Excursion and contour uncertainty regions for latent Gaussian models

David Bolin and Finn Lindgren

Journal of the Royal Statistical Society Series B, 2015, vol. 77, issue 1, 85-106

Abstract: type="main" xml:id="rssb12055-abs-0001">

In several areas of application ranging from brain imaging to astrophysics and geostatistics, an important statistical problem is to find regions where the process studied 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 connected to the problem of multiple significance testing. In this work, a method for solving this problem, as well as the related problem of finding credible 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 by using simulated data and an environmental application is presented.

Date: 2015
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