  Classical assessments of trends in gridded temperature data perform
independent evaluations across the grid, thus, ignoring spatial correlations in
the trend estimates. In particular, this affects assessments of trend
significance as evaluation of the collective significance of individual tests
is commonly neglected. In this article we build a space-time hierarchical
Bayesian model for temperature anomalies where the trend coefficient is modeled
by a latent Gaussian random field. This enables us to calculate simultaneous
credible regions for joint significance assessments. In a case study, we assess
summer season trends in 65 years of gridded temperature data over Europe. We
find that while spatial smoothing generally results in larger regions where the
null hypothesis of no trend is rejected, this is not the case for all
sub-regions.
