A Scalable Bayesian Geospatial Framework for Small-Area Population Estimation from Multiple Sparse Data Sources

Modelled small-area population estimates are increasingly needed where census data are outdated, spatially coarse, incomplete or unavailable. These estimates are often produced at 100-m grids and aggregated to operational units totals, by combining population observations from surveys, health campaigns and partial censuses with satellite-derived settlement data and geospatial covariates. However, the effects of mapped number of buildings, spatial dependence and changes in spatial support on predictive performance and uncertainty remain insufficiently understood. We developed a Bayesian geospatial modelling framework comparing a Gamma people-per-building (PPB) model with a negative binomial (NB) population-count formulation. Both formulations incorporated hierarchical effects, geospatial covariates and a Matérn spatial field implemented in INLA-SPDE. A factorial simulation study, which evaluated the effects of spatial range, spatial variance and missingness, showed that prediction error increased with spatial variance and short-range spatial dependence, with the Gamma formulation producing higher precision and accuracy than the NB model. However, when applied to household listing datasets from five data sources across 2,285 Enumeration Areas (EAs) in Cameroon, both models produced similar 100-km spatial cross-validation RMSEs (1,293.6 and 1,294.4, respectively). Errors increased when predicting regions or data sources excluded from the training sets. After 100-m grid predictions were reaggregated to EA support, predicted-to-observed population ratios were 1.248 for Gamma and 1.388 for NB, with national total posterior population estimates of 29.20 million people (95% CrI: 25.71 – 33.07) and 33.21 million people (28.96 – 38.60), respectively. Similar EA-level predictive performance can mask important differences in geographic transferability, fine-scale downscaling and aggregation; thus, explicit evaluation of spatial support and model form uncertainty is therefore important for high-resolution population estimation. The framework provides a scalable computationally feasible approach to integrating heterogeneous sparse observations with geospatial information while propagating spatial and hierarchical uncertainty.