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‎404.html‎

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<script id="__config" type="application/json">{"base": "/", "features": ["navigation.sections", "toc.follow", "header.autohide"], "search": "/assets/javascripts/workers/search.07f07601.min.js", "translations": {"clipboard.copied": "Copied to clipboard", "clipboard.copy": "Copy to clipboard", "search.result.more.one": "1 more on this page", "search.result.more.other": "# more on this page", "search.result.none": "No matching documents", "search.result.one": "1 matching document", "search.result.other": "# matching documents", "search.result.placeholder": "Type to start searching", "search.result.term.missing": "Missing", "select.version": "Select version"}}</script>
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<script id="__config" type="application/json">{"base": "/", "features": ["navigation.sections", "toc.follow", "header.autohide"], "search": "/assets/javascripts/workers/search.6ce7567c.min.js", "translations": {"clipboard.copied": "Copied to clipboard", "clipboard.copy": "Copy to clipboard", "search.result.more.one": "1 more on this page", "search.result.more.other": "# more on this page", "search.result.none": "No matching documents", "search.result.one": "1 matching document", "search.result.other": "# matching documents", "search.result.placeholder": "Type to start searching", "search.result.term.missing": "Missing", "select.version": "Select version"}}</script>
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‎api/brier/index.html‎

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‎api/crps/index.html‎

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<title>Continuous Ranked Probability Score - Scoringrules</title>
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</span>
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<a href="#scoringrules.crps_mixnorm" class="md-nav__link">
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crps_mixnorm
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<h3 id="scoringrules.crps_mixnorm" class="doc doc-heading">
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<span class="doc doc-object-name doc-function-name">scoringrules.crps_mixnorm</span>
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</h3>
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<div class="language-python doc-signature highlight"><pre><span></span><code><span id="__span-0-1"><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nf">crps_mixnorm</span><span class="p">(</span>
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</span><span id="__span-0-2"><a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a> <span class="n">observation</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
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</span><span id="__span-0-3"><a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">m</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
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</span><span id="__span-0-4"><a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">s</span><span class="p">:</span> <span class="n">ArrayLike</span><span class="p">,</span>
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</span><span id="__span-0-5"><a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="o">/</span><span class="p">,</span>
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</span><span id="__span-0-6"><a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">w</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
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</span><span id="__span-0-7"><a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="n">axis</span><span class="p">:</span> <span class="n">ArrayLike</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span>
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</span><span id="__span-0-8"><a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="o">*</span><span class="p">,</span>
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</span><span id="__span-0-9"><a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">backend</span><span class="p">:</span> <span class="n">Backend</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
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</span><span id="__span-0-10"><a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">ArrayLike</span>
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</span></code></pre></div>
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<div class="doc doc-contents first">
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<p>Compute the closed form of the CRPS for a mixture of normal distributions.</p>
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<p>It is based on the following formulation from
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<a href="https://doi.org/10.1256/qj.05.235">Grimit et al. (2006)</a>:</p>
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<div class="arithmatex">\[ \mathrm{CRPS}(F, y) = \sum_{i=1}^{M} w_{i} A(y - \mu_{i}, \sigma_{i}^{2}) - \frac{1}{2} \sum_{i=1}^{M} \sum_{j=1}^{M} w_{i} w_{j} A(\mu_{i} - \mu_{j}, \sigma_{i}^{2} + \sigma_{j}^{2}), \]</div>
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<p>where <span class="arithmatex">\(F(x) = \sum_{i=1}^{M} w_{i} \Phi \left( \frac{x - \mu_{i}}{\sigma_{i}} \right)\)</span>,
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and <span class="arithmatex">\(A(\mu, \sigma^{2}) = \mu (2 \Phi(\frac{\mu}{\sigma}) - 1) + 2\sigma \phi(\frac{\mu}{\sigma}).\)</span></p>
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<p><span class="doc-section-title">Parameters:</span></p>
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<table>
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<thead>
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<tr>
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<th>Name</th>
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<th>Type</th>
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<th>Description</th>
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<th>Default</th>
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</tr>
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</thead>
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<tbody>
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<tr class="doc-section-item">
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<td><code>observation</code></td>
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<td>
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<code><span title="scoringrules.core.typing.ArrayLike">ArrayLike</span></code>
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</td>
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<td>
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<div class="doc-md-description">
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<p>The observed values.</p>
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</div>
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</td>
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<td>
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<em>required</em>
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</td>
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</tr>
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<td><code>m</code></td>
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<td>
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<code><span title="scoringrules.core.typing.ArrayLike">ArrayLike</span></code>
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</td>
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<td>
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<div class="doc-md-description">
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<p>Means of the component normal distributions.</p>
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</div>
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</td>
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<td>
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<em>required</em>
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</td>
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</tr>
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<td><code>s</code></td>
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<td>
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<code><span title="scoringrules.core.typing.ArrayLike">ArrayLike</span></code>
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</td>
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<td>
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<div class="doc-md-description">
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<p>Standard deviations of the component normal distributions.</p>
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</div>
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</td>
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<td>
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<em>required</em>
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</td>
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<td><code>w</code></td>
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<td>
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<code><span title="scoringrules.core.typing.ArrayLike">ArrayLike</span></code>
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<div class="doc-md-description">
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<p>Non-negative weights assigned to each component.</p>
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</td>
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<td>
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<code>None</code>
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<tr class="doc-section-item">
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<td><code>axis</code></td>
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<td>
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<code><span title="scoringrules.core.typing.ArrayLike">ArrayLike</span></code>
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</td>
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<td>
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<p>The axis corresponding to the mixture components. Default is the last axis.</p>
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</div>
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</td>
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<td>
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<code>-1</code>
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<td><code>backend</code></td>
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<code><span title="scoringrules.core.typing.Backend">Backend</span></code>
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<p>The name of the backend used for computations. Defaults to 'numba' if available, else 'numpy'.</p>
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</td>
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</tbody>
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</table>
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<p><span class="doc-section-title">Returns:</span></p>
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<table>
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<thead>
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<th>Name</th> <th>Type</th>
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<th>Description</th>
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<td><code>score</code></td> <td>
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<code><span title="scoringrules.core.typing.ArrayLike">ArrayLike</span></code>
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</td>
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<p>The CRPS between MixNormal(m, s) and obs.</p>
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</td>
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</table>
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<p><span class="doc-section-title">Examples:</span></p>
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<div class="language-pycon highlight"><pre><span></span><code><span id="__span-0-1"><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">scoringrules</span> <span class="k">as</span> <span class="nn">sr</span>
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</span><span id="__span-0-2"><a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="gp">&gt;&gt;&gt; </span><span class="n">sr</span><span class="o">.</span><span class="n">crps_mixnormal</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.3</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="mf">2.1</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.7</span><span class="p">])</span>
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</span></code></pre></div>
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‎api/energy/index.html‎

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<p>where <span class="arithmatex">\(||\cdot||\)</span> is the euclidean norm over the input dimensions (the variables).</p>
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<p>Computation is performed using the ensemble representation of the vrES in
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