Estimating the Demographic Dynamic of Small Areas with the Kalman Filter

The aim of this chapter is to present a heuristic methodology to estimate the population for small areas. The method is a derivation of the Kalman filter, used to estimate the population without information on births, deaths or migration. The methodology proposed would make it possible to combine different sources of information, such as the census data and geographic information based on the evolution of the habitable area. One advantage of the method proposed in this work is that the estimation of the population is based on information that is entirely different from that normally used by demographers: the area of the geographic zone under study. The method proposed is applied to estimate the population in a hamlet with an area of 2.5 km2 (Villa Milpa Alta in Mexico City) offering reasonably good results. The Kalman filter can also be extremely useful estimating the population in ancient times, where the only source of information is the area inhabited.