uq lecture

lectures/lectures/dynamics.html

@@ -496,7 +496,7 @@ <h2>Fixed Points for Linear Functions</h2>
 <span id="cb2-2"><a href="#cb2-2"></a>eigvals, eigvecs <span class="op">=</span> eig(A)</span>
 <span id="cb2-3"><a href="#cb2-3"></a><span class="bu">print</span>(<span class="ss">f"lambda_1=</span><span class="sc">{</span>eigvals[<span class="dv">0</span>]<span class="sc">}</span><span class="ss">, ||x* - A x*||=</span><span class="sc">{</span>norm(A <span class="op">@</span> eigvecs[:,<span class="dv">0</span>] <span class="op">-</span> eigvecs[:,<span class="dv">0</span>])<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>lambda_1=(1+0j), ||x* - A x*||=1.5700924586837752e-16</code></pre>
+<pre><code>lambda_1=(1+0j), ||x* - A x*||=1.1102230246251565e-16</code></pre>
 </div>
 </div>
 </section>

lectures/lectures/eigenvalue_applications.html

@@ -512,7 +512,7 @@ <h2>Iterating with <span class="math inline">\(\rho(A) &gt; 1\)</span></h2>
 </div><div class="column">
 <div class="cell-output cell-output-stdout">
 <pre><code>rho(A) = 1.079128784747792
-x_200 = [3406689.32410674 6102361.18640517]</code></pre>
+x_200 = [3406689.32410673 6102361.18640516]</code></pre>
 </div>
 </div>
 </div>
@@ -556,7 +556,7 @@ <h2>Iterating with <span class="math inline">\(\rho(A) = 1\)</span></h2>
 <span id="cb8-6"><a href="#cb8-6"></a><span class="bu">print</span>(<span class="ss">f"x_</span><span class="sc">{</span>t<span class="sc">}</span><span class="ss"> = </span><span class="sc">{</span>np<span class="sc">.</span>linalg<span class="sc">.</span>matrix_power(A, t) <span class="op">@</span> x_0<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>check orthogonal: dot(x_1,x_2) approx 0: 0.0
-rho(A) = 1.0000000000000002
+rho(A) = 1.0
 x_200 = [ 0.27639321 -0.17082039]</code></pre>
 </div>
 </div>
@@ -803,7 +803,7 @@ <h2>Condition Numbers of Matrices</h2>
 <span id="cb21-2"><a href="#cb21-2"></a><span class="bu">print</span>(<span class="ss">f"condition(A) = </span><span class="sc">{</span>cond(A)<span class="sc">}</span><span class="ss">, condition(A^(-1)) = </span><span class="sc">{</span>cond(inv(A))<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>condition(I) = 1.0
-condition(A) = 40000001.939191714, condition(A^(-1)) = 40000002.00307444</code></pre>
+condition(A) = 40000001.962777555, condition(A^(-1)) = 40000002.02779216</code></pre>
 </div>
 </div>
 </section>
@@ -859,8 +859,8 @@ <h2>Solving an Example</h2>
 <span id="cb23-8"><a href="#cb23-8"></a><span class="ss">error using inv(A) = </span><span class="sc">{</span>norm(A <span class="op">@</span> c_inv <span class="op">-</span> y, np.inf)<span class="sc">}</span><span class="ss">"</span>)</span>
 <span id="cb23-9"><a href="#cb23-9"></a><span class="bu">print</span>(<span class="ss">f"cond(A) = </span><span class="sc">{</span>cond(A)<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>error = 5.820766091346741e-11, error using inv(A) = 1.3387762010097504e-09
-cond(A) = 564652.3214074654</code></pre>
+<pre><code>error = 1.574562702444382e-11, error using inv(A) = 1.1932570487260818e-09
+cond(A) = 564652.3214000753</code></pre>
 </div>
 </div>
 </section>
@@ -877,8 +877,8 @@ <h2>Things Getting Poorly Conditioned Quickly</h2>
 <span id="cb25-8"><a href="#cb25-8"></a><span class="ss">error using inv(A) = </span><span class="sc">{</span>norm(A <span class="op">@</span> c_inv <span class="op">-</span> y, np.inf)<span class="sc">}</span><span class="ss">"</span>)</span>
 <span id="cb25-9"><a href="#cb25-9"></a><span class="bu">print</span>(<span class="ss">f"cond(A) = </span><span class="sc">{</span>cond(A)<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>error = 1.280568540096283e-09, error using inv(A) = 6.463262252509594e-06
-cond(A) = 4462817558043.969</code></pre>
+<pre><code>error = 5.334186425898224e-10, error using inv(A) = 6.22717197984457e-06
+cond(A) = 4462824600234.486</code></pre>
 </div>
 </div>
 </section>
@@ -895,8 +895,8 @@ <h2>Matrix Inverses Fail Completely for <span class="math inline">\(N = 20\)</sp
 <span id="cb27-8"><a href="#cb27-8"></a><span class="ss">error using inv(A) = </span><span class="sc">{</span>norm(A <span class="op">@</span> c_inv <span class="op">-</span> y, np.inf)<span class="sc">}</span><span class="ss">"</span>)</span>
 <span id="cb27-9"><a href="#cb27-9"></a><span class="bu">print</span>(<span class="ss">f"cond(A) = </span><span class="sc">{</span>cond(A)<span class="sc">:.4g}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>error = 5.820766091346741e-10, error using inv(A) = 2460.8631448635133
-cond(A) = 5.771e+24</code></pre>
+<pre><code>error = 6.784830475226045e-10, error using inv(A) = 31732.823760853855
+cond(A) = 1.697e+24</code></pre>
 </div>
 </div>
 </section>
@@ -917,7 +917,7 @@ <h2>Moral of this Story</h2>
 <span id="cb29-4"><a href="#cb29-4"></a>A_monomial <span class="op">=</span> np.array([[x_i<span class="op">**</span>n <span class="cf">for</span> n <span class="kw">in</span> <span class="bu">range</span>(N <span class="op">+</span> <span class="dv">1</span>)] <span class="cf">for</span> x_i <span class="kw">in</span> x])  <span class="co"># or np.vander</span></span>
 <span id="cb29-5"><a href="#cb29-5"></a><span class="bu">print</span>(<span class="ss">f"cond(A) = </span><span class="sc">{</span>cond(A)<span class="sc">:.4g}</span><span class="ss">, cond(A_monomial) = </span><span class="sc">{</span>cond(A_monomial)<span class="sc">:.4g}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>cond(A) = 3.64e+09, cond(A_monomial) = 1.694e+17</code></pre>
+<pre><code>cond(A) = 3.64e+09, cond(A_monomial) = 2.926e+18</code></pre>
 </div>
 </div>
 

lectures/lectures/index.html

@@ -136,6 +136,7 @@ <h1>Lectures</h1>
 <li><a href="probability.html" target="_blank">Probability, Conditioning, and Independence</a>, <a href="probability.ipynb" target="_blank">Jupyter</a>, <a href="probability.pdf" target="_blank">PDF</a></li>
 <li><a href="stochastic_processes.html" target="_blank">Stochastic Processes</a>, <a href="stochastic_processes.ipynb" target="_blank">Jupyter</a>, <a href="stochastic_processes.pdf" target="_blank">PDF</a></li>
 <li><a href="introduction_to_causality.html" target="_blank">Intro to Causality</a>, <a href="introduction_to_causality.ipynb" target="_blank">Jupyter</a>, <a href="introduction_to_causality.pdf" target="_blank">PDF</a></li>
+<li><a href="uncertainty_bias_variance.qmd.html" target="_blank">Uncertainty Quantification in Applied Economics</a>, <a href="uncertainty_bias_variance.qmd.ipynb" target="_blank">Jupyter</a>, <a href="uncertainty_bias_variance.qmd.pdf" target="_blank">PDF</a></li>
 </ol>
 
 

lectures/lectures/introduction_to_causality.html

@@ -1061,19 +1061,6 @@ <h2>Estimating Treatment Effects Without Randomization</h2>
 </section>
 <section id="estimating-treatment-effects-without-randomization-1" class="slide level2">
 <h2>Estimating Treatment Effects Without Randomization</h2>
-<ul>
-<li><p>Many identification assumptions are based on the idea of <strong>selection on observables</strong></p>
-<ul>
-<li>This means that the treatment assignment is independent of the potential outcomes <em>conditional</em> on the observed covariates</li>
-<li>In other words, <span class="math inline">\(Y_0\)</span> and <span class="math inline">\(Y_1\)</span> are independent of <span class="math inline">\(T\)</span> conditional on <span class="math inline">\(X\)</span></li>
-</ul></li>
-<li><p>This allows us to do things like <strong>match</strong> units in the treatment and control groups that are similar on average</p>
-<ul>
-<li>We can then estimate the treatment effect by comparing the outcomes of the matched units, assuming that the matched units are similar on average</li>
-</ul></li>
-<li><p>Another option is to use <strong>instrumental variables</strong> to estimate the treatment effect</p></li>
-<li><p>Alternatively, a <strong>structural model</strong> can be used to estimate the treatment effect by integrating a theoretical model to fill in the missing counterfactuals</p></li>
-</ul>
 
 <div class="footer footer-default">
 

lectures/lectures/latent_variables.html

@@ -611,9 +611,9 @@ <h2>PCA Without Dimension Reduction</h2>
 <span id="cb4-5"><a href="#cb4-5"></a>  <span class="bu">print</span>(<span class="ss">f"Explained Variance (ordered):</span><span class="ch">\n</span><span class="sc">{</span>pca<span class="sc">.</span>explained_variance_ratio_<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>Singular Values (sqrt eigenvalues):
-[25.0823  1.0254  0.6468]
+[21.5216  0.8732  0.7096]
 Explained Variance (ordered):
-[0.9977 0.0017 0.0007]</code></pre>
+[0.9973 0.0016 0.0011]</code></pre>
 </div>
 </div>
 </section>
@@ -626,8 +626,8 @@ <h2>Dimension Reduction with PCA</h2>
 <span id="cb6-4"><a href="#cb6-4"></a><span class="bu">print</span>(<span class="ss">f"Correlation of Z_1 to Z_hat_1 = </span><span class="sc">{</span>np<span class="sc">.</span>corrcoef(Z.T, Z_hat.T)[<span class="dv">0</span>,<span class="dv">2</span>]<span class="sc">}</span><span class="ss">"</span>)</span>
 <span id="cb6-5"><a href="#cb6-5"></a><span class="bu">print</span>(<span class="ss">f"Correlation of Z_2 to Z_hat_2 = </span><span class="sc">{</span>np<span class="sc">.</span>corrcoef(Z.T, Z_hat.T)[<span class="dv">1</span>,<span class="dv">3</span>]<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>Correlation of Z_1 to Z_hat_1 = 0.9989685407197146
-Correlation of Z_2 to Z_hat_2 = -0.622136330126575</code></pre>
+<pre><code>Correlation of Z_1 to Z_hat_1 = 0.9987396670122092
+Correlation of Z_2 to Z_hat_2 = -0.6413512732572132</code></pre>
 </div>
 </div>
 </section>
@@ -813,7 +813,7 @@ <h2>Plotting Code with Seaborn</h2>
 <span id="cb9-6"><a href="#cb9-6"></a>plt.show()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div><div class="column">
 <div class="cell-output cell-output-display">
-<p><img data-src="latent_variables_files/figure-revealjs/cell-7-output-1.png" width="830" height="449"></p>
+<p><img data-src="latent_variables_files/figure-revealjs/cell-7-output-1.png" width="823" height="449"></p>
 </div>
 </div>
 </div>
@@ -832,7 +832,7 @@ <h2>k-means to Recover the Latent Groups</h2>
 <span id="cb10-4"><a href="#cb10-4"></a>corr <span class="op">=</span> df[<span class="st">"k"</span>].corr(df[<span class="st">"k_hat"</span>])</span>
 <span id="cb10-5"><a href="#cb10-5"></a><span class="bu">print</span>(<span class="ss">f"Correlation between k and k_hat:</span><span class="sc">{</span>corr<span class="sc">:.2f}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>Correlation between k and k_hat:-0.83</code></pre>
+<pre><code>Correlation between k and k_hat:-0.93</code></pre>
 </div>
 </div>
 </section>
@@ -870,7 +870,7 @@ <h2>Potentially Swap <span class="math inline">\(\hat{k}\)</span> and Compare</h
 <span id="cb13-6"><a href="#cb13-6"></a>                         <span class="cf">if</span> x[<span class="st">'k'</span>] <span class="op">==</span> x[<span class="st">'k_hat'</span>] <span class="cf">else</span> <span class="vs">r'$k \neq \hat</span><span class="sc">{k}</span><span class="vs">$'</span>,</span>
 <span id="cb13-7"><a href="#cb13-7"></a>                         axis<span class="op">=</span><span class="dv">1</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>Correlation now 0.8300415031127608</code></pre>
+<pre><code>Correlation now 0.9300465034877902</code></pre>
 </div>
 </div>
 </section>
@@ -886,7 +886,7 @@ <h2>Plotting the Uncovered Latent Groups</h2>
 <span id="cb15-6"><a href="#cb15-6"></a>plt.show()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div><div class="column">
 <div class="cell-output cell-output-display">
-<p><img data-src="latent_variables_files/figure-revealjs/cell-11-output-1.png" width="534" height="376"></p>
+<p><img data-src="latent_variables_files/figure-revealjs/cell-11-output-1.png" width="526" height="376"></p>
 </div>
 </div>
 </div>
@@ -945,7 +945,7 @@ <h2>Digging Deeper</h2>
 <div class="sourceCode cell-code" id="cb19"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb19-1"><a href="#cb19-1"></a>Lambda, Q <span class="op">=</span> eig(A)</span>
 <span id="cb19-2"><a href="#cb19-2"></a><span class="bu">print</span>(np.real(Lambda))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>[ 1.10000000e+00 -2.65486721e-09]</code></pre>
+<pre><code>[ 1.10000000e+00 -2.65486733e-09]</code></pre>
 </div>
 </div>
 <ul>
@@ -968,7 +968,7 @@ <h2>Evolution Matrix is Very Simple with <span class="math inline">\(\lambda_2 =
 <span id="cb21-3"><a href="#cb21-3"></a>q_1_inv <span class="op">=</span> np.reshape(inv(Q)[<span class="dv">0</span>,:], (<span class="dv">1</span>,<span class="dv">2</span>))</span>
 <span id="cb21-4"><a href="#cb21-4"></a>norm(A <span class="op">-</span> lambda_1 <span class="op">*</span> q_1 <span class="op">@</span> q_1_inv) <span class="co"># pretty close to zero!</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-display" data-execution_count="15">
-<pre><code>2.663274529925679e-09</code></pre>
+<pre><code>2.663274500543771e-09</code></pre>
 </div>
 </div>
 </section>
@@ -998,7 +998,7 @@ <h2>Implementation</h2>
 <span id="cb23-5"><a href="#cb23-5"></a><span class="bu">print</span>(<span class="ss">f"norm = </span><span class="sc">{</span>norm(d[:,<span class="dv">1</span>:] <span class="op">-</span> d_hat)<span class="sc">}</span><span class="ss">"</span>)</span>
 <span id="cb23-6"><a href="#cb23-6"></a>y_hat <span class="op">=</span> G <span class="op">@</span> d_hat</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>norm = 2.3494397540428033e-10</code></pre>
+<pre><code>norm = 2.3494410875961204e-10</code></pre>
 </div>
 </div>
 <p>Let’s see if these line up perfectly</p>

lectures/lectures/linear_algebra_foundations.html

@@ -1121,9 +1121,9 @@ <h2>Example of LLS using Scipy</h2>
 <span id="cb48-6"><a href="#cb48-6"></a><span class="bu">print</span>(<span class="ss">f"beta =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>beta<span class="sc">}</span><span class="ch">\n</span><span class="ss">beta_hat =</span><span class="ch">\n</span><span class="sc">{</span>beta_hat<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>beta =
- [-0.81011697  0.47576408 -0.08064125 -0.21201846 -1.02869662]
+ [ 1.27699654  1.24976206 -0.02314793 -0.1603755  -1.71006662]
 beta_hat =
-[-0.81519622  0.47790174 -0.08893845 -0.21818441 -1.02778959]</code></pre>
+[ 1.26798224  1.24374081 -0.02376603 -0.16370129 -1.72027267]</code></pre>
 </div>
 </div>
 </section>
@@ -1135,9 +1135,9 @@ <h2>Solving using the Normal Equations</h2>
 <span id="cb50-2"><a href="#cb50-2"></a><span class="bu">print</span>(<span class="ss">f"beta =</span><span class="ch">\n</span><span class="ss"> </span><span class="sc">{</span>beta<span class="sc">}</span><span class="ch">\n</span><span class="ss">beta_hat =</span><span class="ch">\n</span><span class="sc">{</span>beta_hat<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
 <pre><code>beta =
- [-0.81011697  0.47576408 -0.08064125 -0.21201846 -1.02869662]
+ [ 1.27699654  1.24976206 -0.02314793 -0.1603755  -1.71006662]
 beta_hat =
-[-0.81519622  0.47790174 -0.08893845 -0.21818441 -1.02778959]</code></pre>
+[ 1.26798224  1.24374081 -0.02376603 -0.16370129 -1.72027267]</code></pre>
 </div>
 </div>
 </section>
@@ -1165,7 +1165,7 @@ <h2>Collinearity and Estimation</h2>
 <div class="cell" data-execution_count="29">
 <div class="sourceCode cell-code" id="cb54"><pre class="sourceCode numberSource python number-lines code-with-copy"><code class="sourceCode python"><span id="cb54-1"><a href="#cb54-1"></a><span class="bu">print</span>(<span class="ss">f"cond(X'*X)=</span><span class="sc">{</span>cond(X.T<span class="op">@</span>X)<span class="sc">}</span><span class="ss">, cond(X_col'*X_col)=</span><span class="sc">{</span>cond(X_col.T<span class="op">@</span>X_col)<span class="sc">}</span><span class="ss">"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <div class="cell-output cell-output-stdout">
-<pre><code>cond(X'*X)=2819.3329786399063, cond(X_col'*X_col)=1.2999933999712892e+16</code></pre>
+<pre><code>cond(X'*X)=2819.332978639814, cond(X_col'*X_col)=1.1014450683078442e+16</code></pre>
 </div>
 </div>
 <ul>

lectures/lectures/probability.html

@@ -666,7 +666,7 @@ <h2>Using the <code>discrete_rv</code></h2>
 <pre><code>E(X) = 34500.0
 E(f(X)) = 182.2474487139159
 CDF(X) = [0.2 1.  0.1]
-Samples of X = [40000 15000 40000 40000 40000]</code></pre>
+Samples of X = [40000 40000 10000 40000 40000]</code></pre>
 </div>
 </div>
 </div>
@@ -729,7 +729,7 @@ <h2>The Binomial Distribution</h2>
 <div class="cell-output cell-output-stdout">
 <pre><code>Mean: 5.00
 Variance: 2.50
-Draws of u: [3 5 5 6 6]</code></pre>
+Draws of u: [3 5 7 8 3]</code></pre>
 </div>
 </div>
 </div>

lectures/lectures/stochastic_processes.html

@@ -640,7 +640,7 @@ <h2>Implementation in Python</h2>
 <span id="cb2-14"><a href="#cb2-14"></a>plt.plot(X.T)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </div><div class="column">
 <div class="cell-output cell-output-display">
-<p><img data-src="stochastic_processes_files/figure-revealjs/cell-3-output-1.png" width="805" height="411"></p>
+<p><img data-src="stochastic_processes_files/figure-revealjs/cell-3-output-1.png" width="781" height="411"></p>
 </div>
 </div>
 </div>
@@ -729,7 +729,7 @@ <h2>Simulating Unit Root</h2>
 <h2>Visualizing the Distribution of Many Trajectories</h2>
 <div class="cell" data-execution_count="6">
 <div class="cell-output cell-output-display">
-<p><img data-src="stochastic_processes_files/figure-revealjs/cell-6-output-1.png" width="813" height="429"></p>
+<p><img data-src="stochastic_processes_files/figure-revealjs/cell-6-output-1.png" width="805" height="434"></p>
 </div>
 </div>
 </section>
@@ -976,7 +976,7 @@ <h2>Coding Markov Chain in Python</h2>
 <div class="cell-output cell-output-stdout">
 <pre><code>X_0 = 0, X_1 = 0
 X_t indices =
- [0 0 0 0 0 0 0 0 0 0 0]</code></pre>
+ [0 1 1 1 1 1 1 1 1 1 1]</code></pre>
 </div>
 </div>
 </div>