In no other area is the need for effective analysis of uncertainty more evident than in the problem of evaluating the consequences of increasing atmospheric concentrations of radiatively active gases. The major consequences of concern is global warming, with related environmental effects that include changes in local patterns of precipitation, soil moisture, forest and agricultural productivity, and a potential increase in global mean sea level. In order to identify an optimum set of responses to sea level change, a full characterization of the uncertainties associated with the predictions of future sea level rise is essential. The paper addresses the use of data for identifying and characterizing uncertainties in model parameters and predictions. The Bayesian Monte Carlo method is formally presented and elaborated, and applied to the analysis of the uncertainty in a predictive model for global mean sea level change.