Glaciers in High Mountain Asia are an important freshwater resource for large populations living downstream who rely on runoff for hydropower, irrigation, and municipal use. Projections of glacier mass change and runoff therefore have important socio-economic impacts. In this study, we use a new dataset of geodetic mass balance observations of almost all glaciers in the region to calibrate the Python Glacier Evolution Model (PyGEM) using Bayesian inference. The new dataset enables the model to capture spatial variations in mass balance and the Bayesian inference enables the uncertainty associated with the model parameters to be quantified. Validation with historical mass balance observations shows the model performs well and the uncertainty is well captured. Projections of glacier mass change for 22 General Circulation Models (GCMs) and four Representative Concentration Pathways (RCPs) estimate that by the end of the century glaciers in High Mountain Asia will lose between 3311% (RCP2.6) and 689% (RCP8.5) of their total mass relative to 2015. Considerable spatial and temporal variability exists between regions due to the climate forcing and glacier characteristics (hypsometry, ice thickness, elevation range). Projections of annual glacier runoff reveal most monsoon-fed river basins (Ganges, Brahmaputra) will hit a maximum (peak water) prior to 2050, while the Indus and other westerlies-fed river basins will likely hit peak water after 2050 due to significant contributions from excess glacier meltwater. Monsoon-fed watersheds are projected to experience large reductions in end-of-summer glacier runoff. Uncertainties in projections at regional scales are dominated by the uncertainty associated with the climate forcing, while at the individual glacier level, uncertainties associated with model parameters can be significant.