{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:50:40Z","timestamp":1791323440303,"version":"4.3.1"},"reference-count":41,"publisher":"Institute of Mathematical Statistics","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ann. Statist."],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:p>We consider diffusion of independent molecules in an insulated Euclidean domain with unknown diffusivity parameter. At a random time and position, the molecules may bind and stop diffusing in dependence of a given \u201cbinding potential.\u201d The binding process can be modeled by an additive random functional corresponding to the canonical construction of a \u201ckilled\u201d diffusion Markov process. We study the problem of conducting inference on the infinite-dimensional diffusion parameter from a histogram plot of the \u201ckilling\u201d positions of the process. We show first that these positions follow a Poisson point process whose intensity measure is determined by the solution of a Schr\u00f6dinger-type equation. The inference problem can then be recast as a nonlinear inverse problem for this partial differential equation, which we show to be consistently solvable in a Bayesian way under natural conditions on the initial state of the system, provided the binding potential is not too \u201caggressive.\u201d In the proofs, we obtain novel posterior contraction rate results for high-dimensional Poisson count data that are of independent interest. A numerical illustration of the estimator by MCMC methods is also provided.<\/jats:p>","DOI":"10.1214\/26-aos2633","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T12:47:42Z","timestamp":1790945262000},"page":"2234-2259","source":"Crossref","is-referenced-by-count":0,"title":["Inferring diffusivity from killed diffusion"],"prefix":"10.1214","volume":"54","author":[{"given":"Richard","family":"Nickl","sequence":"first","affiliation":[{"name":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fanny","family":"Seizilles","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"7","doi-asserted-by":"publisher","unstructured":"<small>Cotter, S. L.<\/small>, <small>Roberts, G. 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Supplement to \u201cInferring diffusivity from killed diffusion.\u201d <a href=\"https:\/\/doi.org\/10.1214\/26-AOS2633SUPP\">https:\/\/doi.org\/10.1214\/26-AOS2633SUPP<\/a>","DOI":"10.1214\/26-AOS2633SUPP"}],"container-title":["The Annals of Statistics"],"original-title":[],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T21:05:24Z","timestamp":1791320724000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/annals-of-statistics\/volume-54\/issue-5\/Inferring-diffusivity-from-killed-diffusion\/10.1214\/26-AOS2633.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":41,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1214\/26-aos2633","relation":{},"ISSN":["0090-5364","2168-8966"],"issn-type":[{"value":"0090-5364","type":"print"},{"value":"2168-8966","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,1]]}}}