  Decision trees built with data remain in widespread use for nonparametric
prediction. Predicting probability distributions is preferred over point
predictions when uncertainty plays a prominent role in analysis and
decision-making. We study modifying a tree to produce nonparametric predictive
distributions. We find the standard method for building trees may not result in
good predictive distributions and propose changing the splitting criteria for
trees to one based on proper scoring rules. Analysis of both simulated data and
several real datasets demonstrates that using these new splitting criteria
results in trees with improved predictive properties considering the entire
predictive distribution.
