Bayesian approach with the power prior for road safety analysis

Drawing inference from current data could be more reliable if similar data based on previous studies are used. We propose a full Bayesian approach with the power prior to utilize these data. The power prior is constructed by raising the likelihood function of the historical data to the power a₀; where 0 ≤ a₀ ≤ 1. The power prior is a useful informative prior in Bayesian inference. We use the power prior to estimate regression coefficients and to calculate the accident reduction factors of some covariates including median strips and guardrails. We also compare our method with the empirical Bayes method. We demonstrate our results with several sets of real data. The data were collected for two rural national roads of Korea in the year 2002. The computations are executed with the Metropolis-Hastings algorithm which is a popular technique in the Markov chain and Monte Carlo methods.