We provide a new analysis of glacial isostatic adjustment (GIA) with the goal of assembling the model uncertainty statistics required for rigorously extracting trends in surface mass from the Gravity Recovery and Climate Experiment (GRACE) mission. Such statistics are essential for deciphering sea level, ocean mass, and hydrological changes because the latter signals can be relatively small (≤2 mm/yr water height equivalent) over very large regions, such as major ocean basins and watersheds. With abundant new >7 year continuous measurements of vertical land motion (VLM) reported by Global Positioning System stations on bedrock and new relative sea level records, our new statistical evaluation of GIA uncertainties incorporates Bayesian methodologies. A unique aspect of the method is that both the ice history and 1-D Earth structure vary through a total of 128,000 forward models. We find that best fit models poorly capture the statistical inferences needed to correctly invert for lower mantle viscosity and that GIA uncertainty exceeds the uncertainty ascribed to trends from 14 years of GRACE data in polar regions.