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Providing transport users and operators with accurate forecasts on traveltimes is challenging due to a highly stochastic traffic environment. Publictransport users are particularly sensitive to unexpected waiting times, whichnegatively affect their perception on the system's reliability. In this paperwe develop a robust model for real-time bus travel time prediction that departfrom Gaussian assumptions by using Student-$t$ errors. The proposed approachuses spatiotemporal characteristics from the route and previous bus trips tomodel short-term effects, and date/time variables and Gaussian processes forlong-run forecasts. The model allows for flexible modeling of mean, varianceand kurtosis spaces. We propose algorithms for Bayesian inference and forcomputing probabilistic forecast distributions. Experiments are performed usingdata from high-frequency buses in Stockholm, Sweden. Results show thatStudent-$t$ models outperform Gaussian ones in terms of log-posteriorpredictive power to forecast bus delays at specific stops, which reveals theimportance of accounting for predictive uncertainty in model selection.Estimated Student-$t$ regressions capture typical temporal variability betweenwithin-day hours and different weekdays. Strong spatiotemporal effects aredetected for incoming buses from immediately previous stops, which is in linewith many recently developed models. We finally show how Bayesian inferencenaturally allows for predictive uncertainty quantification, e.g. by returningthe predictive probability that the delay of an incoming bus exceeds a giventhreshold.

Robust Real-Time Delay Predictions in a Network of High-Frequency Urban Buses