  An important issue when using Machine Learning algorithms in recent research
is the lack of interpretability. Although these algorithms provide accurate
point predictions for various learning problems, uncertainty estimates
connected with point predictions are rather sparse. A contribution to this gap
for the Random Forest Regression Learner is presented here. Based on its
Out-of-Bag procedure, several parametric and non-parametric prediction
intervals are provided for Random Forest point predictions and theoretical
guarantees for its correct coverage probability is delivered. In a second part,
a thorough investigation through Monte-Carlo simulation is conducted evaluating
the performance of the proposed methods from three aspects: (i) Analyzing the
correct coverage rate of the proposed prediction intervals, (ii) Inspecting
interval width and (iii) Verifying the competitiveness of the proposed
intervals with existing methods. The simulation yields that the proposed
prediction intervals are robust towards non-normal residual distributions and
are competitive by providing correct coverage rates and comparably narrow
interval lengths, even for comparably small samples.
