Appropriate hazardous accident site identification and discrimination is a fundamental difficulty that confronts traffic safety researchers. Readily employed Bayesian methods can redress this difficulty and are the focus of this thesis. Accident analysis, including hazardous site identification, invariably requires the specification of some defined distributional function. However, several different distributions have been proposed to model traffic accidents, and so the most suitable model amongst these must be appropriately determined and selected. Model selection should satisfactorily fulfill two requisite criteria; firstly, that the best model is discriminated, and secondly, that this best distribution adequately describes the data. To help satisfy these requirements we introduce the averaged Bayes factor, a new method that determines the best model from likely candidate distributions, and we propose a new Bayesian procedure that facilitates the quantitative assessment of model adequacy. In addition, a method quantifying the power of detecting model inadequacy is presented. With the specification of an appropriate accident distribution, procedures facilitating hazardous site identification, ranking and selection are then proposed. These procedures are accomplished using the hierarchical Bayesian method and three intuitive quantitative strategies. Especially useful is a variation of the posterior probability that gives the probability each particular site is worst and by how much it is worst. All proposed techniques are illustrated using previously published accident data from 35 sites in Auckland, New Zealand.