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  <doc>
    <id>7928</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>196</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>8</issue>
    <volume>13</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification</title>
    <abstract language="eng">Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design.</abstract>
    <parentTitle language="eng">Algorithms</parentTitle>
    <identifier type="doi">10.3390/a13080196</identifier>
    <identifier type="arxiv">2007.05236</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-08-10</enrichment>
    <author>Luc Bonnet</author>
    <submitter>Tim Sullivan</submitter>
    <author>Jean-Luc Akian</author>
    <author>Éric Savin</author>
    <author>T. J. Sullivan</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
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