Accurate estimates of glacier surface elevation changes are paramount for various aspects of the study of the cryosphere, from glacier flow and thickness estimates to hydrological forecasts and projections of sea-level-rise. We present a novel probabilistic framework to filter outliers and estimate uncertainties in glacier surface elevation changes computed from the subtraction of digital elevation models (DEM). Our methodology frames outlier filtering as a Bayesian inference problem, thus characterizing the state of knowledge on glacier surface elevation changes through the posterior distribution as the combination of glacier volume variation observations and prior knowledge arising from previously collected data and/or modeled results. We validate this technique with experiments using Gaussian random fields to generate artificial noise in glacier surface elevation variation observations and show that the model satisfactorily culls the simulated outliers. Surface elevation change estimates are consistent with results computed from widely-used outlier filtering and uncertainty estimation techniques. The Bayesian framework allows unifying DEM error models with physical considerations on glacier surface elevation changes within a simple, statistically coherent model preventing temporal correlation and additional biases in other techniques. On the basis of these results, we discuss the implications of DEM uncertainty and offer suggestions for the glaciological community.