Efficient Monte Carlo for High Excursions of Gaussian Random Fields

Details Efficient Monte Carlo for High Excursions of Gaussian Random Fields Efficient Monte Carlo for High Excursions of Gaussian Random Fields

2010-05-05

arxiv.org/abs/1005.0812v3

Mathematics

Probability

Scientific paper

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, $b$. Naive Monte Carlo takes an exponential, in $b$, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynomial complexity in $b$, assuming only that the mean and covariance functions are Holder continuous. We also explain how to fine tune the construction of our procedures in the presence of additional regularity, such as homogeneity and smoothness, in order to further improve the efficiency.

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