  This paper considers the problem of simultaneously estimating rare-event
probabilities for a class of Gaussian random fields. A conventional rare-event
simulation method is usually tailored to a specific rare event and consequently
would lose estimation efficiency for different events of interest, which often
results in additional computational cost in such simultaneous estimation
problem. To overcome this issue, we propose a uniformly efficient estimator for
a general family of H\"older continuous Gaussian random fields. We establish
the asymptotic and uniform efficiency of the proposed method and also conduct
simulation studies to illustrate its effectiveness.
