  To facilitate effective decision-making, gridded satellite precipitation
products should include uncertainty estimates. Machine learning has been
proposed for issuing such estimates. However, most existing algorithms for this
purpose rely on quantile regression. Distributional regression offers distinct
advantages over quantile regression, including the ability to model
intermittency as well as a stronger ability to extrapolate beyond the training
data, which is critical for predicting extreme precipitation. In this work, we
introduce the concept of distributional regression for the engineering task of
creating precipitation datasets through data merging. Building upon this
concept, we propose new ensemble learning methods that can be valuable not only
for spatial prediction but also for prediction problems in general. These
methods exploit conditional zero-adjusted probability distributions estimated
with generalized additive models for location, scale, and shape (GAMLSS),
spline-based GAMLSS and distributional regression forests as well as their
ensembles (stacking based on quantile regression, and equal-weight averaging).
To identify the most effective methods for our specific problem, we compared
them to benchmarks using a large, multi-source precipitation dataset. Stacking
emerged as the most successful strategy. Three specific stacking methods
achieved the best performance based on the quantile scoring rule, although the
ranking of these methods varied across quantile levels. This suggests that a
task-specific combination of multiple algorithms could yield significant
benefits.
