{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T08:04:34Z","timestamp":1767859474906,"version":"3.49.0"},"reference-count":54,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2020,3,18]],"date-time":"2020-03-18T00:00:00Z","timestamp":1584489600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Academy of Finland Profi 5 funding for mathematics and AI"},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["312123"],"award-info":[{"award-number":["312123"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Finnish Centre of Excellence in Inverse Modelling and Imaging","award":["2018\u20132025"],"award-info":[{"award-number":["2018\u20132025"]}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N032055\/1"],"award-info":[{"award-number":["EP\/N032055\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/M020533\/1"],"award-info":[{"award-number":["EP\/M020533\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Improved DNA technology has made it practical to estimate single-nucleotide polymorphism (SNP)-heritability among distantly related individuals with unknown relationships. For growth- and development-related traits, it is meaningful to base SNP-heritability estimation on longitudinal data due to the time-dependency of the process. However, only few statistical methods have been developed so far for estimating dynamic SNP-heritability and quantifying its full uncertainty.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>We introduce a completely tuning-free Bayesian Gaussian process (GP)-based approach for estimating dynamic variance components and heritability as their function. For parameter estimation, we use a modern Markov Chain Monte Carlo method which allows full uncertainty quantification. Several datasets are analysed and our results clearly illustrate that the 95% credible intervals of the proposed joint estimation method (which \u2018borrows strength\u2019 from adjacent time points) are significantly narrower than of a two-stage baseline method that first estimates the variance components at each time point independently and then performs smoothing. We compare the method with a random regression model using MTG2 and BLUPF90 software and quantitative measures indicate superior performance of our method. Results are presented for simulated and real data with up to 1000 time points. Finally, we demonstrate scalability of the proposed method for simulated data with tens of thousands of individuals.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>The C++ implementation dynBGP and simulated data are available in GitHub: https:\/\/github.com\/aarjas\/dynBGP. The programmes can be run in R. Real datasets are available in QTL archive: https:\/\/phenome.jax.org\/centers\/QTLA.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/btaa199","type":"journal-article","created":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T20:11:26Z","timestamp":1584475886000},"page":"3795-3802","source":"Crossref","is-referenced-by-count":7,"title":["Estimation of dynamic SNP-heritability with Bayesian Gaussian process models"],"prefix":"10.1093","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9545-0244","authenticated-orcid":false,"given":"Arttu","family":"Arjas","sequence":"first","affiliation":[{"name":"Research Unit of Mathematical Sciences , University of Oulu, Oulu FI-90014, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3756-8121","authenticated-orcid":false,"given":"Andreas","family":"Hauptmann","sequence":"additional","affiliation":[{"name":"Research Unit of Mathematical Sciences , University of Oulu, Oulu FI-90014, Finland"},{"name":"Department of Computer Science , University College London, London WC1E 6BT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2808-2768","authenticated-orcid":false,"given":"Mikko J","family":"Sillanp\u00e4\u00e4","sequence":"additional","affiliation":[{"name":"Research Unit of Mathematical Sciences , University of Oulu, Oulu FI-90014, Finland"},{"name":"Infotech Oulu , University of Oulu, Oulu FI-90014, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,3,18]]},"reference":[{"key":"2023063011070690800_btaa199-B1","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1080\/01621459.1993.10476321","article-title":"Bayesian analysis of binary and polychotomous response data","volume":"88","author":"Albert","year":"1993","journal-title":"J. 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