that reasonable results are typically obtained with a default prior specification. However, the publicly available implementation of the BART algorithm in the R package BayesTree is not fast enough to be considered interactive with over a thousand observations, and is unlikely to even run with 50,000 to 100,000 observations. In this paper we show how the BART algorithm may be modified and then computed using single program, multiple data (SPMD) parallel computation implemented using the Message Passing Interface (MPI) library. The approach scales nearly linearly in the number of processor cores, enabling the practitioner to perform statistical inference on massive datasets. Our approach can also handle datasets too massive to fit on any single data repository.

stat.CO↗