Parameter Calibration in Crowd Simulation Models using Approximate Bayesian Computation

Nikolai Bode

doi:10.17815/cd.2020.68

Abstract

Simulation models for pedestrian crowds are a ubiquitous tool in research and industry. It is crucial that the parameters of these models are calibrated carefully and ultimately it will be of interest to compare competing models to decide which model is best suited for a particular purpose. In this contribution, I demonstrate how Approximate Bayesian Computation (ABC), which is already a popular tool in other areas of science, can be used for model fitting and model selection in a pedestrian dynamics context. I fit two different models for pedestrian dynamics to data on a crowd passing in one direction through a bottleneck. One model describes movement in continuous-space, the other model is a cellular automaton and thus describes movement in discrete-space. In addition, I compare models to data using two metrics. The first is based on egress times and the second on the velocity of pedestrians in front of the bottleneck. My results show that while model fitting is successful, a substantial degree of uncertainty about the value of some model parameters remains after model fitting. Importantly, the choice of metric in model fitting can influence parameter estimates. Model selection is inconclusive for the egress time metric but supports the continuous-space model for the velocity-based metric. These findings show that ABC is a flexible approach and highlights the difficulties associated with model fitting and model selection for pedestrian dynamics. ABC requires many simulation runs and choosing appropriate metrics for comparing data to simulations requires careful attention. Despite this, I suggest ABC is a promising tool, because it is versatile and easily implemented for the growing number of openly available crowd simulators and data sets.

Highlights

Simulation models for pedestrian crowds are a widely used tool [1]
Comparing the posterior distributions obtained from fitting the model using the two different distance measures between data and simulations reveals that the choice of distance measure can have a substantial effect on the parameter estimates and on model calibration
While the estimate for parameter kk is robust to the choice of distance measure in the Approximate Bayesian Computation (ABC) model fitting (Fig. 3d), the mean of parameter vv0 is shifted with model fitting using the speed field leading to a lower estimate of vv0, on average

Summary

Introduction

Simulation models for pedestrian crowds are a widely used tool [1]. The dynamics these models produce are controlled by parameters that capture the preferred speed of pedestrians or the strength of interactions between pedestrians, for example [1]. A range of approaches for calibrating model parameters have been suggested [2,4,5,6,7,8] They compare models to empirical data at a microscopic level (e.g. trajectories [5]) or at a macroscopic level, where summary statistics for simulations and data are compared (e.g. pedestrian flows [2]). Parameter estimates are found by optimising the objective function While this approach is valid, it has three major shortcomings. This approach yields point-estimates for parameters and provides no information on the uncertainty associated with estimates This approach is not suited for model comparison, where the relative quality of different models in describing data is established. All numerical optimization procedures are liable to getting stuck in local optima, meaning that the true optimal solution may not be found

Methods

Results

Conclusion