Document Zbl 1541.62096

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Neerl.</a> <a href="/?q=in%3A506153" title="Articles in this Issue">74, No. 2, 125-144 (2020)</a>. </div> <div class="abstract">Summary: Dynamic processes are crucial in many empirical fields, such as in oceanography, climate science, and engineering. Processes that evolve through time are often well described by systems of ordinary differential equations (ODEs). Fitting ODEs to data has long been a bottleneck because the analytical solution of general systems of ODEs is often not explicitly available. We focus on a class of inference techniques that uses smoothing to avoid direct integration. In particular, we develop a Bayesian smooth-and-match strategy that approximates the ODE solution while performing Bayesian inference on the model parameters. We incorporate in the strategy two main sources of uncertainty: the noise level of the measured observations and the model approximation error. We assess the performance of the proposed approach in an extensive simulation study and on a canonical data set of neuronal electrical activity.<br class="zbmathjax-paragraph">{© 2019 The Authors. <span class="zbmathjax-textit">Statistica Neerlandica</span> © 2019 VVS}</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7778421">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G08" title="MSC2020">62G08</a> </td> <td class="space"> Nonparametric regression and quantile regression </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62F15" title="MSC2020">62F15</a> </td> <td class="space"> Bayesian inference </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62J07" title="MSC2020">62J07</a> </td> <td class="space"> Ridge regression; shrinkage estimators (Lasso) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AMCMC">MCMC</a>; <a href="/?q=ut%3Apenalized+splines">penalized splines</a>; <a href="/?q=ut%3Aridge+regression">ridge regression</a>; <a href="/?q=ut%3Asmoothing">smoothing</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11132">gamair</a>; <a href="/software/14377">CollocInfer</a>; <a href="/software/6099">gss</a>; <a href="/software/25417">deGradInfer</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1541.62096" data-ciurl="/ci/07778421" data-biburl="/bibtex/07778421.bib" data-amsurl="/amsrefs/07778421.bib" data-xmlurl="/xml/07778421.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07778421.pdf" title="Zbl 1541.62096 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1111/stan.12192" aria-label="DOI for “Bayesian smooth-and-match inference for ordinary differential equations models linear in the parameters”" title="10.1111/stan.12192">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Barber, D., On solving ordinary differential equations using Gaussian processes, 2014</td> </tr><tr> <td>[2]</td> <td class="space">Barber, D.; Wang, Y., Gaussian processes for Bayesian estimation in ordinary differential equations, 1485-1493, 2014</td> </tr><tr> <td>[3]</td> <td class="space">Bhaumik, P.; Ghosal, S., Bayesian two‐step estimation in differential equation models, Electronic Journal of Statistics, 9, 2, 3124-3154, 2015 · <a href="/1330.62273" class="nowrap">Zbl 1330.62273</a></td> </tr><tr> <td>[4]</td> <td class="space">Bhaumik, P.; Ghosal, S., Efficient Bayesian estimation and uncertainty quantification in ordinary differential equation models, Bernoulli, 23, 4B, 3537-3570, 2017 · <a href="/1459.62048" class="nowrap">Zbl 1459.62048</a></td> </tr><tr> <td>[5]</td> <td class="space">Bonhoeffer, S.; May, R. 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