Document Zbl 0799.62003

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Probab. Lett.</a> <a href="/?q=in%3A21472" title="Articles in this Issue">20, No. 4, 287-294 (1994)</a>. </div> <div class="abstract">Summary: We consider the problem of measuring Bayesian robustness of classes of contaminated priors. Two classes of priors in the neighborhood of the elicited prior are considered: one is the usual $\varepsilon$- contaminated class and the other one is a geometric mixing class. A global measure, using $\varphi$-divergence of the posterior distribution and its curvature, is introduced. Calculation of ranges of the curvatures are demonstrated through examples. It is shown that the curvature formulas give unified answers irrespective of the choice of the $\varphi$-functions. It is also observed that the variation of the posterior divergence measures and their curvature are especially useful for multidimensional problems.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A633492">Cited in <strong>34</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62A01" title="MSC2020">62A01</a> </td> <td class="space"> Foundations and philosophical topics in statistics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62B10" title="MSC2020">62B10</a> </td> <td class="space"> Statistical aspects of information-theoretic topics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aepsilon-contamination+classes+of+priors">epsilon-contamination classes of priors</a>; <a href="/?q=ut%3Ageometric+contamination">geometric contamination</a>; <a href="/?q=ut%3Aphi-+divergence+measures">phi- divergence measures</a>; <a href="/?q=ut%3ABayesian+robustness">Bayesian robustness</a>; <a href="/?q=ut%3Aelicited+prior">elicited prior</a>; <a href="/?q=ut%3Ageometric+mixing+class">geometric mixing class</a>; <a href="/?q=ut%3Acurvature">curvature</a>; <a href="/?q=ut%3Aexamples">examples</a>; <a href="/?q=ut%3Aposterior+divergence+measures">posterior divergence measures</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 0799.62003" data-ciurl="/ci/00633492" data-biburl="/bibtex/00633492.bib" data-amsurl="/amsrefs/00633492.bib" data-xmlurl="/xml/00633492.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/00633492.pdf" title="Zbl 0799.62003 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/10.1016/0167-7152(94)90016-7" aria-label="DOI for “Robust Bayesian analysis using divergence measures”" title="10.1016/0167-7152(94)90016-7">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">Atkinson, A. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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