Bayesian approaches to the study of politics are increasingly popular. But Bayesian approaches to modeling multiple time series have not been critically evaluated. This is in spite of the potential value of these models in international relations, political economy, and other fields of our discipline. We review recent developments in Bayesian multi-equation time series modeling in theory testing, forecasting, and policy analysis. Methods for constructing Bayesian measures of uncertainty of impulse responses (Bayesian shape error bands) are explained. A reference prior for these models that has proven useful in short- and medium-term forecasting in macroeconomics is described. Once modified to incorporate our experience analyzing political data and our theories, this prior can enhance our ability to forecast over the short and medium terms complex political dynamics like those exhibited by certain international conflicts. In addition, we explain how contingent Bayesian forecasts can be constructed, contingent Bayesian forecasts that embody policy counterfactuals. The value of these new Bayesian methods is illustrated in a reanalysis of the Israeli-Palestinian conflict of the 1980s.