A microsimulation model and its calculations are described, and the results that are subsequently used to determine indicators for traffic safety are presented. The method demonstrates which changes occur at the level of traffic flow (number of vehicles per section of road) and at the vehicle level (vehicles choosing different routes). The best-known safety indicator in this type of model is the conflict situation, in which two vehicles approach each other and, if no action is taken, a crash will occur. These conflict situations are detected in the simulation model. This method does not necessarily relate directly to any actual observed conflicts or recorded crashes. The quantitative relationship is examined between detected conflicts at junctions in the model and recorded crashes at the same locations in the real world. The methods chosen for detecting conflicts and for selecting crashes are explained. A microsimulation model was constructed for a regional road network. The conflicts in this network were detected, and the recorded crashes were selected. The results show a quantitative relationship between the number of conflicts at priority junctions and the number of passing motor vehicles on one hand and the number of observed crashes on the other hand. When crashes and conflicts are divided into crash categories, junctions with signals clearly show substantial differences between the relative numbers of frontal crashes and frontal conflicts.

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Summary.Risk is at the centre of many policy decisions in companies, governments and other institutions.The risk of road fatalities concerns local governments in planning countermeasures, the risk and severity of counterparty default concerns bank risk managers daily and the risk of infection has actuarial and epidemiological consequences. However, risk cannot be observed directly and it usually varies over time. We introduce a general multivariate time series model for the analysis of risk based on latent processes for the exposure to an event, the risk of that event occurring and the severity of the event. Linear state space methods can be used for the statistical treatment of the model. The new framework is illustrated for time series of insurance claims, credit card purchases and road safety. It is shown that the general methodology can be effectively used in the assessment of risk.

A multivariate non-linear time series model for road safety data is presented. The model is applied in a case-study into the development of a yearly time series of numbers of fatal accidents (inside and outside urban areas) and numbers of kilometres driven by motor vehicles in the Netherlands between 1961 and 2000. The model accounts for missing entries in the disaggregated numbers of kilometres driven although the aggregated numbers are observed throughout. We consider a multivariate non-linear time series model for the analysis of these data. The model consists of dynamic unobserved factors for exposure and risk that are related in a non-linear way to the number of fatal accidents. The multivariate dimension of the model is due to its inclusion of multiple time series for inside and outside urban areas. Approximate maximum likelihood methods based on the extended Kalman filter are utilized for the estimation of unknown parameters. The latent factors are estimated by extended smoothing methods. It is concluded that the salient features of the observed time series are captured by the model in a satisfactory way. Copyright (c) 2010 Royal Statistical Society.