Original Article
Excursion and contour uncertainty regions for latent Gaussian models
Summary
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.
Citing Literature
Number of times cited according to CrossRef: 37
- Cláudia Jardim Santos, Bernardo Gomes, Ana Isabel Ribeiro, Mapping Geographical Patterns and High Rate Areas for Sexually Transmitted Infections in Portugal, Sexually Transmitted Diseases, 10.1097/OLQ.0000000000001122, 47, 4, (261-268), (2020).
- Noel Cressie, Thomas Suesse, Great expectations and even greater exceedances from spatially referenced data, Spatial Statistics, 10.1016/j.spasta.2020.100420, (100420), (2020).
- Kevin Bulthuis, Frank Pattyn, Maarten Arnst, A Multifidelity Quantile-Based Approach for Confidence Sets of Random Excursion Sets with Application to Ice-Sheet Dynamics, SIAM/ASA Journal on Uncertainty Quantification, 10.1137/19M1280466, 8, 3, (860-890), (2020).
- Arne Nothdurft, Climate sensitive single tree growth modeling using a hierarchical Bayes approach and integrated nested Laplace approximations (INLA) for a distributed lag model, Forest Ecology and Management, 10.1016/j.foreco.2020.118497, 478, (118497), (2020).
- Olena Oliveira, Ana Isabel Ribeiro, Elias Teixeira Krainski, Teresa Rito, Raquel Duarte, Margarida Correia-Neves, Using Bayesian spatial models to map and to identify geographical hotspots of multidrug-resistant tuberculosis in Portugal between 2000 and 2016, Scientific Reports, 10.1038/s41598-020-73759-w, 10, 1, (2020).
- Parisa Naseri, Hamid Alavi Majd, Seyyed Mohammad Tabatabaei, Integrated nested Laplace approximation method for hierarchical Bayesian inference of spatial model with application to functional magnetic resonance imaging data, Communications in Statistics - Theory and Methods, 10.1080/03610926.2020.1776327, (1-24), (2020).
- Bernard X.W. Liew, Yu (Ryan) Yue, Corrado Cescon, Marco Barbero, Deborah Falla, Influence of experimental pain on the spatio-temporal activity of upper trapezius during dynamic lifting – an investigation using Bayesian spatio-temporal ANOVA, Journal of Electromyography and Kinesiology, 10.1016/j.jelekin.2019.05.018, (2019).
- Garyfallos Konstantinoudis, Dominic Schuhmacher, Håvard Rue, Ben Spycher, Discrete versus continuous domain models for disease mapping, Spatial and Spatio-temporal Epidemiology, 10.1016/j.sste.2019.100319, (100319), (2019).
- J. M. C. Pereira, M. A. Amaral Turkman, K. F. Turkman, D. Oom, Anthromes displaying evidence of weekly cycles in active fire data cover 70% of the global land surface, Scientific Reports, 10.1038/s41598-019-47678-4, 9, 1, (2019).
- Amanda F. Mejia, Yu (Ryan) Yue, David Bolin, Finn Lindgren, Martin A. Lindquist, A Bayesian General Linear Modeling Approach to Cortical Surface fMRI Data Analysis, Journal of the American Statistical Association, 10.1080/01621459.2019.1611582, (1-26), (2019).
- Dario Azzimonti, David Ginsbourger, Jérémy Rohmer, Déborah Idier, Profile Extrema for Visualizing and Quantifying Uncertainties on Excursion Regions: Application to Coastal Flooding, Technometrics, 10.1080/00401706.2018.1562987, (1-27), (2019).
- Dario Azzimonti, David Ginsbourger, Clément Chevalier, Julien Bect, Yann Richet, Adaptive Design of Experiments for Conservative Estimation of Excursion Sets, Technometrics, 10.1080/00401706.2019.1693427, (1-14), (2019).
- Mohamed Reda El Amri, Céline Helbert, Olivier Lepreux, Miguel Munoz Zuniga, Clémentine Prieur, Delphine Sinoquet, Data-driven stochastic inversion via functional quantization, Statistics and Computing, 10.1007/s11222-019-09888-8, (2019).
- Kevin Bulthuis, Maarten Arnst, Sainan Sun, Frank Pattyn, Uncertainty quantification of the multi-centennial response of the Antarctic ice sheet to climate change, The Cryosphere, 10.5194/tc-13-1349-2019, 13, 4, (1349-1380), (2019).
- Emanuele Giorgi, Ali Abdirahman Osman, Abdikarin Hussein Hassan, Abdi Abdillahi Ali, Faisa Ibrahim, Jamal G. H. Amran, Abdisalan M. Noor, Robert W. Snow, Using non-exceedance probabilities of policy-relevant malaria prevalence thresholds to identify areas of low transmission in Somalia, Malaria Journal, 10.1186/s12936-018-2238-0, 17, 1, (2018).
- Damaris K. Kinyoki, Grainne M. Moloney, Olalekan A. Uthman, Elijah O. Odundo, Ngianga-Bakwin Kandala, Abdisalan M. Noor, Robert W. Snow, James A. Berkley, Co-morbidity of malnutrition with falciparum malaria parasitaemia among children under the aged 6–59 months in Somalia: a geostatistical analysis, Infectious Diseases of Poverty, 10.1186/s40249-018-0449-9, 7, 1, (2018).
- Per Sidén, Finn Lindgren, David Bolin, Mattias Villani, Efficient Covariance Approximations for Large Sparse Precision Matrices, Journal of Computational and Graphical Statistics, 10.1080/10618600.2018.1473782, 27, 4, (898-909), (2018).
- A Adin, D Lee, T Goicoa, María Dolores Ugarte, A two-stage approach to estimate spatial and spatio-temporal disease risks in the presence of local discontinuities and clusters, Statistical Methods in Medical Research, 10.1177/0962280218767975, (096228021876797), (2018).
- Dario Azzimonti, David Ginsbourger, Estimating Orthant Probabilities of High-Dimensional Gaussian Vectors with An Application to Set Estimation, Journal of Computational and Graphical Statistics, 10.1080/10618600.2017.1360781, 27, 2, (255-267), (2017).
- Håvard Rue, Andrea Riebler, Sigrunn H. Sørbye, Janine B. Illian, Daniel P. Simpson, Finn K. Lindgren, Bayesian Computing with INLA: A Review, Annual Review of Statistics and Its Application, 10.1146/annurev-statistics-060116-054045, 4, 1, (395-421), (2017).
- Anders Eklund, Martin A. Lindquist, Mattias Villani, A Bayesian heteroscedastic GLM with application to fMRI data with motion spikes, NeuroImage, 10.1016/j.neuroimage.2017.04.069, 155, (354-369), (2017).
- Per Sidén, Anders Eklund, David Bolin, Mattias Villani, Fast Bayesian whole-brain fMRI analysis with spatial 3D priors, NeuroImage, 10.1016/j.neuroimage.2016.11.040, 146, (211-225), (2017).
- Joshua P. French, Seth McGinnis, Armin Schwartzman, Assessing NARCCAP climate model effects using spatial confidence regions, Advances in Statistical Climatology, Meteorology and Oceanography, 10.5194/ascmo-3-67-2017, 3, 2, (67-92), (2017).
- Max Sommerfeld, Stephan Sain, Armin Schwartzman, Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate, Journal of the American Statistical Association, 10.1080/01621459.2017.1341838, (1-14), (2017).
- Z. I. Botev, The normal law under linear restrictions: simulation and estimation via minimax tilting, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 10.1111/rssb.12162, 79, 1, (125-148), (2016).
- Matthew M. Dunlop, Marco A. Iglesias, Andrew M. Stuart, Hierarchical Bayesian level set inversion, Statistics and Computing, 10.1007/s11222-016-9704-8, 27, 6, (1555-1584), (2016).
- David Bolin, Finn Lindgren, Quantifying the Uncertainty of Contour Maps, Journal of Computational and Graphical Statistics, 10.1080/10618600.2016.1228537, 26, 3, (513-524), (2016).
- Damaris K Kinyoki, Ngianga-Bakwin Kandala, Samuel O Manda, Elias T Krainski, Geir-Arne Fuglstad, Grainne M Moloney, James A Berkley, Abdisalan M Noor, Assessing comorbidity and correlates of wasting and stunting among children in Somalia using cross-sectional household surveys: 2007 to 2010, BMJ Open, 10.1136/bmjopen-2015-009854, 6, 3, (e009854), (2016).
- Damaris K. Kinyoki, James A. Berkley, Grainne M. Moloney, Elijah O. Odundo, Ngianga-Bakwin Kandala, Abdisalan M. Noor, Environmental predictors of stunting among children under-five in Somalia: cross-sectional studies from 2007 to 2010, BMC Public Health, 10.1186/s12889-016-3320-6, 16, 1, (2016).
- Massimo Ventrucci, Daniela Cocchi, Marian Scott, Smoothing of land use maps for trend and change detection in urbanization, Environmental and Ecological Statistics, 10.1007/s10651-016-0354-y, 23, 4, (565-584), (2016).
- Dario Azzimonti, Julien Bect, Clément Chevalier, David Ginsbourger, Quantifying Uncertainties on Excursion Sets Under a Gaussian Random Field Prior, SIAM/ASA Journal on Uncertainty Quantification, 10.1137/141000749, 4, 1, (850-874), (2016).
- D. Simpson, J. B. Illian, F. Lindgren, S. H. Sørbye, H. Rue, Going off grid: computationally efficient inference for log-Gaussian Cox processes, Biometrika, 10.1093/biomet/asv064, 103, 1, (49-70), (2016).
- Ana Isabel Ribeiro, Elias Teixeira Krainski, Roseanne Autran, Hugo Teixeira, Marilia Sá Carvalho, Maria de Fátima de Pina, The influence of socioeconomic, biogeophysical and built environment on old-age survival in a Southern European city, Health & Place, 10.1016/j.healthplace.2016.08.008, 41, (100-109), (2016).
- Jon Wakefield, Daniel Simpson, Jessica Godwin, Comment: Getting into Space with a Weight Problem, Journal of the American Statistical Association, 10.1080/01621459.2016.1200918, 111, 515, (1111-1118), (2016).
- Simon Barthelmé, Fast matrix computations for functional additive models, Statistics and Computing, 10.1007/s11222-014-9490-0, 25, 1, (47-63), (2014).
- Sara Martino, Andrea Riebler, Integrated Nested Laplace Approximations (INLA), Wiley StatsRef: Statistics Reference Online, 10.1002/9781118445112, (1-19), (2014).
- Peter Guttorp, Alex Januzzi, Marie Novak, Harry Podschwit, Lee Richardson, Colin D. Sowder, Aaron Zimmerman, David Bolin, Aila Särkkä, Assessing the Uncertainty in Projecting Local Mean Sea Level from Global Temperature, Journal of Applied Meteorology and Climatology, 10.1175/JAMC-D-13-0308.1, 53, 9, (2163-2170), (2014).
