  Recent experimental and empirical observations have demonstrated that
stochasticity plays a critical role in car following (CF) dynamics. To
reproduce the observations, quite a few stochastic CF models have been
proposed. However, while calibrating the deterministic CF models is well
investigated, studies on how to calibrate the stochastic models are lacking.
Motivated by this fact, this paper aims to address this fundamental research
gap. Firstly, the CF experiment under the same driving environment is conducted
and analyzed. Based on the experimental results, we test two previous
calibration methods, i.e., the method to minimize the Multiple Runs Mean
(MRMean) error and the method of maximum likelihood estimation (MLE).
Deficiencies of the two methods have been identified. Next, we propose a new
method to minimize the Multiple Runs Minimum (MRMin) error. Calibration based
on the experimental data and the synthetic data demonstrates that the new
method outperforms the two previous methods. Furthermore, the mechanisms of
different methods are explored from the perspective of error analysis. The
analysis indicates that the new method can be regarded as a nested optimization
model. The method separates the aleatoric errors caused by stochasticity from
the epistemic error caused by parameters, and it is able to deal with the two
kinds of errors effectively. Finally, we find that under the calibration
framework of stochastic CF models, the calibrated parameter set using spacing
as MoP may not always outperform that using velocity as MoP. These findings are
expected to enhance the understanding of the role of stochasticity in CF
dynamics where the new calibration framework for stochastic CF models is
established.
