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Documenter.jl committed Mar 13, 2024
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-06T12:06:27","documenter_version":"1.3.0"}}
{"documenter":{"julia_version":"1.10.2","generation_timestamp":"2024-03-13T15:31:38","documenter_version":"1.3.0"}}
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10 changes: 5 additions & 5 deletions dev/examples/ks_paleojump/index.html
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fig, ax = lines(t, xtrend; axis = (ylabel = "NGRIP (processed)", xlabel = "time"))
lines!(ax, t, xloess; linewidth = 2)
fig</code></pre><img src="ed8cabe2.png" alt="Example block output"/><p>For the window, since we are using a sliding window here, we will be using a window of length 500 (which is approximately 1/2 to 1/4 the span between typical transitions found by (<a href="../../refs/#rasmussen-stratigraphic-2014">Rasmussen <em>et al.</em>, 2014</a>)).</p><pre><code class="language-julia hljs">window = 500</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">500</code></pre><h2 id="Defining-the-change-metric-function"><a class="docs-heading-anchor" href="#Defining-the-change-metric-function">Defining the change metric function</a><a id="Defining-the-change-metric-function-1"></a><a class="docs-heading-anchor-permalink" href="#Defining-the-change-metric-function" title="Permalink"></a></h2><p>HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested in the value of the test iself (the so-called KS-statistic), rather than a p-value. To this end, we define the following function to compute the statistic, which also normalizes it as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>).</p><pre><code class="language-julia hljs">using HypothesisTests
fig</code></pre><img src="5801bd1a.png" alt="Example block output"/><p>For the window, since we are using a sliding window here, we will be using a window of length 500 (which is approximately 1/2 to 1/4 the span between typical transitions found by (<a href="../../refs/#rasmussen-stratigraphic-2014">Rasmussen <em>et al.</em>, 2014</a>)).</p><pre><code class="language-julia hljs">window = 500</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">500</code></pre><h2 id="Defining-the-change-metric-function"><a class="docs-heading-anchor" href="#Defining-the-change-metric-function">Defining the change metric function</a><a id="Defining-the-change-metric-function-1"></a><a class="docs-heading-anchor-permalink" href="#Defining-the-change-metric-function" title="Permalink"></a></h2><p>HypothesisTest.jl implements the Kolmogorov-Smirnov test, however here we are interested in the value of the test iself (the so-called KS-statistic), rather than a p-value. To this end, we define the following function to compute the statistic, which also normalizes it as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>).</p><pre><code class="language-julia hljs">using HypothesisTests

function normalized_KS_statistic(timeseries)
N = length(timeseries)
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density!(ax, q; label = &quot;D_KS = $(D_KS)&quot;)
end
axislegend(ax)
fig</code></pre><img src="fc04c012.png" alt="Example block output"/><h2 id="Perform-the-sliding-window-analysis"><a class="docs-heading-anchor" href="#Perform-the-sliding-window-analysis">Perform the sliding window analysis</a><a id="Perform-the-sliding-window-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Perform-the-sliding-window-analysis" title="Permalink"></a></h2><p>This is just a straightforward call to <a href="../../api/#TransitionsInTimeseries.estimate_changes"><code>estimate_changes</code></a>. In fact, it is even simpler than the tutorial. Here we skip completely the &quot;indicator&quot; estimation step, and we evaluate the change metric directly on input data. We do this by simply passing <code>nothing</code> as the indicators.</p><pre><code class="language-julia hljs">using TransitionsInTimeseries
fig</code></pre><img src="f2819d31.png" alt="Example block output"/><h2 id="Perform-the-sliding-window-analysis"><a class="docs-heading-anchor" href="#Perform-the-sliding-window-analysis">Perform the sliding window analysis</a><a id="Perform-the-sliding-window-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Perform-the-sliding-window-analysis" title="Permalink"></a></h2><p>This is just a straightforward call to <a href="../../api/#TransitionsInTimeseries.estimate_changes"><code>estimate_changes</code></a>. In fact, it is even simpler than the tutorial. Here we skip completely the &quot;indicator&quot; estimation step, and we evaluate the change metric directly on input data. We do this by simply passing <code>nothing</code> as the indicators.</p><pre><code class="language-julia hljs">using TransitionsInTimeseries

config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 500)

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fig
end

visualize_results(results)</code></pre><img src="4241f4cd.png" alt="Example block output"/><p>By overplotting the (smoothened) NGRIP timeseries and the normalized KS-statistic, it already becomes pretty clear that the statistic peaks when transitions occur.</p><p>The same thing happens if we alter the window duration</p><pre><code class="language-julia hljs">config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200)
visualize_results(results)</code></pre><img src="a2ae2b48.png" alt="Example block output"/><p>By overplotting the (smoothened) NGRIP timeseries and the normalized KS-statistic, it already becomes pretty clear that the statistic peaks when transitions occur.</p><p>The same thing happens if we alter the window duration</p><pre><code class="language-julia hljs">config = SlidingWindowConfig(nothing, normalized_KS_statistic; width_cha = 200)
results = estimate_changes(config, xtrend, t)
visualize_results(results)</code></pre><img src="2bb7916b.png" alt="Example block output"/><p>So one can easily obtain extra confidence by varying window size as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>).</p><h2 id="Identifying-&quot;confident&quot;-transitions"><a class="docs-heading-anchor" href="#Identifying-&quot;confident&quot;-transitions">Identifying &quot;confident&quot; transitions</a><a id="Identifying-&quot;confident&quot;-transitions-1"></a><a class="docs-heading-anchor-permalink" href="#Identifying-&quot;confident&quot;-transitions" title="Permalink"></a></h2><p>As this identification here is done via a simple threshold, identifying the transitions is a nearly trivial call to <a href="../../api/#TransitionsInTimeseries.significant_transitions"><code>significant_transitions</code></a> with <a href="../../api/#TransitionsInTimeseries.ThresholdSignificance"><code>ThresholdSignificance</code></a></p><pre><code class="language-julia hljs">signif = ThresholdSignificance(0.5) # or any other threshold
visualize_results(results)</code></pre><img src="b6611089.png" alt="Example block output"/><p>So one can easily obtain extra confidence by varying window size as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>).</p><h2 id="Identifying-&quot;confident&quot;-transitions"><a class="docs-heading-anchor" href="#Identifying-&quot;confident&quot;-transitions">Identifying &quot;confident&quot; transitions</a><a id="Identifying-&quot;confident&quot;-transitions-1"></a><a class="docs-heading-anchor-permalink" href="#Identifying-&quot;confident&quot;-transitions" title="Permalink"></a></h2><p>As this identification here is done via a simple threshold, identifying the transitions is a nearly trivial call to <a href="../../api/#TransitionsInTimeseries.significant_transitions"><code>significant_transitions</code></a> with <a href="../../api/#TransitionsInTimeseries.ThresholdSignificance"><code>ThresholdSignificance</code></a></p><pre><code class="language-julia hljs">signif = ThresholdSignificance(0.5) # or any other threshold
flags = significant_transitions(results, signif)

fig = visualize_results(results)
axDKS = content(fig[2,1])
vlines!(axDKS, results.t_change[vec(flags)], color = (&quot;red&quot;, 0.25))
fig</code></pre><img src="323b304c.png" alt="Example block output"/><p>We could proceed with a lot of preprocessing as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>) but we skip this here for the sake of simplicity.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../logistic/">« Permutation entropy for dynamic regime changes</a><a class="docs-footer-nextpage" href="../do-events/">Dansgaard-Oescher events and Critical Slowing Down »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 6 March 2024 12:06">Wednesday 6 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
fig</code></pre><img src="49311be6.png" alt="Example block output"/><p>We could proceed with a lot of preprocessing as in (<a href="../../refs/#Bagniewski2021">Bagniewski <em>et al.</em>, 2021</a>) but we skip this here for the sake of simplicity.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../logistic/">« Permutation entropy for dynamic regime changes</a><a class="docs-footer-nextpage" href="../do-events/">Dansgaard-Oescher events and Critical Slowing Down »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.3.0 on <span class="colophon-date" title="Wednesday 13 March 2024 15:31">Wednesday 13 March 2024</span>. Using Julia version 1.10.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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