{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/global-envelope-tests-for-spatial-processes","title":"Global envelope tests for spatial processes","arxiv_id":"1307.0239","date":"2013-06-30","proceeding":null,"authors":["Mari Myllymäki","Tomás Mrkvicka","Pavel Grabarnik","Henri Seijo","Ute Hahn"],"abstract":"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 $\\alpha$ 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 $I$:(1) ordering the empirical and simulated functions based on their $r$-wise ranks among each other, and (2) the construction of envelopes for a deviation test. These new tests allow the a priori selection of the global $\\alpha$ and they yield $p$-values. We illustrate these tests using simulated and real point pattern data.","url_abs":"http://arxiv.org/abs/1307.0239v4","url_pdf":"http://arxiv.org/pdf/1307.0239v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"global-envelope-tests-for-spatial-processes","repo_url":"https://github.com/myllym/spptest","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"global-envelope-tests-for-spatial-processes","repo_url":"https://github.com/myllym/GET","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}