<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>6123</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-11-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Empirical Bayes Methods, Reference Priors, Cross Entropy and the EM Algorithm</title>
    <abstract language="eng">When estimating a probability density within the empirical Bayes framework, the non-parametric maximum likelihood estimate (NPMLE) usually tends to overfit the data. This issue is usually taken care of by regularization - a penalization term is subtracted from the marginal log-likelihood before the maximization step, so that the estimate favors smooth solutions, resulting in the so-called maximum penalized likelihood estimation (MPLE).&#13;
The majority of penalizations currently in use are rather arbitrary brute-force solutions, which lack invariance under transformation of the parameters(reparametrization) and measurements.&#13;
This contradicts the principle that, if the underlying model&#13;
has several equivalent formulations, the methods of inductive inference should lead to consistent results. Motivated by this principle and using an information-theoretic point of view, we suggest an entropy-based penalization term that guarantees this kind of invariance. The resulting density estimate can be seen as a generalization of reference priors. Using the reference prior as a hyperprior, on the other hand, is argued to be a poor choice for regularization. We also present an insightful connection between the NPMLE, the cross entropy&#13;
and the principle of minimum discrimination information suggesting another method of inference that contains the doubly-smoothed maximum likelihood estimation as a special case.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61230</identifier>
    <author>Ilja Klebanov</author>
    <submitter>Ilja Klebanov</submitter>
    <author>Alexander Sikorski</author>
    <author>Christof Schütte</author>
    <author>Susanna Röblitz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-56</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>parameter estimation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bayesian inference</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bayesian hierarchical modeling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperparameter</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperprior</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>EM algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NPMLE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MPLE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>DS-MLE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>principle of maximum entropy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross entropy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>minimum discrimination information</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reference prior</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Jeffreys prior</value>
    </subject>
    <collection role="ccs" number="F.">Theory of Computation</collection>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMath-CH6">ECMath-CH6</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6123/EmpiricalBayesReferencePriorsCrossEntropyEMAlgorithm.pdf</file>
  </doc>
  <doc>
    <id>6130</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-12-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Empirical Bayes Methods for Prior Estimation in Systems Medicine</title>
    <abstract language="eng">One of the main goals of mathematical modelling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Therefore, before applying Bayes’ rule separately to the data of each patient (which is typically performed using a non-informative prior), it is meaningful to use empirical Bayes methods in order to construct an informative prior from all available data. We compare the performance of four priors - a non-informative prior and priors chosen by nonparametric maximum likelihood estimation (NPMLE), by maximum penalized lilelihood estimation (MPLE) and by doubly-smoothed maximum likelihood estimation (DS-MLE) - by applying them to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-61307</identifier>
    <identifier type="arxiv">1612.01403</identifier>
    <author>Ilja Klebanov</author>
    <submitter>Ilja Klebanov</submitter>
    <author>Alexander Sikorski</author>
    <author>Christof Schütte</author>
    <author>Susanna Röblitz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-57</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Parameter estimation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bayesian inference</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bayesian hierarchical modelling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NPMLE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>MPLE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>DS-MLE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>EM algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Jeffreys prior</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reference prior</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperparameter</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyperprior</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>principle of maximum entropy</value>
    </subject>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMath-CH6">ECMath-CH6</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6130/EmpiricalBayesSystemsMedicine.pdf</file>
  </doc>
  <doc>
    <id>6092</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-07-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Follicular maturation in cows: mathematical models and data</title>
    <parentTitle language="eng">10. European Conference on Mathematical and Theoretical Biology</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Alexander Lange</author>
    <submitter>Alexander Lange</submitter>
    <author>Julia Plöntzke</author>
    <author>Stefan Schäfer</author>
    <author>Susanna Röblitz</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="BovSys">BovSys</collection>
  </doc>
  <doc>
    <id>6093</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>poster</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modelling of glucose-insulin metabolism and its effect on the estrous cycle in bovine</title>
    <parentTitle language="eng">Annual Meeting of the Population Approach Group in Europe</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Mohamed Omari</author>
    <submitter> Lange</submitter>
    <author>Julia Plöntzke</author>
    <author>Mascha Berg</author>
    <author>Susanna Röblitz</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="BovSys">BovSys</collection>
    <collection role="persons" number="omari">Omari, Mohamed</collection>
  </doc>
  <doc>
    <id>5979</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mathematical Modelling of Follicular Maturation in Cows and Women</title>
    <parentTitle language="deu">49. Jahrestagung der Physiologie und Pathologie der Fortpflanzung und gleichzeitig 41. Veterinär-Humanmedizinische Gemeinschaftstagung 2016, Leipzig.</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
    <author>Stefan Schäfer</author>
    <submitter>Bodo Erdmann</submitter>
    <author>Julia Plöntzke</author>
    <author>Susanna Röblitz</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="BovSys">BovSys</collection>
    <collection role="projects" number="PAEON">PAEON</collection>
  </doc>
  <doc>
    <id>5584</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An integrative approach for model driven computation of treatments in reproductive medicine</title>
    <parentTitle language="eng">BIOMAT - Proceedings of the 15th International Symposium on Mathematical and Computational Biology, Rorkee, India</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-57103</enrichment>
    <author>Rainald Ehrig</author>
    <submitter>Mascha Berg</submitter>
    <author>Thomas Dierkes</author>
    <author>Stefan Schäfer</author>
    <author>Susanna Röblitz</author>
    <author>Enrico Tronci</author>
    <author>Toni Mancini</author>
    <author>Ivano Salvo</author>
    <author>Vadim Alimguzhin</author>
    <author>Federico Mari</author>
    <author>Igor Melatti</author>
    <author>Annalisa Massini</author>
    <author>Tillmann H. C. Krüger</author>
    <author>Marcel Egli</author>
    <author>Fabian Ille</author>
    <author>Brigitte Leeners</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="PAEON">PAEON</collection>
  </doc>
  <doc>
    <id>5747</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-02-16</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Prior estimation and Bayesian inference from large cohort data sets</title>
    <abstract language="eng">One of the main goals of mathematical modelling in systems biology related to medical applications is to obtain patient-specific parameterisations and model predictions.&#13;
In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Using these population data, we propose an iterative algorithm for contructing an informative prior distribution, which then serves as the basis for computing patient-specific posteriors and obtaining individual predictions. We demonsrate the performance of our method by applying it to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modelling.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57475</identifier>
    <author>Ilja Klebanov</author>
    <submitter>Ilja Klebanov</submitter>
    <author>Alexander Sikorski</author>
    <author>Christof Schütte</author>
    <author>Susanna Röblitz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-09</number>
    </series>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="ECMath-CH6">ECMath-CH6</collection>
    <collection role="persons" number="sikorski">Sikorski, Alexander</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5747/ZR-16-09_revised_version.pdf</file>
  </doc>
  <doc>
    <id>5710</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-01-20</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Integrative Approach for Model Driven Computation of Treatments in Reproductive Medicine</title>
    <abstract language="eng">We present an overview of the current status of the European collaborative&#13;
project PAEON. The challenge of PAEON is to provide specialists in reproduc-&#13;
tive medicine with a computerised model of the menstrual cycle under normal&#13;
and various pathological conditions, which will allow them to get further in-&#13;
sight in fertility dynamics. This model also enables the simulation of treatment&#13;
protocols, which were used within in vitro fertilization. By the definition of&#13;
virtual patients through biologically admissible parametrizations our approach&#13;
allows not only the evaluation of a given treatment strategy in silico, but also&#13;
the design and optimization of such protocols. Once a protocol is formalized&#13;
in the virtual hospital, the success can be controlled by a treatment execution&#13;
monitor, which works then as a clinical decision support system. All these tools&#13;
will be combined in a virtual hospital environment, enabling the access to the&#13;
PAEON services through the web.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57103</identifier>
    <enrichment key="SourceTitle">Appeared in: 15th International Symposium on Mathematical and Computational Biology, Rorkee, India</enrichment>
    <author>Rainald Ehrig</author>
    <submitter>Mascha Berg</submitter>
    <author>Thomas Dierkes</author>
    <author>Stefan Schäfer</author>
    <author>Susanna Röblitz</author>
    <author>Enrico Tronci</author>
    <author>Toni Mancini</author>
    <author>Ivano Salvo</author>
    <author>Vadim Alimguzhin</author>
    <author>Federico Mari</author>
    <author>Igor Melatti</author>
    <author>Annalisa Massini</author>
    <author>Tillmann H. C. Krüger</author>
    <author>Marcel Egli</author>
    <author>Fabian Ille</author>
    <author>Brigitte Leeners</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-04</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="PAEON">PAEON</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5710/Ehrig_et_al.pdf</file>
  </doc>
  <doc>
    <id>5703</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-01-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Exploration of different wave patterns in a model of the bovine estrous cycle by Fourier analysis</title>
    <abstract language="eng">Cows typically have different numbers of follicular waves during their hormonal cycle. Understanding the underlying regulations leads to insights into the reasons for declined fertility, a phenomenon that has been observed during the last decades. We present a systematic approach based on Fourier analysis to examine how parameter changes in a model of the bovine estrous cycle lead to different wave patterns. Even without any biological considerations, this allows to detect the responsible model parameters that control the type of periodicity of the solution, thus supporting experimental planning of animal scientists.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-57039</identifier>
    <enrichment key="SourceTitle">appeared in BIOMAT - Proceedings of the 14th International Symposium on Mathematical and Computational Biology, Bedlewo, Poland, 2015</enrichment>
    <author>Claudia Stötzel</author>
    <submitter>Susanna Röblitz</submitter>
    <author>Rainald Ehrig</author>
    <author>H. Marike T. Boer</author>
    <author>Julia Plöntzke</author>
    <author>Susanna Röblitz</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-02</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="BovSys">BovSys</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5703/Fourier_ZIB_report.pdf</file>
  </doc>
</export-example>
