Abstract
In this work we have applied a methodology consisting in a Bayesian hierarchical modelling and EWMA Charts for the evaluation of the trend of accident rates in a transportation corridor in Spain. We illustrate how to identify trends or patterns in the average (joint set of segments of the corridor) and specific (individual) segments of different interurban roads using annual observed accident frequencies; we also derive the predictive density function for future observations.
For an assumed Poisson distribution on the number of accidents, a gamma prior and an appropriate hyperprior, a full hierarchical bayes formulation is used to estimate the accident rate for 84 segments (682 km) of a typical Spanish corridor from the period 2001-2007. Subsequently, the prior and posterior distributions are smoothed over time using an exponentially weighted moving average. Further we derive the predictive density function of a future observation, which can be applied in a multiple regression model to analyse the effect of traffic conditions and road types on accident frequency.
The results of the MCMC computation of the very spread set of accident rates, in 84 segments of Spanish road types like highways, single carriageway roads, in the Madrid-Barcelona corridor, allows for the comparison of the their values and time evolution. A typical EWMA chart shows the safety performance evolution as well the confidence limits in each segment type and allows for outlier identification, which includes both atypically safe and dangerous segments.
In a nutshell, the methodology has been useful for the purposes of our study: a tool for the monitoring of trends, as well as for the identification of outlier segments and reasonable MCMC computational cost.
Keywords: Bayesian models, Hierarchical Bayes, trend analysis, accident rate, transportation corridor, non homogeneous Poisson models.