Uncertainty quantification on simulation analysis driven by random forests

We consider simulation-based estimation where the inputs are calibrated from predictive models generated by random forests (RFs). RF is a common technique to produce ensemble predictions by aggregating many individual decision trees. This problem arises in data-driven applications such as individualized surgery operations scheduling and supply chain management. We investigate the estimation of the output variance contributed from the noises in the input prediction, which can be used to construct output confidence intervals. In particular, we study the integration of simulation runs with a recently proposed infinitesimal jackknife estimator that can reduce the computational burden from double layers of bootstrapping. We demonstrate our scheme with an elementary numerical example.