Our aim is to estimate the abundance of eggs
of the mosquito Aedes aegypti, one of the
vectors responsible for transmitting dengue
fever. We have available the abundance of eggs
observed at n locations, during T consecutive
weeks, in Recife, a city in the Northeast of
Brazil. More specifically, the abundances were
observed at n=84 locations from May 2004 until
May 2006. Because of fund limitations, the n
locations were divided into K groups, and at
each week t, samples were collected only at the
locations belonging to group k=1,2,...,K, such
that n=n_1+n_2+...n_K, where n_k is the number
of locations in group k. Therefore, we have
observations missing by design, leading to a
spatio-temporal misalignment of the data. We
propose a spatio-temporal model which naturally
accounts for the misalignment present in the
data and borrows strength among the observed
locations, across the different weeks, to learn
about the behavior of the abundance of eggs
during this period. The temporal structure is
modelled through dynamic linear models and the
spatial structure is captured through Gaussian
processes. Inference procedure is based on the
Bayesian paradigm, which naturally provides
uncertainties about our estimates, especially
for the missing observations. .