The mean and the median relative errors (which are same for population density and count predictions) are reported in columns (7) and (8), respectively.<sup>23</sup> The mean and median relative errors of the model are 37% and 28%, and 35% and 29%, without and with the additional weight correction. Using only public imagery, the mean and median REs are 34% and 28%, and 34% and 28% without and with weights correction, respectively. These mean REs are lower than most top-down estimates, except Facebook and WorldPop 2015. The median REs are higher than only Facebook and Worldpop 2015, and comparable to GHSL and GPW 2015 and much lower compared to GPW, Worldpop, and Landscan (all in 2010).<sup>24</sup> The coefficient of variation (CV) of predicted density estimates for each sub-district based on the HIES model in combination with satellite imagery is low, at about 11%. This is four times lower than the CV of the survey estimates themselves, which stands at 45.2%. The increase in precision due to the incorporation of satellite imagery is tantamount to increasing the share of sampled villages in the population from 17%, which is currently the case, to a remarkable 80%.<sup>25</sup> This is striking but not surprising because the model predicts with an out-of-sample _R_<sup>2</sup> of about 0.80 and the imagery covers all villages.

# **5 Discussion and Conclusion**

Existing methods of estimating local population use a “top-down” dasymetric mapping approach to distribute census data based on a set of covariates derived from satellite imagery. These are only as accurate as the source data—the census—and hence their accuracy declines as the census itself ages. We propose a “bottom-up” technique by pairing survey data with satellite imagery using Poisson regressions employing variables selected based on LASSO regularization. This model can yield population density predictions in areas where the survey was not conducted, and can be repeated frequently using periodic survey and satellite data to frequently track population changes. We apply the method in the context of Sri Lanka to predict population density at the lowest administrative level, the Gram Niladhari (GN) division (village-level). Our model uses the Sri Lankan Household Income and Expenditure Survey (HIES), and predicts density out-of-sample in the non-HIES villages.

Two aspects of our results stand out. First, our performance is better than the only

> 23 The relative error with respect to the census is the same for population density and population count because the only difference between the two is the multiplicative factor, village-area. 24 We conducted a similar exercise using population count as the dependent variable in the model, from which we directly obtained population predictions. The accuracies of these predictions are reported in Table S10. Examining the _R_<sup>2</sup> , SRC, and Mean RE, it is evident that the population predictions derived indirectly using a density-based model by multiplying density predictions with village-area (as in Table 9) performs much better than obtaining population count predictions from a population-based model.

> 25 The CV of 45.2% was obtained by manually calculating the mean CVs from a synthetic 80% sample of the census.

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