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Excursion and contour uncertainty regions for latent Gaussian models

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  • David Bolin
  • Finn Lindgren

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.

Suggested Citation

  • David Bolin & Finn Lindgren, 2015. "Excursion and contour uncertainty regions for latent Gaussian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 85-106, January.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:1:p:85-106
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.77.issue-1
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    Citations

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    Cited by:

    1. Damaris K. Kinyoki & Samuel O. Manda & Grainne M. Moloney & Elijah O. Odundo & James A. Berkley & Abdisalan M. Noor & Ngianga-Bakwin Kandala, 2017. "Modelling the Ecological Comorbidity of Acute Respiratory Infection, Diarrhoea and Stunting among Children Under the Age of 5 Years in Somalia," International Statistical Review, International Statistical Institute, vol. 85(1), pages 164-176, April.
    2. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
    3. Lindgren, Finn & Rue, Håvard, 2015. "Bayesian Spatial Modelling with R-INLA," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i19).
    4. Tobias Fissler & Jana Hlavinov'a & Birgit Rudloff, 2019. "Elicitability and Identifiability of Systemic Risk Measures," Papers 1907.01306, arXiv.org, revised Oct 2019.
    5. Hannah M. Director & Adrian E. Raftery, 2022. "Contour models for physical boundaries enclosing star‐shaped and approximately star‐shaped polygons," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1688-1720, November.
    6. Peter A. Gao & Hannah M. Director & Cecilia M. Bitz & Adrian E. Raftery, 2022. "Probabilistic Forecasts of Arctic Sea Ice Thickness," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 280-302, June.
    7. Karine Hagesæther Foss & Gunhild Elisabeth Berget & Jo Eidsvik, 2022. "Using an autonomous underwater vehicle with onboard stochastic advection‐diffusion models to map excursion sets of environmental variables," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    8. Peter F. Craigmile & Peter Guttorp, 2022. "A combined estimate of global temperature," Environmetrics, John Wiley & Sons, Ltd., vol. 33(3), May.
    9. Jonas Wallin & David Bolin, 2015. "Geostatistical Modelling Using Non-Gaussian Matérn Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 872-890, September.
    10. David Bolin & Vilhelm Verendel & Meta Berghauser Pont & Ioanna Stavroulaki & Oscar Ivarsson & Erik Håkansson, 2021. "Functional ANOVA modelling of pedestrian counts on streets in three European cities," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1176-1198, October.

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