This thesis explores several Bayesian methods for empirically modeling macroeconomic and financial time series. A common problem in all empirical studies is that the number of observations is small relative to the number of potential variables. This raises problems for conventional econometric methods. Intuitively, there is not enough information in the data to estimate large models in an unrestricted fashion. Therefore, one major contribution of this thesis is to explore econometric methods which are useful in such an environment.