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<title>Weighted average algorithms — DQPB: software for calculating disequilibrium U-Pb ages</title>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">Weighted average algorithms</a><ul>
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<section id="weighted-average-algorithms">
<h1>Weighted average algorithms<a class="headerlink" href="#weighted-average-algorithms" title="Permalink to this heading"></a></h1>
<p>The following weighted average algorithms may be selected when computing Pb/U ages, modified <span class="math notranslate nohighlight">\(^{207}\mathrm{Pb}\)</span> ages, or calculating a weighted average for arbitrary data.</p>
<section id="classical">
<span id="classical-wav"></span><h2>Classical<a class="headerlink" href="#classical" title="Permalink to this heading"></a></h2>
<p>This routine computes a weighted average using standard classical statistics equations (i.e., those given in <a class="reference internal" href="references.html#powell1988" id="id1"><span>[POWELL1988]</span></a>; <a class="reference internal" href="references.html#lyons1988" id="id2"><span>[LYONS1988]</span></a>; <a class="reference internal" href="references.html#mclean2011" id="id3"><span>[MCLEAN2011]</span></a> etc.). Where uncertainty covariances are negligible, these equations reduce to the standard error weighted mean <a class="reference internal" href="references.html#taylor1997" id="id4"><span>[TAYLOR1997]</span></a>. If the MSWD exceeds a lower one-sided confidence interval threshold value (85% by default, equivalent to a ‘probability of fit’ value of 0.15) then analytical errors are expanded by <span class="math notranslate nohighlight">\(\sqrt{\mathrm{MSWD}}\)</span> in an effort to account for excess scatter, and further multiplied by the 95th percentile of a Student’s t distribution (with n – 1 degrees of freedom) to obtain 95% confidence limits following the approach of Isoplot <a class="reference internal" href="references.html#ludwig2012" id="id5"><span>[LUDWIG2012]</span></a>. Where the probability of fit is below a reasonable lower limit (say, 0.05), use of this approach is questionable and a robust approach should be considered instead.</p>
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<span id="spine-wav"></span><h2>Spine<a class="headerlink" href="#spine" title="Permalink to this heading"></a></h2>
<p>A robust version of the spine linear regression algorithm that is capable of accounting for uncertainty correlations (details provided in Appendix A of the <a class="reference external" href="https://gchron.copernicus.org/preprints/gchron-2022-24/gchron-2022-24.pdf">manuscript</a>).</p>
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