A ground motion prediction equation estimates the mean and variance of ground shaking with distance from an earthquake source. Current relationships use regression techniques that treat the input variables or parameters as exact, neglecting the uncertainties associated with the measurement of shear wave velocity, moment magnitude, and site-to-source distance. This parameter uncertainty propagates through the regression procedure and results in model uncertainty that overestimates the inherent variability of the ground motion. This report discusses methods of estimating the statistical uncertainty of the input parameters, and procedures for incorporating the parameter uncertainty into the regression of ground motion data using a Bayesian framework. This results in a better measure of the uncertainties inherent in the phenomena of ground motion attenuation and a reduced and more accurately defined model variance. A reduced model variance translates to a better constrained estimate of ground shaking for projects designed for rare events or events toward the tail of the distribution.