Bayesian methodology to estimate and update safety performance functions under limited data conditions: a sensitivity analysis.

In road safety studies, decision makers must often cope with limited data conditions. In such circumstances, the maximum likelihood estimation (MLE), which relies on asymptotic theory, is unreliable and prone to bias. Moreover, it has been reported in the literature that (a) Bayesian estimates might be significantly biased when using non-informative prior distributions under limited data conditions, and that (b) the calibration of limited data is plausible when existing evidence in the form of proper priors is introduced into analyses. Although the Highway Safety Manual (2010) (HSM) and other research studies provide calibration and updating procedures, the data requirements can be very taxing. This paper presents a practical and sound Bayesian method to estimate and/or update safety performance function (SPF) parameters combining the information available from limited data with the SPF parameters reported in the HSM. The proposed Bayesian updating approach has the advantage of requiring fewer observations to get reliable estimates. This paper documents this procedure. The adopted technique is validated by conducting a sensitivity analysis through an extensive simulation study with 15 different models, which include various prior combinations. This sensitivity analysis contributes to our understanding of the comparative aspects of a large number of prior distributions. Furthermore, the proposed method contributes to unification of the Bayesian updating process for SPFs. The results demonstrate the accuracy of the developed methodology. Therefore, the suggested approach offers considerable promise as a methodological tool to estimate and/or update baseline SPFs and to evaluate the efficacy of road safety countermeasures under limited data conditions.