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For example, intrinsic GPs can accommodate spatial domains arising as complex subsets of Euclidean space. Intrinsic GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the approach proposed is to utilize the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels. This enables intrinsic GPs to be practically applied in great generality, whereas existing approaches for smoothing on constrained domains are limited to simple special cases. The broad utilities of the intrinsic GP approach are illustrated through simulation studies and data examples.<\/jats:p>","DOI":"10.1111\/rssb.12320","type":"journal-article","created":{"date-parts":[[2019,4,19]],"date-time":"2019-04-19T16:55:41Z","timestamp":1555692941000},"page":"603-627","source":"Crossref","is-referenced-by-count":24,"title":["Intrinsic Gaussian Processes on Complex Constrained Domains"],"prefix":"10.1093","volume":"81","author":[{"given":"Mu","family":"Niu","sequence":"first","affiliation":[{"name":"Plymouth University \u00a0 UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pokman","family":"Cheung","sequence":"additional","affiliation":[{"name":", London, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lizhen","family":"Lin","sequence":"additional","affiliation":[{"name":"University of Notre Dame \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenwen","family":"Dai","sequence":"additional","affiliation":[{"name":"University of Sheffield and Amazon \u00a0 UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Neil","family":"Lawrence","sequence":"additional","affiliation":[{"name":"University of Sheffield and Amazon \u00a0 UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Dunson","sequence":"additional","affiliation":[{"name":"Duke University, Durham \u00a0 USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,4,19]]},"reference":[{"key":"2023022002404385000_","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1111\/cgf.13251","article-title":"Stochastic heat kernel estimation on sampled manifolds","volume":"36","author":"Aumentado-Armstrong","year":"2017","journal-title":"Comput. 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