  The goal of this paper is to give confidence regions for the excursion set of
a spatial function above a given threshold from repeated noisy observations on
a fine grid of fixed locations. Given an asymptotically Gaussian estimator of
the target function, a pair of data-dependent nested excursion sets are
constructed that are sub- and super-sets of the true excursion set,
respectively, with a desired confidence. Asymptotic coverage probabilities are
determined via a multiplier bootstrap method, not requiring Gaussianity of the
original data nor stationarity or smoothness of the limiting Gaussian field.
The method is used to determine regions in North America where the mean summer
and winter temperatures are expected to increase by mid 21st century by more
than 2 degrees Celsius.
