  An interesting statistical problem is to find regions where some studied
process exceeds a certain level. Estimating such regions so that the
probability for exceeding the level in the entire set is equal to some
predefined value is a difficult problem that occurs in several areas of
applications ranging from brain imaging to astrophysics. In this work, a method
for solving this problem, as well as the related problem of finding uncertainty
regions for contour curves, for latent Gaussian models is proposed. The method
is based on using a parametric family for the excursion sets in combination
with a sequential importance sampling method for estimating joint
probabilities. The accuracy of the method is investigated using simulated data
and two environmental applications are presented. In the first application,
areas where the air pollution in the Piemonte region in northern Italy exceeds
the daily limit value, set by the European Union for human health protection,
are estimated. In the second application, regions in the African Sahel that
experienced an increase in vegetation after the drought period in the early
1980s are estimated.
