  In this paper we set out general principles and develop geostatistical
methods for the analysis of data from spatio-temporally referenced prevalence
surveys. Our objective is to provide a tutorial guide that can be used in order
to identify parsimonious geostatistical models for prevalence mapping. A
general variogram-based Monte Carlo procedure is proposed to check the validity
of the modelling assumptions. We describe and contrast likelihood-based and
Bayesian methods of inference, showing how to account for parameter uncertainty
under each of the two paradigms. We also describe extensions of the standard
model for disease prevalence that can be used when stationarity of the
spatio-temporal covariance function is not supported by the data. We discuss
how to define predictive targets and argue that exceedance probabilities
provide one of the most effective ways to convey uncertainty in prevalence
estimates. We describe statistical software for the visualization of
spatio-temporal predictive summaries of prevalence through interactive
animations. Finally, we illustrate an application to historical malaria
prevalence data from 1334 surveys conducted in Senegal between 1905 and 2014.
