Bayesian inference methods to calibrate crowd dynamics models for safety applications

Abstract

Crowd simulation is a crucial tool to assess risks and engineer crowd safety at events and in built infrastructure. Simulations can be used for what-if studies, for real-time predictions, as well as to develop regulations for crowd safety. A reliable prediction requires a carefully calibrated model. Model parameters are often calibrated as point estimates, single parameter values for which the model evaluation fits given data best. In contrast, Bayesian inference provides a full posterior distribution for the fitted parameters that includes the residual uncertainty after calibration. In this work, we calibrate a microscopic model and an emulator derived from a microscopic model for crowd dynamics using point estimates and Approximate Bayesian Computation. We calibrate on data measuring the flow through a key scenario of crowd safety: a bottleneck. We vary the bottleneck width and demonstrate via three case studies the advantages and shortcomings of the two calibration techniques. In a case with a unimodal posterior, both methods yield similar results. However, one safety-relevant case study, that mimics the dynamics of evacuating people squeezing through an opening, exhibits a faster-is-slower dynamic where multiple free-flow speeds lead to the same flow. In this case, only Bayesian inference reveals the true bimodal shape of the posterior distribution. For multidimensional calibration, we illustrate that Bayesian inference allows accurate calibration by describing parameter relations. We conclude that, in practice, point estimation often seems sufficient, but Bayesian inference methods are necessary to capture important structural information about the uncertain parameters, and thus the physics of safety.