{"title":"关于基于 PDE 的精确算子与马特恩协方差之间关系的说明","authors":"Umberto Villa, Thomas O'Leary-Roseberry","doi":"arxiv-2407.00471","DOIUrl":null,"url":null,"abstract":"The purpose of this technical note is to summarize the relationship between\nthe marginal variance and correlation length of a Gaussian random field with\nMat\\'ern covariance and the coefficients of the corresponding\npartial-differential-equation (PDE)-based precision operator.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on the relationship between PDE-based precision operators and Matérn covariances\",\"authors\":\"Umberto Villa, Thomas O'Leary-Roseberry\",\"doi\":\"arxiv-2407.00471\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this technical note is to summarize the relationship between\\nthe marginal variance and correlation length of a Gaussian random field with\\nMat\\\\'ern covariance and the coefficients of the corresponding\\npartial-differential-equation (PDE)-based precision operator.\",\"PeriodicalId\":501215,\"journal\":{\"name\":\"arXiv - STAT - Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - STAT - Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.00471\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - STAT - Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.00471","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A note on the relationship between PDE-based precision operators and Matérn covariances
The purpose of this technical note is to summarize the relationship between
the marginal variance and correlation length of a Gaussian random field with
Mat\'ern covariance and the coefficients of the corresponding
partial-differential-equation (PDE)-based precision operator.
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