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Water point mapping databases, generated through surveys of water sources such as wells and boreholes, are now available in many low and middle income countries, but often suffer from incomplete coverage. To address the partial coverage in such databases and gain insights into spatial patterns of water resource use, this study investigated the use of a maximum entropy (MaxEnt) approach to predict the geospatial distribution of drinking-water sources, using two types of unimproved sources in Kenya as illustration. Geographic locations of unprotected dug wells and surface water sources derived from the Water Point Data Exchange (WPDx) database were used as inputs to the MaxEnt model alongside geological/hydrogeological and socio-economic covariates. Predictive performance of the MaxEnt models was high (all > 0.9) based on Area Under the Receiver Operator Curve (AUC), and the predicted spatial distribution of water point was broadly consistent with household use of these unimproved drinking-water sources reported in household survey and census data. In developing countries where geospatial datasets concerning drinking-water sources often have necessarily limited resolution or incomplete spatial coverage, the modelled surface can provide an initial indication of the geography of unimproved drinking-water sources to target unserved populations and assess water source vulnerability to contamination and hazards.