{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T06:44:47Z","timestamp":1791960287224,"version":"4.3.4"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":906,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1513076"],"award-info":[{"award-number":["1513076"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,12,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>An integro-difference equation can be represented as a hierarchical spatiotemporal dynamic model using appropriate parameterizations. The dynamics of the process defined by an integro-difference equation depends on the choice of a bivariate kernel distribution, where more flexible shapes generally result in more flexible models. Under a Bayesian modelling framework, we consider the use of the stable family of distributions for the kernel, as they are infinitely divisible and offer a variety of tail behaviours, orientations and skewness. Many of the attributes of the bivariate stable distribution are controlled by a measure, which we model using a flexible Bernstein polynomial basis prior. The method is the first attempt to incorporate non-Gaussian kernels in a two-dimensional integro-difference equation model and will be shown to improve prediction over the Gaussian kernel model for a data set of Pacific sea surface temperatures.<\/jats:p>","DOI":"10.1111\/rssb.12393","type":"journal-article","created":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T21:22:52Z","timestamp":1605043372000},"page":"1371-1392","source":"Crossref","is-referenced-by-count":4,"title":["Spatiotemporal Modelling using Integro-Difference Equations with Bivariate Stable Kernels"],"prefix":"10.1093","volume":"82","author":[{"given":"Robert","family":"Richardson","sequence":"first","affiliation":[{"name":"Brigham Young University , Provo , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Athanasios","family":"Kottas","sequence":"additional","affiliation":[{"name":"University of California , Santa Cruz , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bruno","family":"Sans\u00f3","sequence":"additional","affiliation":[{"name":"University of California , Santa Cruz , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,9,1]]},"reference":[{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/S0034-4257(70)80002-5","article-title":"Estimation of sea surface temperature from space","volume":"1","author":"Anding","year":"1970","journal-title":"Remote Sens. Environ."},{"key":"2023022501100473700_","first-page":"119","article-title":"Generalized double Pareto shrinkage","volume":"23","author":"Armagan","year":"2013","journal-title":"Statist. Sin."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1175\/1520-0477(1999)080<0217:PSOSAD>2.0.CO;2","article-title":"Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997\u201398 El Ni\u00f1o episode and the 1998 La Ni\u00f1a onset","volume":"80","author":"Barnston","year":"1999","journal-title":"Bull. Am. Meteorol. Soc."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"3953","DOI":"10.1175\/1520-0442(2001)013<3953:LLPOPS>2.0.CO;2","article-title":"Long-lead prediction of Pacific SSTs via Bayesian dynamic modeling","volume":"13","author":"Berliner","year":"2000","journal-title":"J. Clim."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1111\/1467-9868.00269","article-title":"Blur-generated non-separable space\u2013time models","volume":"62","author":"Brown","year":"2000","journal-title":"J. R. Statist. Soc."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1038\/321827a0","article-title":"Experimental forecasts of El Ni\u00f1o","volume":"321","author":"Cane","year":"1986","journal-title":"Nature"},{"key":"2023022501100473700_","volume-title":"Statistics for Spatio-temporal Data","author":"Cressie","year":"2011"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/0034-4257(81)90021-3","article-title":"A method for satellite identification of surface temperature fields of subpixel resolution","volume":"11","author":"Dozier","year":"1981","journal-title":"Remote Sens. Environ."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1111\/j.1467-9892.1994.tb00184.x","article-title":"Data augmentation and dynamic linear models","volume":"15","author":"Fr\u00fchwirth-Schnatter","year":"1994","journal-title":"J. Time Ser. Anal."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11749-008-0114-x","article-title":"Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds","volume":"17","author":"Gneiting","year":"2008","journal-title":"TEST"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1009666805688","article-title":"A process-convolution approach to modelling temperatures in the North Atlantic Ocean","volume":"5","author":"Higdon","year":"1998","journal-title":"Environ. Ecol. Statist."},{"key":"2023022501100473700_","volume-title":"ideq: an R package for dynamic spatio-temporal models","author":"Huch","year":"2019"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1029\/2005GL022738","article-title":"On the definition of El Ni\u00f1o and associated seasonal average US weather anomalies","volume":"32","author":"Larkin","year":"2005","journal-title":"Geophys. Res. Lett."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1198\/jasa.2009.0018","article-title":"A spatio-temporal model for mean, anomaly, and trend fields of North Atlantic sea surface temperature","volume":"104","author":"Lemos","year":"2009","journal-title":"J. Am. Statist. Ass."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"3217","DOI":"10.1016\/j.jspi.2011.04.008","article-title":"Geometric stick-breaking processes for continuous-time Bayesian nonparametric modeling","volume":"141","author":"Mena","year":"2011","journal-title":"J. Statist. Planng Inf."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1007\/s00180-013-0396-7","article-title":"Multivariate elliptically contoured stable distributions: theory and estimation","volume":"28","author":"Nolan","year":"2013","journal-title":"Computnl Statist."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1002\/wics.1286","article-title":"Financial modeling with heavy-tailed stable distributions","volume":"6","author":"Nolan","year":"2014","journal-title":"Wiley Interdisc. Rev. Computnl Statist."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"3240","DOI":"10.1175\/JCLI3420.1","article-title":"Did the ECMWF seasonal forecast model outperform statistical ENSO forecast models over the last 15 years?","volume":"18","author":"van Oldenborgh","year":"2005","journal-title":"J. Clim."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0377-0427(95)00144-1","article-title":"Generalized stable models for financial asset returns","volume":"70","author":"Panorska","year":"1996","journal-title":"J. Computnl Appl. Math."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1175\/1520-0442(1993)006<1067:PONSST>2.0.CO;2","article-title":"Prediction of Ni\u00f1o 3 sea surface temperatures using linear inverse modeling","volume":"6","author":"Penland","year":"1993","journal-title":"J. Clim."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"105","DOI":"10.2307\/3315494","article-title":"Bayesian density estimation using Bernstein polynomials","volume":"27","author":"Petrone","year":"1999","journal-title":"Can. J. Statist."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"2652","DOI":"10.1175\/1520-0469(1985)042<2652:ENALN>2.0.CO;2","article-title":"El Ni\u00f1o and La Ni\u00f1a","volume":"42","author":"Philander","year":"1985","journal-title":"J. Atmos. Sci."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/0047-259X(72)90038-3","article-title":"Multivariate stable distributions","volume":"2","author":"Press","year":"1972","journal-title":"J. Multiv. Anal."},{"key":"2023022501100473700_","volume-title":"R: a Language and Environment for Statistical Computing","author":"R Core Team","year":"2019"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.csda.2016.11.011","article-title":"Flexible integro-difference equation modeling for spatio-temporal data","volume":"109","author":"Richardson","year":"2017","journal-title":"Computnl Statist. Data Anal."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s11222-016-9719-1","article-title":"Bayesian non-parametric modeling for integro-difference equations","volume":"28","author":"Richardson","year":"2018","journal-title":"Statist. Comput."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","DOI":"10.1002\/env.2456","article-title":"Sparsity in nonlinear dynamic spatiotemporal models using implied advection","volume":"28","author":"Richardson","year":"2017","journal-title":"Environmetrics"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"1606","DOI":"10.1175\/1520-0493(1987)115<1606:GARSPP>2.0.CO;2","article-title":"Global and regional scale precipitation patterns associated with the El Ni\u00f1o\/Southern Oscillation","volume":"115","author":"Ropelewski","year":"1987","journal-title":"Mnthly Weath. Rev."},{"key":"2023022501100473700_","first-page":"133","article-title":"Stable non-Gaussian random processes","volume":"13","author":"Samorodnitsky","year":"1997","journal-title":"Econmetr. Theory"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1109\/TSP.2008.2008550","article-title":"Estimation and model selection for an IDE-based spatio-temporal model","volume":"57","author":"Scerri","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"1452","DOI":"10.1214\/12-AOAS564","article-title":"A dynamic nonstationary spatio-temporal model for short term prediction of precipitation","volume":"6","author":"Sigrist","year":"2012","journal-title":"Ann. Appl. Statist."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1191\/1471082x02st029oa","article-title":"Stationary space-time Gaussian fields and their time autoregressive representation","volume":"2","author":"Storvik","year":"2002","journal-title":"Statist. Modllng"},{"key":"2023022501100473700_","volume-title":"Bayesian Forecasting and Dynamic Models","author":"West","year":"2006"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1191\/1471082x02st036oa","article-title":"A kernel-based spectral model for non-Gaussian spatio-temporal processes","volume":"2","author":"Wikle","year":"2002","journal-title":"Statist. Modllng"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1093\/biomet\/86.4.815","article-title":"A dimension-reduced approach to space-time Kalman filtering","volume":"86","author":"Wikle","year":"1999","journal-title":"Biometrika"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1111\/j.1467-9892.2011.00729.x","article-title":"Polynomial nonlinear spatio-temporal integro-difference equation models","volume":"32","author":"Wikle","year":"2011","journal-title":"J. Time Ser. Anal."},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11749-010-0209-z","article-title":"A general science-based framework for dynamical spatiotemporal models","volume":"19","author":"Wikle","year":"2010","journal-title":"TEST"},{"key":"2023022501100473700_","doi-asserted-by":"crossref","first-page":"1133","DOI":"10.1198\/016214505000000682","article-title":"A kernel-based spatio-temporal dynamical model for nowcasting weather radar reflectivities","volume":"100","author":"Xu","year":"2005","journal-title":"J. Am. Statist. Ass."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12393","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12393","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/am-pdf\/10.1111\/rssb.12393","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/82\/5\/1371\/49321108\/jrsssb_82_5_1371.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/82\/5\/1371\/49321108\/jrsssb_82_5_1371.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,12]],"date-time":"2023-10-12T00:20:52Z","timestamp":1697070052000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/82\/5\/1371\/7056058"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,1]]},"references-count":38,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2020,9,1]]},"published-print":{"date-parts":[[2020,12,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12393","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2020,12]]},"published":{"date-parts":[[2020,9,1]]}}}