Strong ground motion attenuation relationships estimate the mean and variance of ground shaking as it decreases with distance from an earthquake source. Current relationships use “classical” regression techniques that treat the input variables or parameters as exact, neglecting the uncertainties associated with the measurement of ground acceleration, moment magnitude, site-to-source distance, shear wave velocity, etc. This leads to a poorly constrained estimate of the uncertainty of strong ground motions. This paper discusses the work in progress on; a) estimating the statistics of parameter uncertainty, and b) incorporating the parameter uncertainty into the regression of strong motion attenuation data using a Bayesian framework. The results are an improved understanding of the uncertainties inherent in the phenomena of strong ground motion attenuation, a reduced and better defined model variance, and better constrained estimates of rarer events associated with ground accelerations towards the tail of the distribution.