Probabilistic prediction by means of the propagation of response variable uncertainty through a Monte Carlo approach in regression random forest: Application to soil moisture regionalization

Abstract

Probabilistic predictions aim to produce a prediction interval with probabilities associated with each possible outcome instead of a single value for each outcome. In multiple regression problems, this can be achieved by propagating the known uncertainties in data of the response variables through a Monte Carlo approach. This paper presents an analysis of the impact of the training response variable uncertainty on the prediction uncertainties with the help of a comparison with probabilistic prediction obtained with quantile regression random forest. The result is an uncertainty quantification of the impact on the prediction. The approach is illustrated with the example of the probabilistic regionalization of soil moisture derived from cosmic-ray neutron sensing measurements, providing a regional-scale soil moisture map with data uncertainty quantification covering the Selke river catchment, eastern Germany.