Excursion and contour uncertainty regions for latent Gaussian models

By David Bolin, Finn Lindgren. 2012

138 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7b819b2d9026fce7c3d77231ffc4c9504018a5a5

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Citations in the corpus

The normal law under linear restrictions: simulation and estimation via minimax tilting (2016, methodology): “…Davison, 2013; Genton et al., 2011); computation of simultaneous conﬁdence bands (Aza¨ıs et al., 2010); uncertainty regions for latent Gaussian models (Bolin and Lindgren, 2015); ﬁtting mixed e ﬀ ects models with censored data (Gr¨un and Hornik, 2012); and probit regression (Albert and Chib,…”
Geostatistical Modelling Using Non‐Gaussian Matérn Fields (2015, background): “Thus, the distributional assumptions are especially important if we are interested in predicting the probability for large amounts of precipitation or if we are interested in regions where the latent process exceeds a certain level, which is often important in applications (Bolin & Lindgren, 2015).”
Spatial modelling with R-INLA: A review (2018, methodology): “It also simpliﬁes the computation of excursion sets and uncertainty measures for contour maps, as shown by Bolin and Lindgren (2015) and Bolin and Lindgren (2017).”
Bayesian Spatial Modelling with R-INLA (2015, unknown): “A non-parametric approach using similar GMRF models is available in the LatticeKrig package in CRAN (Nychka, Hammerling, Sain, and Lenssen 2013).”
Bayesian Computing with INLA: A Review (2016, methodology): “, 2015), BAPC (Riebler and Held, 2016), diseasemapping and geostatp (Brown, 2015), and Bivand et al. (2015). Similarly, the excursions package for calculating joint exceedance probabilities in GMRFs (Bolin and Lindgren, 2015, 2016) includes an interface to analyse LGMs estimated by R-INLA. Recent wo”