Bayesian spatio-temporal models for mapping urban pedestrian traffic

Understanding the distribution of traffic in time and space over available infrastructure is a fundamental problem in transportation research. However, pedestrian activity is rarely mapped at fine resolution over large spatiotemporal scales, such as city centres, despite the fact that this information is crucial for assessing the effects of infrastructure changes, for supporting planning and policy formulation, and for estimating economic activity. Here we formulate Bayesian hierarchical spatio-temporal models to map pedestrian traffic based on publicly available pedestrian count data, properties of the street network, and features of the urban environment, such as nearby shops or public transport stops. We employ the accurate and computationally efficient Integrated Nested Laplace Approximation inference method combined with Stochastic Partial Differential Equations for spatial effects (INLA-SPDE) to calibrate models on a large hourly count data set from sensors installed across the city centre of Melbourne, Australia. Using this modelling paradigm, we demonstrate the importance of structured space-time and time-time interaction terms within models. These terms estimate how the relative busyness of locations changes over time or how peak traffic times vary across days, for example. We also show the relevance of built environment features, although their predictive capability is smaller than that of interaction terms, and we use our models to map the uncertainty of pedestrian traffic estimation based on data availability. Finally, we show, with reference to the example of the Covid-19 pandemic, how the Bayesian framework permits tracking changes in traffic dynamics over time. The flexibility of our models means they can be extended for further applications.