{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T07:11:43Z","timestamp":1783494703590,"version":"3.55.0"},"reference-count":63,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,2,13]],"date-time":"2024-02-13T00:00:00Z","timestamp":1707782400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000121","name":"DMS","doi-asserted-by":"publisher","award":["2113468"],"award-info":[{"award-number":["2113468"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["IFML 2019844"],"award-info":[{"award-number":["IFML 2019844"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100016117","name":"Hanns Seidel Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100016117","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,7,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We propose a new method to estimate a root-directed spanning tree from extreme data. Prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and on new data. We prove that the new estimator is consistent under a max-linear Bayesian network model with noise. 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