  Household survey data from the Demographic and Health Surveys (DHS) Program
is published with GPS coordinates. However, almost all geostatistical analyses
of such data ignore that the published GPS coordinates are randomly displaced
(jittered). In this short report, we develop a geostatistical model that
accounts for the positional uncertainty when analysing DHS surveys, and provide
a fast implementation using Template Model Builder. The key focus is inference
with Gaussian random fields under positional uncertainty, and our approach
works for both Gaussian and non-Gaussian likelihoods. A simulation study with a
binomial observation model shows that the new approach performs equally or
better than the common approach of ignoring jittering, both in terms of more
accurate parameter estimates and improved predictive measures. We demonstrate
that the improvement would be larger under stronger jittering. An analysis of
contraceptive use in Kenya shows that the approach is fast and easy to use in
practice.
