  Providing transport users and operators with accurate forecasts on travel
times is challenging due to a highly stochastic traffic environment. Public
transport users are particularly sensitive to unexpected waiting times, which
negatively affect their perception on the system's reliability. In this paper
we develop a robust model for real-time bus travel time prediction that depart
from Gaussian assumptions by using Student-$t$ errors. The proposed approach
uses spatiotemporal characteristics from the route and previous bus trips to
model short-term effects, and date/time variables and Gaussian processes for
long-run forecasts. The model allows for flexible modeling of mean, variance
and kurtosis spaces. We propose algorithms for Bayesian inference and for
computing probabilistic forecast distributions. Experiments are performed using
data from high-frequency buses in Stockholm, Sweden. Results show that
Student-$t$ models outperform Gaussian ones in terms of log-posterior
predictive power to forecast bus delays at specific stops, which reveals the
importance of accounting for predictive uncertainty in model selection.
Estimated Student-$t$ regressions capture typical temporal variability between
within-day hours and different weekdays. Strong spatiotemporal effects are
detected for incoming buses from immediately previous stops, which is in line
with many recently developed models. We finally show how Bayesian inference
naturally allows for predictive uncertainty quantification, e.g. by returning
the predictive probability that the delay of an incoming bus exceeds a given
threshold.
