Original Article
Global envelope tests for spatial processes
Summary
Envelope tests are a popular tool in spatial statistics, where they are used in goodness‐of‐fit testing. These tests graphically compare an empirical function T(r) with its simulated counterparts from the null model. However, the type I error probability α is conventionally controlled for a fixed distance r only, whereas the functions are inspected on an interval of distances I. In this study, we propose two approaches related to Barnard's Monte Carlo test for building global envelope tests on I: ordering the empirical and simulated functions on the basis of their r‐wise ranks among each other, and the construction of envelopes for a deviation test. These new tests allow the a priori choice of the global α and they yield p‐values. We illustrate these tests by using simulated and real point pattern data.
Citing Literature
Number of times cited according to CrossRef: 54
- Tomáš Mrkvička, Jiří Dvořák, Jonatan A. González, Jorge Mateu, Revisiting the random shift approach for testing in spatial statistics, Spatial Statistics, 10.1016/j.spasta.2020.100430, (100430), (2020).
- Mari Myllymäki, Mikko Kuronen, Tomáš Mrkvička, Testing global and local dependence of point patterns on covariates in parametric models, Spatial Statistics, 10.1016/j.spasta.2020.100436, (100436), (2020).
- Hongxiang Wang, Zhonghua Zhao, Mari Myllymäki, Arne Pommerening, Spatial size diversity in natural and planted forest ecosystems: Revisiting and extending the concept of spatial size inequality, Ecological Informatics, 10.1016/j.ecoinf.2020.101054, (101054), (2020).
- Wenlin Dai, Tomáš Mrkvička, Ying Sun, Marc G. Genton, Functional outlier detection and taxonomy by sequential transformations, Computational Statistics & Data Analysis, 10.1016/j.csda.2020.106960, (106960), (2020).
- Timothy M. Pollington, Michael J. Tildesley, T. Déirdre Hollingsworth, Lloyd A.C. Chapman, Developments in statistical inference when assessing spatiotemporal disease clustering with the tau statistic, Spatial Statistics, 10.1016/j.spasta.2020.100438, (100438), (2020).
- Joseph Lewis, Visibility of the Gask Ridge road from simulated Watchtowers: A Monte Carlo testing approach, Journal of Archaeological Science: Reports, 10.1016/j.jasrep.2020.102482, 33, (102482), (2020).
- Zbyněk Pawlas, Iva Karafiátová, Luděk Heller, Random tessellations marked with crystallographic orientations, Spatial Statistics, 10.1016/j.spasta.2020.100469, 39, (100469), (2020).
- Heidi S. Christensen, Jesper Møller, Modelling spine locations on dendrite trees using inhomogeneous Cox point processes, Spatial Statistics, 10.1016/j.spasta.2020.100478, (100478), (2020).
- Pekka Vakkari, Mari Rusanen, Juha Heikkinen, Tea Huotari, Katri Kärkkäinen, Patterns of genetic variation in leading-edge populations of Quercus robur: genetic patchiness due to family clusters, Tree Genetics & Genomes, 10.1007/s11295-020-01465-9, 16, 5, (2020).
- Johan Debayle, Vesna Gotovac Ðogaš, Kateřina Helisová, Jakub Staněk, Markéta Zikmundová, Assessing Similarity of Random sets via Skeletons, Methodology and Computing in Applied Probability, 10.1007/s11009-020-09785-y, (2020).
- Eric Berry, Yen-Chi Chen, Jessi Cisewski-Kehe, Brittany Terese Fasy, Functional summaries of persistence diagrams, Journal of Applied and Computational Topology, 10.1007/s41468-020-00048-w, (2020).
- Jakob G. Rasmussen, Heidi S. Christensen, Point Processes on Directed Linear Networks, Methodology and Computing in Applied Probability, 10.1007/s11009-020-09777-y, (2020).
- Ana C. Cebrián, Jesús Abaurrea, Jesús Asín, Testing independence between two nonhomogeneous point processes in time, Journal of Statistical Computation and Simulation, 10.1080/00949655.2020.1792471, (1-24), (2020).
- Claes Andersson, Tomáš Mrkvička, Inference for cluster point processes with over- or under-dispersed cluster sizes, Statistics and Computing, 10.1007/s11222-020-09960-8, (2020).
- Trevor Harris, J. Derek Tucker, Bo Li, Lyndsay Shand, Elastic Depths for Detecting Shape Anomalies in Functional Data, Technometrics, 10.1080/00401706.2020.1811156, (1-11), (2020).
- Veronika Římalová, Alessandra Menafoglio, Alessia Pini, Vilém Pechanec, Eva Fišerová, A permutation approach to the analysis of spatiotemporal geochemical data in the presence of heteroscedasticity, Environmetrics, 10.1002/env.2611, 31, 4, (2019).
- Celia Chaiban, Christophe Biscio, Weerapong Thanapongtharm, Michael Tildesley, Xiangming Xiao, Timothy P. Robinson, Sophie O. Vanwambeke, Marius Gilbert, Point pattern simulation modelling of extensive and intensive chicken farming in Thailand: Accounting for clustering and landscape characteristics, Agricultural Systems, 10.1016/j.agsy.2019.03.004, 173, (335-344), (2019).
- Yousef Erfanifard, Krzysztof Stereńczak, Stanisław Miścicki, Management strategies alter competitive interactions and structural properties of Norway spruce in mixed stands of Bialowieża Forest, Poland, Forest Ecology and Management, 10.1016/j.foreco.2019.01.035, 437, (87-98), (2019).
- Jiří Dvořák, Jesper Møller, Tomáš Mrkvička, Samuel Soubeyrand, Quick inference for log Gaussian Cox processes with non-stationary underlying random fields, Spatial Statistics, 10.1016/j.spasta.2019.100388, (100388), (2019).
- Arne Pommerening, Pavel Grabarnik, Arne Pommerening, Pavel Grabarnik, Spatial Methods of Tree Interaction Analysis, Individual-based Methods in Forest Ecology and Management, 10.1007/978-3-030-24528-3, (99-197), (2019).
- Arne Pommerening, Arvid Svensson, Zhonghua Zhao, Hongxiang Wang, Mari Myllymäki, Spatial species diversity in temperate species-rich forest ecosystems: Revisiting and extending the concept of spatial species mingling, Ecological Indicators, 10.1016/j.ecolind.2019.05.060, 105, (116-125), (2019).
- Bimal Bhattarai, Rohan Kumar Yadav, Hui-Seon Gang, Jae-Young Pyun, Geomagnetic Field Based Indoor Landmark Classification Using Deep Learning, IEEE Access, 10.1109/ACCESS.2019.2902573, 7, (33943-33956), (2019).
- C. Andersson, T. Rajala, A. Särkkä, A Bayesian hierarchical point process model for epidermal nerve fiber patterns, Mathematical Biosciences, 10.1016/j.mbs.2019.04.010, (2019).
- M. Kruuse, E. Tempel, R. Kipper, R. S. Stoica, Photometric redshift galaxies as tracers of the filamentary network, Astronomy & Astrophysics, 10.1051/0004-6361/201935096, 625, (A130), (2019).
- Jesús Fernández-Habas, Pilar Fernández-Rebollo, Mónica Rivas Casado, Alma María García Moreno, Begoña Abellanas, Spatio-temporal analysis of oak decline process in open woodlands: A case study in SW Spain, Journal of Environmental Management, 10.1016/j.jenvman.2019.109308, 248, (109308), (2019).
- Vesna Gotovac Dogaš, Kateřina Helisová, Testing Equality of Distributions of Random Convex Compact Sets via Theory of 𝕹$\mathfrak {N}$-Distances, Methodology and Computing in Applied Probability, 10.1007/s11009-019-09747-z, (2019).
- Tomáš Mrkvička, Tomáš Roskovec, Michael Rost, A Nonparametric Graphical Tests of Significance in Functional GLM, Methodology and Computing in Applied Probability, 10.1007/s11009-019-09756-y, (2019).
- Jesper Møller, Heidi S. Christensen, Francisco Cuevas-Pacheco, Andreas D. Christoffersen, Structured Space-Sphere Point Processes and K-Functions, Methodology and Computing in Applied Probability, 10.1007/s11009-019-09712-w, (2019).
- Francisco Cuevas, Denis Allard, Emilio Porcu, Fast and exact simulation of Gaussian random fields defined on the sphere cross time, Statistics and Computing, 10.1007/s11222-019-09873-1, (2019).
- B Retter, J Hatchell, Tim Naylor, Spatial Statistics in Star Forming Regions: Testing the Limits of Randomness, Monthly Notices of the Royal Astronomical Society, 10.1093/mnras/stz1279, (2019).
- Kateřina Koňasová, Jiří Dvořák, Stochastic Reconstruction for Inhomogeneous Point Patterns, Methodology and Computing in Applied Probability, 10.1007/s11009-019-09738-0, (2019).
- Christophe A. N. Biscio, Jesper Møller, The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications, Journal of Computational and Graphical Statistics, 10.1080/10618600.2019.1573686, (1-21), (2019).
- Wenlin Dai, Marc G. Genton, Directional outlyingness for multivariate functional data, Computational Statistics & Data Analysis, 10.1016/j.csda.2018.03.017, (2018).
- Elizabeth Gusmán-M., Marcelino de la Cruz, Carlos Iván Espinosa, Adrián Escudero, Focusing on individual species reveals the specific nature of assembly mechanisms in a tropical dry-forest, Perspectives in Plant Ecology, Evolution and Systematics, 10.1016/j.ppees.2018.07.004, 34, (94-101), (2018).
- P. Grabarnik, M. Myllymäki, undefined, , 10.17537/icmbb18.111, (2018).
- Jesper Møller, Andreas D. Christoffersen, Pair correlation functions and limiting distributions of iterated cluster point processes, Journal of Applied Probability, 10.1017/jpr.2018.50, 55, 3, (789-809), (2018).
- Francisco Cuevas-Pacheco, Jesper Møller, Log Gaussian Cox processes on the sphere, Spatial Statistics, 10.1016/j.spasta.2018.06.002, 26, (69-82), (2018).
- T. Rajala, D. J. Murrell, S. C. Olhede, Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection, Journal of the Royal Statistical Society: Series C (Applied Statistics), 10.1111/rssc.12281, 67, 5, (1237-1273), (2018).
- David J. Murrell, A global envelope test to detect non‐random bursts of trait evolution, Methods in Ecology and Evolution, 10.1111/2041-210X.13006, 9, 7, (1739-1748), (2018).
- Yousef Erfanifard, Hong Hai Nguyen, John Paul Schmidt, Andrew Rayburn, Fine-scale intraspecific interactions and environmental heterogeneity drive the spatial structure in old-growth stands of a dioecious plant, Forest Ecology and Management, 10.1016/j.foreco.2018.05.041, 425, (92-99), (2018).
- L. Heinrich, Asymptotic goodness-of-fit tests for point processes based on scaled empirical K -functions , Statistics, 10.1080/02331888.2018.1460367, 52, 4, (829-851), (2018).
- Henrike Häbel, Tuomas Rajala, Mariagrazia Marucci, Catherine Boissier, Katja Schladitz, Claudia Redenbach, Aila Särkkä, A three-dimensional anisotropic point process characterization for pharmaceutical coatings, Spatial Statistics, 10.1016/j.spasta.2017.05.003, 22, (306-320), (2017).
- Jesper Møller, Rasmus Waagepetersen, Some Recent Developments in Statistics for Spatial Point Patterns, Annual Review of Statistics and Its Application, 10.1146/annurev-statistics-060116-054055, 4, 1, (317-342), (2017).
- T. Després, L. Vítková, R. Bače, V. Čada, P. Janda, M. Mikoláš, J. S. Schurman, V. Trotsiuk, M. Svoboda, Past disturbances and intraspecific competition as drivers of spatial pattern in primary spruce forests, Ecosphere, 10.1002/ecs2.2037, 8, 12, (e02037), (2017).
- Edith Gabriel, A. Baddeley, E. Rubak, R. Turner: Spatial Point Patterns: Methodology and Applications with R, Mathematical Geosciences, 10.1007/s11004-016-9670-x, 49, 6, (815-817), (2017).
- Marek Šmejkal, Daniel Ricard, Lukáš Vejřík, Tomáš Mrkvička, Lucie Vebrová, Roman Baran, Petr Blabolil, Zuzana Sajdlová, Ivana Vejříková, Marie Prchalová, Jan Kubečka, Seasonal and daily protandry in a cyprinid fish, Scientific Reports, 10.1038/s41598-017-04827-x, 7, 1, (2017).
- Adrian Baddeley, Andrew Hardegen, Thomas Lawrence, Robin K. Milne, Gopalan Nair, Suman Rakshit, On two-stage Monte Carlo tests of composite hypotheses, Computational Statistics & Data Analysis, 10.1016/j.csda.2017.04.003, 114, (75-87), (2017).
- Suman Rakshit, Gopalan Nair, Adrian Baddeley, Second-order analysis of point patterns on a network using any distance metric, Spatial Statistics, 10.1016/j.spasta.2017.10.002, 22, (129-154), (2017).
- Radu S. Stoica, Anne Philippe, Pablo Gregori, Jorge Mateu, ABC Shadow algorithm: a tool for statistical analysis of spatial patterns, Statistics and Computing, 10.1007/s11222-016-9682-x, 27, 5, (1225-1238), (2016).
- Tomáš Mrkvička, Mari Myllymäki, Ute Hahn, Multiple Monte Carlo testing, with applications in spatial point processes, Statistics and Computing, 10.1007/s11222-016-9683-9, 27, 5, (1239-1255), (2016).
- Antonín Koubek, Zbyněk Pawlas, Tim Brereton, Björn Kriesche, Volker Schmidt, Testing the random field model hypothesis for random marked closed sets, Spatial Statistics, 10.1016/j.spasta.2016.03.001, 16, (118-136), (2016).
- Jesper Møller, Farzaneh Safavimanesh, Jakob Gulddahl Rasmussen, The cylindrical $K$-function and Poisson line cluster point processes, Biometrika, 10.1093/biomet/asw044, 103, 4, (937-954), (2016).
- D. Stoyan, Point process statistics: application to modern and contemporary art and design, Journal of Mathematics and the Arts, 10.1080/17513472.2016.1208980, 10, 1-4, (20-34), (2016).
- Svend V. Nielsen, Simon Simonsen, Asger Hobolth, Inferring Population Genetic Parameters: Particle Filtering, HMM, Ripley’s K-Function or Runs of Homozygosity?, Algorithms in Bioinformatics, 10.1007/978-3-319-43681-4_19, (234-245), (2016).
