This talk concern epidemiological data that has been aggregated to fall within a spatial region, an interval of time or both. Such aggregated spatio-temporal data can have the added complexity that the boundaries of the geographic regions change over time. The result is that over the period of entire study we can't say what the case count is for any subdivision within the study
For such data, we advocate the use of EMS algorithms introduced by Silverman et al (1990) and Nychka (1990) for image reconstruction. We concern ourselves with the appropriate choice of the S-step by reviewing earlier work on local-EM and proposing an alternative based on a root Gaussian Cox process. Both offer disciplined choices for the S-step while the later has the benefit of being embedded in a traditional parametric model for patio-temporal data. This allows us to exploit Gaussian Markov random field approximations found in Lindgren et al (2011) which in turn permits the use of sparse matrix algorithms leading to significant computational gains.