Selected aspects of prior and likelihood information for a Bayesian classifier in a road safety analysis

The development of the Bayesian logistic regression model classifying the road accident severity is discussed. The already exploited informative priors (method of moments, maximum likelihood estimation, and two-stage Bayesian updating), along with the original idea of a Boot prior proposal, are investigated when no expert opinion has been available. In addition, two possible approaches to updating the priors, in the form of unbalanced and balanced training data sets, are presented. The obtained logistic Bayesian models are assessed on the basis of a deviance information criterion (DIC), highest probability density (HPD) intervals, and coefficients of variation estimated for the model parameters. The verification of the model accuracy has been based on sensitivity, specificity and the harmonic mean of sensitivity and specificity, all calculated from a test data set. The models obtained from the balanced training data set have a better classification quality than the ones obtained from the unbalanced training data set. The two-stage Bayesian updating prior model and the Boot prior model, both identified with the use of the balanced training data set, outperform the non-informative, method of moments, and maximum likelihood estimation prior models. It is important to note that one should be careful when interpreting the parameters since different priors can lead to different models.