finished formatting math-prob; partially formatted loss-fun

_book/qmd/association-general.html

@@ -2272,6 +2272,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-assoc-gen-cont">Continuous</
 <li><p><u>Misc</u></p>
 <ul>
 <li>For the Pearson coefficient. variables must be Normally distributed. Also, zero does not determine independence between two variables, as only a linear dependence between the variables can be determined and the variables may have a nonlinear relationship.</li>
+<li>Also see <a href="../qmd/association-general.html#sec-assoc-gen-disc" style="color: green">Discrete</a> &gt;&gt; Tau Star</li>
 </ul></li>
 <li><p><u>Spearman’s Rank</u></p>
 <p><span class="math display">\[
@@ -2506,6 +2507,17 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-assoc-gen-disc">Discrete</h2
 <li><span style="color: #990000">{</span><a href="https://andrisignorell.github.io/DescTools/reference/GoodmanKruskalGamma.html" style="color: #990000">DescTools::GoodmanKruskalGamma</a><span style="color: #990000">}</span></li>
 </ul></li>
 </ul></li>
+<li><u>Tau Star</u> (<span class="math inline">\(\tau^*\)</span>)
+<ul>
+<li>AKA Bergsma-Dassios sign covariance</li>
+<li>Rank correlation measure that’s designed for ordinal variables, but evidently also applicable to continuous variables</li>
+<li>Fixes some deficiencies with Kendall’s Tau and Spearman’s Rank</li>
+<li>Packages
+<ul>
+<li><span style="color: #990000">{</span><a href="https://cran.r-project.org/web/packages/TauStar/index.html" style="color: #990000">TauStar</a><span style="color: #990000">}</span> - Efficient Computation and Testing of the Bergsma-Dassios Sign Covariance</li>
+</ul></li>
+<li>Range: [0, 1] where the 0 indicates independence</li>
+</ul></li>
 </ul>
 </section>
 <section id="sec-assoc-gen-mix" class="level2 unnumbered">
@@ -3376,7 +3388,7 @@ <h3 class="unnumbered anchored" data-anchor-id="sec-assoc-gen-nonlin-depm">DepM<
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_book/qmd/causal-inference.html

@@ -3098,7 +3098,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-causinf-medanal">Mediation A
 <ul>
 <li><span style="color: #990000">{</span><a href="https://github.com/nt-williams/lcmmtp" style="color: #990000">lcmmtp</a><span style="color: #990000">}</span> - Efficient and flexible causal mediation with longitudinal mediators, treatments, and confounders using modified treatment policies
 <ul>
-<li>Paper: <a href="https://arxiv.org/html/2403.09928v1">Identification and estimation of mediational effects of longitudinal modified treatment policies</a></li>
+<li>Paper: <a href="https://arxiv.org/html/2403.09928v1">Identification and estimation of mediational effects of longitudinal modified treatment policies</a> w/analysis code</li>
 </ul></li>
 </ul></li>
 <li>Papers
@@ -4172,7 +4172,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-causinf-othart">Other Articl
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_book/qmd/clustering-general.html

@@ -2431,6 +2431,11 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-clust-gen-kmeans">K-Means</h
 <li>Also applicable to densely observed data</li>
 <li>Employs the basis function expansion (i.e.&nbsp;splines) to model the cluster centers</li>
 </ul></li>
+<li><span style="color: #990000">{</span><a href="https://cran.r-project.org/web/packages/sparcl/index.html" style="color: #990000">sparcl</a><span style="color: #990000">}</span> - Sparse Hierarchical Clustering and Sparse K-Means Clustering</li>
+<li><span style="color: #990000">{</span><a href="https://cran.r-project.org/web/packages/clusterHD/index.html" style="color: #990000">clusterHD</a><span style="color: #990000">}</span> (Paper) - Regularized k-Means through hard thresholding
+<ul>
+<li>Uses a <span class="math inline">\(\mathcal{L}_0\)</span> penalty to induce sparsity in the variables</li>
+</ul></li>
 </ul></li>
 <li>For choosing the number of clusters, elbow method (i.e.&nbsp;WSS) is usually awful if there are more than few clusters. Recommended: Calinski-Harabasz Index and BIC then Silhouette Coefficient or Davies-Bouldin Index (See <a href="../qmd/diagnostics-clustering.html#sec-diag-clust-sphcent" style="color: green">Diagnostics, Clustering &gt;&gt; Spherical/Centroid Based</a> (<a href="https://towardsdatascience.com/are-you-still-using-the-elbow-method-5d271b3063bd">article</a>)</li>
 <li>Base R <code>kmeans</code> uses the Hartigan-Wong algorithm
@@ -3079,7 +3084,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-clust-gen-dbscan">DBSCAN</h2
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_book/qmd/confidence-and-prediction-intervals.html

@@ -2122,6 +2122,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-cipi-misc">Misc</h2>
 <ul>
 <li>The way to estimate SATE of regressing the outcome on treatment group and covariates yields an unbiased estimate of the SATE; however, the standard error is a little too big, which means the confidence interval is a little too wide. The reason for this is that the correct standard error depends on the correlation between potential outcomes, but we cannot estimate a correlation between two variables if each trial participant only gives us one of the two values we wish to correlate.</li>
 </ul></li>
+<li><span style="color: #990000">{</span><a href="https://markjrieke.github.io/workboots/" style="color: #990000">workboots</a><span style="color: #990000">}</span> - Bootstrap prediction intervals for arbitrary model types from a tidymodel workflow.</li>
 </ul></li>
 <li>SE used for CIs of the difference in proportion<br>
 <span class="math display">\[
@@ -3278,7 +3279,7 @@ <h3 class="unnumbered anchored" data-anchor-id="sec-cipi-conf-viz">Visualization
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_book/qmd/db-postgres.html

@@ -2988,7 +2988,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-db-pstgr-perftun">Performanc
 <li>Filters should be placed as close to the top of the query as possible.</li>
 <li>Reduce disk IO operations when needed</li>
 </ul></li>
-<li>Sometimes even adding the correct index and (correctly) <em>not</em> using a function on that index will still result in a sequential scan.
+<li>Sometimes even adding the correct index, (correctly) <em>not</em> using a function on that index, etc., the query will still be executed using a sequential scan.
 <ul>
 <li>One possible reason is that the un-indexed query had been used for so long that the internal statistics indicated that a sequential scan should be used even with the new index present.</li>
 <li>Solutions
@@ -3728,7 +3728,7 @@ <h2 class="unnumbered anchored" data-anchor-id="sec-db-pstgr-backups">Back-Ups</
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