Propensity score analysis (PSA) has been used in a variety of settings, such as education, epidemiology, and sociology. Most typically, propensity score analysis has been implemented within the conventional frequentist perspective of statistics. This perspective, as is well known, does not account for uncertainty in either the parameters of the propensity score model or the causal model. Indeed, the conventional implementation of PSA does not allow prior information to enter into the analysis. To account for uncertainty in model parameters we must adopt a Bayesian perspective. Thus, the purpose of this paper is to provide a review and comparative investigation of frequentist and Bayesian propensity score analysis as a means of warranting causal inferences in observational settings.