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  <doc>
    <id>6632</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1600</pageFirst>
    <pageLast>1629</pageLast>
    <pageNumber/>
    <edition/>
    <issue>4</issue>
    <volume>6</volume>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-01-04</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Random forward models and log-likelihoods in Bayesian inverse problems</title>
    <abstract language="eng">We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems.  Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods.  We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods.  Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations.</abstract>
    <parentTitle language="eng">SIAM/ASA Journal on Uncertainty Quantification</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66324</identifier>
    <identifier type="arxiv">1712.05717</identifier>
    <identifier type="doi">10.1137/18M1166523</identifier>
    <enrichment key="AcceptedDate">2018</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Han Cheng Lie</author>
    <submitter>T. J. Sullivan</submitter>
    <author>T. J. Sullivan</author>
    <author>Aretha Teckentrup</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-03</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bayesian inverse problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>random likelihood</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>surrogate model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>posterior consistency</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>probabilistic numerics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>uncertainty quantification</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>randomised misfit</value>
    </subject>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="msc" number="68-XX">COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="SFB1114 A06">SFB1114 A06</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6632/random-bip.pdf</file>
  </doc>
</export-example>
