Uncertainties in the estimation of parameters for common-cause failure models arise not only because of the small number of common-cause failure events but also because recorded events may not be relevant to the analysis of a particular plant. The data base for a plant-specific analysis may therefore be uncertain. A Bayesian methodology for treating data base uncertainties in the estimation of common-cause failure model parameters is developed and applied to a three-pump auxiliary feedwater system. Sensitivity analyses show that the results are not strongly sensitive to assumptions concerning prior distribution type and shape, but do depend somewhat on the degree of state-of-knowledge dependence between uncertain events. These analyses also show that ignoring the uncertainties in the data can lead to significant estimation errors. Finally, an approximate methodology for treating uncertain data is examined; this method provides reasonable estimates of the mean values of the common-cause failure model parameters, but underpredicts the uncertainty in these parameters.