Quantifying the rate of extraction from groundwater bores can be essential for regional scale groundwater management and impact assessment. However, regions that are large and remote with many poorly accessible groundwater bores pose great challenges for metering. In the Surat and Bowen Basins in Queensland, Australia, more than 30000 groundwater bores exist; however almost none are metered. Our research uses a case study of the Surat and Bowen Basins to develop new stochastic estimation methods that provide estimates of long term annual average groundwater extractions and their uncertainty. The method involves the collation of multiple sources of extraction estimates ranging from metering to qualitative information; and a set of spatial and temporal data that are potential predictors of extraction. These data are used to construct a generalised linear model to estimate property scale extraction. These estimates are downscaled to bore scale extraction with an occurrence probability model, followed by magnitude distribution for those bores with non-zero extractions. Stochastic simulation allows a comprehensive infilling of long-term annual average extraction rates at all properties, aquifers and all known bores. However, significant limitations remain both in the data-base used and in the generalised linear model, particularly related to attribution of property-scale water demand and temporal variability.