diff --git a/doc/pub/week37/html/._week37-bs000.html b/doc/pub/week37/html/._week37-bs000.html
index 624185444..f48891b7c 100644
--- a/doc/pub/week37/html/._week37-bs000.html
+++ b/doc/pub/week37/html/._week37-bs000.html
@@ -306,7 +306,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Sep 18, 2023</h4>
+<h4>September 9, 2024</h4>
 </center> <!-- date -->
 <br>
 
@@ -347,7 +347,7 @@ MathJax.Hub.Config({
 </footer>
 -->
 <center style="font-size:80%">
-<!-- copyright --> &copy; 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 </center>
 </body>
 </html>
diff --git a/doc/pub/week37/html/._week37-bs001.html b/doc/pub/week37/html/._week37-bs001.html
index 3c75192be..bfeb32c30 100644
--- a/doc/pub/week37/html/._week37-bs001.html
+++ b/doc/pub/week37/html/._week37-bs001.html
@@ -293,22 +293,9 @@ MathJax.Hub.Config({
 <div class="panel panel-default">
 <div class="panel-body">
 <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+<!-- * <a href="https://youtu.be/YOBBr_toYxc" target="_self">Video of Lecture</a> -->
+<!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_self">Whiteboard notes</a> -->
 <ul>
-  <li> Lecture from last week on calculations of expectation values</li>
-  <li> Exercise for week 37</li>
-  <li> Work on project 1</li>
-  <li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
-  <li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_self">Wessel van Wieringen's</a> article is highly recommended.</li>
-</ul>
-</div>
-</div>
-  
-<div class="panel panel-default">
-<div class="panel-body">
-<!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
-<ul>
-  <li> <a href="https://youtu.be/YOBBr_toYxc" target="_self">Video of Lecture</a></li>
-  <li> <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_self">Whiteboard notes</a></li>
   <li> Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff</li>
   <li> Statistical interpretation of Ridge and Lasso regression</li>
   <li> Readings and Videos:</li>
@@ -323,6 +310,20 @@ MathJax.Hub.Config({
 </div>
 
 
+<div class="panel panel-default">
+<div class="panel-body">
+<!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
+<ul>
+  <li> Calculations of expectation values</li>
+  <li> Exercise set for week 37</li>
+  <li> Work on project 1</li>
+  <li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
+  <li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_self">Wessel van Wieringen's</a> article is highly recommended.</li>
+</ul>
+</div>
+</div>
+  
+
 <p>
 <!-- navigation buttons at the bottom of the page -->
 <ul class="pagination">
diff --git a/doc/pub/week37/html/week37-bs.html b/doc/pub/week37/html/week37-bs.html
index 624185444..f48891b7c 100644
--- a/doc/pub/week37/html/week37-bs.html
+++ b/doc/pub/week37/html/week37-bs.html
@@ -306,7 +306,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Sep 18, 2023</h4>
+<h4>September 9, 2024</h4>
 </center> <!-- date -->
 <br>
 
@@ -347,7 +347,7 @@ MathJax.Hub.Config({
 </footer>
 -->
 <center style="font-size:80%">
-<!-- copyright --> &copy; 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 </center>
 </body>
 </html>
diff --git a/doc/pub/week37/html/week37-reveal.html b/doc/pub/week37/html/week37-reveal.html
index 060553146..fc009dff3 100644
--- a/doc/pub/week37/html/week37-reveal.html
+++ b/doc/pub/week37/html/week37-reveal.html
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Sep 18, 2023</h4>
+<h4>September 9, 2024</h4>
 </center> <!-- date -->
 <br>
 
@@ -192,7 +192,7 @@ MathJax.Hub.Config({
 
 
 <center style="font-size:80%">
-<!-- copyright --> &copy; 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 </center>
 </section>
 
@@ -200,31 +200,12 @@ MathJax.Hub.Config({
 <h2 id="plans-for-week-37">Plans for week 37 </h2>
 
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Material for the active learning sessions on Tuesday and Wednesday</b>
+<b>Material for the lecture on Monday September 9</b>
 <p>
+<!-- * <a href="https://youtu.be/YOBBr_toYxc" target="_blank">Video of Lecture</a> -->
+<!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_blank">Whiteboard notes</a> -->
 <ul>
 
-<p><li> Lecture from last week on calculations of expectation values</li>
-
-<p><li> Exercise for week 37</li>
-
-<p><li> Work on project 1</li>
-
-<p><li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
-
-<p><li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_blank">Wessel van Wieringen's</a> article is highly recommended.</li>
-</ul>
-</div>
-  
-<div class="alert alert-block alert-block alert-text-normal">
-<b>Material for the lecture on Thursday September 7</b>
-<p>
-<ul>
-
-<p><li> <a href="https://youtu.be/YOBBr_toYxc" target="_blank">Video of Lecture</a></li>
-
-<p><li> <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_blank">Whiteboard notes</a></li>
-
 <p><li> Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff</li>
 
 <p><li> Statistical interpretation of Ridge and Lasso regression</li>
@@ -243,6 +224,24 @@ MathJax.Hub.Config({
 <p>
 </ul>
 </div>
+
+
+<div class="alert alert-block alert-block alert-text-normal">
+<b>Material for the active learning sessions on Tuesday and Wednesday</b>
+<p>
+<ul>
+
+<p><li> Calculations of expectation values</li>
+
+<p><li> Exercise set for week 37</li>
+
+<p><li> Work on project 1</li>
+
+<p><li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
+
+<p><li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_blank">Wessel van Wieringen's</a> article is highly recommended.</li>
+</ul>
+</div>
 </section>
 
 <section>
diff --git a/doc/pub/week37/html/week37-solarized.html b/doc/pub/week37/html/week37-solarized.html
index 53f5455b9..b0db0dd30 100644
--- a/doc/pub/week37/html/week37-solarized.html
+++ b/doc/pub/week37/html/week37-solarized.html
@@ -254,7 +254,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Sep 18, 2023</h4>
+<h4>September 9, 2024</h4>
 </center> <!-- date -->
 <br>
 
@@ -264,23 +264,11 @@ MathJax.Hub.Config({
 <h2 id="plans-for-week-37">Plans for week 37 </h2>
 
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Material for the active learning sessions on Tuesday and Wednesday</b>
+<b>Material for the lecture on Monday September 9</b>
 <p>
+<!-- * <a href="https://youtu.be/YOBBr_toYxc" target="_blank">Video of Lecture</a> -->
+<!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_blank">Whiteboard notes</a> -->
 <ul>
-  <li> Lecture from last week on calculations of expectation values</li>
-  <li> Exercise for week 37</li>
-  <li> Work on project 1</li>
-  <li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
-  <li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_blank">Wessel van Wieringen's</a> article is highly recommended.</li>
-</ul>
-</div>
-  
-<div class="alert alert-block alert-block alert-text-normal">
-<b>Material for the lecture on Thursday September 7</b>
-<p>
-<ul>
-  <li> <a href="https://youtu.be/YOBBr_toYxc" target="_blank">Video of Lecture</a></li>
-  <li> <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_blank">Whiteboard notes</a></li>
   <li> Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff</li>
   <li> Statistical interpretation of Ridge and Lasso regression</li>
   <li> Readings and Videos:</li>
@@ -294,6 +282,19 @@ MathJax.Hub.Config({
 </div>
 
 
+<div class="alert alert-block alert-block alert-text-normal">
+<b>Material for the active learning sessions on Tuesday and Wednesday</b>
+<p>
+<ul>
+  <li> Calculations of expectation values</li>
+  <li> Exercise set for week 37</li>
+  <li> Work on project 1</li>
+  <li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
+  <li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_blank">Wessel van Wieringen's</a> article is highly recommended.</li>
+</ul>
+</div>
+  
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="material-from-last-week-and-relevant-for-the-weekly-exercises">Material from last week and relevant for the weekly exercises </h2>
 
@@ -2410,7 +2411,7 @@ plt.show()
 
 <!-- ------------------- end of main content --------------- -->
 <center style="font-size:80%">
-<!-- copyright --> &copy; 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 </center>
 </body>
 </html>
diff --git a/doc/pub/week37/html/week37.html b/doc/pub/week37/html/week37.html
index 4c6769fea..cbffe8490 100644
--- a/doc/pub/week37/html/week37.html
+++ b/doc/pub/week37/html/week37.html
@@ -331,7 +331,7 @@ MathJax.Hub.Config({
 </center>
 <br>
 <center>
-<h4>Sep 18, 2023</h4>
+<h4>September 9, 2024</h4>
 </center> <!-- date -->
 <br>
 
@@ -341,23 +341,11 @@ MathJax.Hub.Config({
 <h2 id="plans-for-week-37">Plans for week 37 </h2>
 
 <div class="alert alert-block alert-block alert-text-normal">
-<b>Material for the active learning sessions on Tuesday and Wednesday</b>
+<b>Material for the lecture on Monday September 9</b>
 <p>
+<!-- * <a href="https://youtu.be/YOBBr_toYxc" target="_blank">Video of Lecture</a> -->
+<!-- * <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_blank">Whiteboard notes</a> -->
 <ul>
-  <li> Lecture from last week on calculations of expectation values</li>
-  <li> Exercise for week 37</li>
-  <li> Work on project 1</li>
-  <li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
-  <li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_blank">Wessel van Wieringen's</a> article is highly recommended.</li>
-</ul>
-</div>
-  
-<div class="alert alert-block alert-block alert-text-normal">
-<b>Material for the lecture on Thursday September 7</b>
-<p>
-<ul>
-  <li> <a href="https://youtu.be/YOBBr_toYxc" target="_blank">Video of Lecture</a></li>
-  <li> <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf" target="_blank">Whiteboard notes</a></li>
   <li> Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff</li>
   <li> Statistical interpretation of Ridge and Lasso regression</li>
   <li> Readings and Videos:</li>
@@ -371,6 +359,19 @@ MathJax.Hub.Config({
 </div>
 
 
+<div class="alert alert-block alert-block alert-text-normal">
+<b>Material for the active learning sessions on Tuesday and Wednesday</b>
+<p>
+<ul>
+  <li> Calculations of expectation values</li>
+  <li> Exercise set for week 37</li>
+  <li> Work on project 1</li>
+  <li> See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.</li>
+  <li> For more discussions of Ridge regression and calculation of averages, <a href="https://arxiv.org/abs/1509.09169" target="_blank">Wessel van Wieringen's</a> article is highly recommended.</li>
+</ul>
+</div>
+  
+
 <!-- !split --><br><br><br><br><br><br><br><br><br><br>
 <h2 id="material-from-last-week-and-relevant-for-the-weekly-exercises">Material from last week and relevant for the weekly exercises </h2>
 
@@ -2487,7 +2488,7 @@ plt<span style="color: #666666">.</span>show()
 
 <!-- ------------------- end of main content --------------- -->
 <center style="font-size:80%">
-<!-- copyright --> &copy; 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
+<!-- copyright --> &copy; 1999-2024, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
 </center>
 </body>
 </html>
diff --git a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz
index 86d968ac7..18070b5a0 100644
Binary files a/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz and b/doc/pub/week37/ipynb/ipynb-week37-src.tar.gz differ
diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb
index 39771732f..94e3e70ef 100644
--- a/doc/pub/week37/ipynb/week37.ipynb
+++ b/doc/pub/week37/ipynb/week37.ipynb
@@ -2,8 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "9e3d6c33",
-   "metadata": {},
+   "id": "672fea2a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
     "doconce format html week37.do.txt --no_mako -->\n",
@@ -12,45 +14,32 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c4bf45e",
-   "metadata": {},
+   "id": "479a6913",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "# Week 37: Statistical interpretations and Resampling Methods\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
     "\n",
-    "Date: **Sep 18, 2023**\n",
-    "\n",
-    "Copyright 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
+    "Date: **September 9, 2024**\n",
     "\n",
     "<!-- todo add link to videos and add link to Van Wieringens notes -->"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "af4e71fa",
-   "metadata": {},
+   "id": "10b8f456",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plans for week 37\n",
     "\n",
-    "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
-    "\n",
-    "  * Lecture from last week on calculations of expectation values\n",
-    "\n",
-    "  * Exercise for week 37\n",
-    "\n",
-    "  * Work on project 1\n",
-    "\n",
-    "  * See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.\n",
-    "\n",
-    "  * For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended.\n",
-    "\n",
-    "  \n",
-    "**Material for the lecture on Thursday September 7.**\n",
-    "\n",
-    "  * [Video of Lecture](https://youtu.be/YOBBr_toYxc)\n",
-    "\n",
-    "  * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf)\n",
+    "**Material for the lecture on Monday September 9.**\n",
     "\n",
+    "<!-- * [Video of Lecture](https://youtu.be/YOBBr_toYxc) -->\n",
+    "<!-- * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf) -->\n",
     "  * Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff\n",
     "\n",
     "  * Statistical interpretation of Ridge and Lasso regression\n",
@@ -63,21 +52,37 @@
     "\n",
     "    * [Video on Bootstrapping](https://www.youtube.com/watch?v=Xz0x-8-cgaQ)\n",
     "\n",
-    "    * [Video on bias-variance tradeoff](https://www.youtube.com/watch?v=EuBBz3bI-aA)"
+    "    * [Video on bias-variance tradeoff](https://www.youtube.com/watch?v=EuBBz3bI-aA)\n",
+    "\n",
+    "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
+    "\n",
+    "  * Calculations of expectation values\n",
+    "\n",
+    "  * Exercise set for week 37\n",
+    "\n",
+    "  * Work on project 1\n",
+    "\n",
+    "  * See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.\n",
+    "\n",
+    "  * For more discussions of Ridge regression and calculation of averages, [Wessel van Wieringen's](https://arxiv.org/abs/1509.09169) article is highly recommended."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a30b83bd",
-   "metadata": {},
+   "id": "f7e43b1b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Material from last week and relevant for the weekly exercises"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "603e5939",
-   "metadata": {},
+   "id": "af6a447a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Linking the regression analysis with a statistical interpretation\n",
     "\n",
@@ -103,8 +108,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6d1b655",
-   "metadata": {},
+   "id": "b6b7ea38",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*} \n",
@@ -117,8 +124,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ac423bb",
-   "metadata": {},
+   "id": "e53d8d41",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The randomness of $\\varepsilon_i$ implies that\n",
     "$\\mathbf{y}_i$ is also a random variable. In particular,\n",
@@ -134,8 +143,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a321bc7e",
-   "metadata": {},
+   "id": "401644e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Assumptions made\n",
     "\n",
@@ -146,8 +157,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a058a44f",
-   "metadata": {},
+   "id": "0603387c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n",
@@ -156,8 +169,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ca5aeb9",
-   "metadata": {},
+   "id": "eb2b6edf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We approximate this function with our model from the solution of the linear regression equations, that is our\n",
     "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with"
@@ -165,8 +180,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a064201",
-   "metadata": {},
+   "id": "f1a08194",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n",
@@ -175,8 +192,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc70ead9",
-   "metadata": {},
+   "id": "ad40fa0b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Expectation value and variance\n",
     "\n",
@@ -185,8 +204,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9beae550",
-   "metadata": {},
+   "id": "d3a4907d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*} \n",
@@ -199,8 +220,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0ab7cc5",
-   "metadata": {},
+   "id": "d7908c9c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "while\n",
     "its variance is"
@@ -208,8 +231,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a6900e18",
-   "metadata": {},
+   "id": "2528f74e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n",
@@ -229,8 +254,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe9b0d2f",
-   "metadata": {},
+   "id": "525f3a59",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n",
     "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD)."
@@ -238,8 +265,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be36f9aa",
-   "metadata": {},
+   "id": "ead1d419",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Expectation value and variance for $\\boldsymbol{\\beta}$\n",
     "\n",
@@ -248,8 +277,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3717afd4",
-   "metadata": {},
+   "id": "e471f7ab",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n",
@@ -258,8 +289,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f75bbc6c",
-   "metadata": {},
+   "id": "7886e97f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This means that the estimator of the regression parameters is unbiased.\n",
     "\n",
@@ -270,8 +303,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "501aab1c",
-   "metadata": {},
+   "id": "49c32ca5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\begin{eqnarray*}\n",
@@ -299,8 +334,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "882b7267",
-   "metadata": {},
+   "id": "9bd27980",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have used  that $\\mathbb{E} (\\mathbf{y} \\mathbf{y}^{T}) =\n",
     "\\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} +\n",
@@ -319,8 +356,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7993235",
-   "metadata": {},
+   "id": "184f9c3b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbb{E} \\big[ \\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\beta}.\n",
@@ -329,8 +368,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27dfe1f9",
-   "metadata": {},
+   "id": "d0f46be1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We see clearly that \n",
     "$\\mathbb{E} \\big[ \\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}} \\big] \\not= \\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}$ for any $\\lambda > 0$.\n",
@@ -340,8 +381,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1ccc9c9",
-   "metadata": {},
+   "id": "03e3ac5f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mbox{Var}[\\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}}]=\\sigma^2[  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}  \\mathbf{X}^{T} \\mathbf{X} \\{ [  \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n",
@@ -350,8 +393,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b51caf8",
-   "metadata": {},
+   "id": "13ec2524",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero. \n",
     "\n",
@@ -360,8 +405,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b6c2347",
-   "metadata": {},
+   "id": "58c3f236",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mbox{Var}[\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}]-\\mbox{Var}(\\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}})=\\sigma^2 [  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [  \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n",
@@ -370,8 +417,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b622b81",
-   "metadata": {},
+   "id": "bfcfc2a0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The difference is non-negative definite since each component of the\n",
     "matrix product is non-negative definite. \n",
@@ -382,16 +431,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc281f57",
-   "metadata": {},
+   "id": "f3a9f084",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Material for lecture Thursday September 14"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b1262baf",
-   "metadata": {},
+   "id": "a4338936",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Deriving OLS from a probability distribution\n",
     "\n",
@@ -411,8 +464,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a14cfe86",
-   "metadata": {},
+   "id": "d7566301",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "y_i\\sim \\mathcal{N}(\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta}, \\sigma^2)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n",
@@ -421,8 +476,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56fe0849",
-   "metadata": {},
+   "id": "c8af7fae",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Independent and Identically Distrubuted (iid)\n",
     "\n",
@@ -432,8 +489,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "afed97f2",
-   "metadata": {},
+   "id": "959e33e8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(y_i, \\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]},\n",
@@ -442,8 +501,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4b5884d",
-   "metadata": {},
+   "id": "c847b78b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which reads as finding the likelihood of an event $y_i$ with the input variables $\\boldsymbol{X}$ given the parameters (to be determined) $\\boldsymbol{\\beta}$.\n",
     "\n",
@@ -452,8 +513,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c949c06",
-   "metadata": {},
+   "id": "75c188ba",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{y},\\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}=\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta}).\n",
@@ -462,8 +525,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "113e3658",
-   "metadata": {},
+   "id": "60b89ba3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We will write this in a more compact form reserving $\\boldsymbol{D}$ for the domain of events, including the ouputs (targets) and the inputs. That is\n",
     "in case we have a simple one-dimensional input and output case"
@@ -471,8 +536,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6851f92d",
-   "metadata": {},
+   "id": "fd5d5a54",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})].\n",
@@ -481,8 +548,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9266f3e0",
-   "metadata": {},
+   "id": "56f25582",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In the more general case the various inputs should be replaced by the possible features represented by the input data set $\\boldsymbol{X}$. \n",
     "We can now rewrite the above probability as"
@@ -490,8 +559,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "287d1ae7",
-   "metadata": {},
+   "id": "9974b303",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n",
@@ -500,16 +571,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b27ae15",
-   "metadata": {},
+   "id": "4112e053",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "It is a conditional probability (see below) and reads as the likelihood of a domain of events $\\boldsymbol{D}$ given a set of parameters $\\boldsymbol{\\beta}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "05685291",
-   "metadata": {},
+   "id": "7be4a14c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Maximum Likelihood Estimation (MLE)\n",
     "\n",
@@ -537,8 +612,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9219f05a",
-   "metadata": {},
+   "id": "35078f48",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## A new Cost Function\n",
     "\n",
@@ -547,8 +624,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fba0d995",
-   "metadata": {},
+   "id": "cb25ead1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})},\n",
@@ -557,16 +636,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c19bfc19",
-   "metadata": {},
+   "id": "5cc80036",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which becomes"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6de82f09",
-   "metadata": {},
+   "id": "8ebc6099",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}.\n",
@@ -575,16 +658,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adfc6771",
-   "metadata": {},
+   "id": "3160dff4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Taking the derivative of the *new* cost function with respect to the parameters $\\beta$ we recognize our familiar OLS equation, namely"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a1ecd0dd",
-   "metadata": {},
+   "id": "8a3aaa69",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right) =0,\n",
@@ -593,16 +680,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91a37c0d",
-   "metadata": {},
+   "id": "7af6708c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which leads to the well-known OLS equation for the optimal paramters $\\beta$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "11677560",
-   "metadata": {},
+   "id": "c82e095e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n",
@@ -611,16 +702,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8099810c",
-   "metadata": {},
+   "id": "9431eca4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f9232f8c",
-   "metadata": {},
+   "id": "1db6c222",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More basic Statistics and Bayes' theorem\n",
     "\n",
@@ -637,8 +732,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9088ea5d",
-   "metadata": {},
+   "id": "98c457ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X \\cup Y)= p(X)+p(Y)-p(X \\cap Y).\n",
@@ -647,16 +744,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a43a59f",
-   "metadata": {},
+   "id": "b6a3893f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "**The product rule (aka joint probability) is given by.**"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4cf876a2",
-   "metadata": {},
+   "id": "17f0e52e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X \\cup Y)= p(X,Y)= p(X\\vert Y)p(Y)=p(Y\\vert X)p(X),\n",
@@ -665,8 +766,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19f3bd61",
-   "metadata": {},
+   "id": "c2bfaea6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we read $p(X\\vert Y)$ as the likelihood of obtaining $X$ given $Y$.\n",
     "\n",
@@ -675,8 +778,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4df8724",
-   "metadata": {},
+   "id": "377eefdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Marginal Probability\n",
     "\n",
@@ -685,8 +790,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a137b317",
-   "metadata": {},
+   "id": "6da6253e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X)=\\sum_{i=0}^{n-1}p(X,Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert Y=y_i)p(Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert y_i)p(y_i).\n",
@@ -695,8 +802,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83858731",
-   "metadata": {},
+   "id": "e5906b3e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Conditional  Probability\n",
     "\n",
@@ -705,8 +814,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee5dab96",
-   "metadata": {},
+   "id": "792d292c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)}=\\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}.\n",
@@ -715,8 +826,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb03bfdd",
-   "metadata": {},
+   "id": "c3bc0674",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Bayes' Theorem\n",
     "\n",
@@ -725,8 +838,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72b69902",
-   "metadata": {},
+   "id": "0faadf3f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)},\n",
@@ -735,16 +850,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a876747",
-   "metadata": {},
+   "id": "a2d478a7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which we can rewrite as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2424f759",
-   "metadata": {},
+   "id": "d51ac6ce",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X\\vert Y)= \\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}=\\frac{p(Y\\vert X)p(X)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)},\n",
@@ -753,16 +872,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f33b3f29",
-   "metadata": {},
+   "id": "91d489d9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which is Bayes' theorem. It allows us to evaluate the uncertainty in in $X$ after we have observed $Y$. We can easily interchange $X$ with $Y$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b73e0693",
-   "metadata": {},
+   "id": "ebe26b44",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Interpretations of Bayes' Theorem\n",
     "\n",
@@ -778,8 +901,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2bc10db",
-   "metadata": {},
+   "id": "a67660e2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example of Usage of Bayes' theorem\n",
     "\n",
@@ -797,8 +922,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f41d3f9b",
-   "metadata": {},
+   "id": "40b7eac0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X=1\\vert Y=1) =0.8.\n",
@@ -807,8 +934,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe20e517",
-   "metadata": {},
+   "id": "16a3b6ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "This obviously sounds  scary since many would conclude that if the test is positive, there is a likelihood of $80\\%$ for having cancer.\n",
     "It is however not correct, as the following Bayesian analysis shows."
@@ -816,8 +945,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d003d5d8",
-   "metadata": {},
+   "id": "f41ccc6d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Doing it correctly\n",
     "\n",
@@ -827,8 +958,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07a5ca9c",
-   "metadata": {},
+   "id": "ae81305b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(Y=1) =0.004.\n",
@@ -837,16 +970,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91485638",
-   "metadata": {},
+   "id": "f4829b81",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We need also to account for the fact that the test may produce a false positive result (false alarm). Let us here assume that we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "be6de757",
-   "metadata": {},
+   "id": "812273af",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(X=1\\vert Y=0) =0.1.\n",
@@ -855,16 +992,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51263519",
-   "metadata": {},
+   "id": "31ecba0e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Using Bayes' theorem we can then find the posterior probability that the person has breast cancer in case of a positive test, that is we can compute"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5b2dc226",
-   "metadata": {},
+   "id": "ca6682ec",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(Y=1\\vert X=1)=\\frac{p(X=1\\vert Y=1)p(Y=1)}{p(X=1\\vert Y=1)p(Y=1)+p(X=1\\vert Y=0)p(Y=0)}=\\frac{0.8\\times 0.004}{0.8\\times 0.004+0.1\\times 0.996}=0.031.\n",
@@ -873,16 +1014,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e241fbc1",
-   "metadata": {},
+   "id": "662eaffb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "That is, in case of a positive test, there is only a $3\\%$ chance of having breast cancer!"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "42db70df",
-   "metadata": {},
+   "id": "08d5551d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Bayes' Theorem and Ridge and Lasso Regression\n",
     "\n",
@@ -893,8 +1038,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed75a460",
-   "metadata": {},
+   "id": "03f3de9c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})],\n",
@@ -903,16 +1050,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c826a95f",
-   "metadata": {},
+   "id": "c57ace49",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "is given by"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "70a426f9",
-   "metadata": {},
+   "id": "cb014b2b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n",
@@ -921,16 +1072,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a90b1b91",
-   "metadata": {},
+   "id": "1054d47e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In Bayes' theorem this function plays the role of the so-called likelihood. We could now ask the question what is the posterior probability of a parameter set $\\boldsymbol{\\beta}$ given a domain of events $\\boldsymbol{D}$?  That is, how can we define the posterior probability"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "3f5a6f0b",
-   "metadata": {},
+   "id": "1485d44c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D}).\n",
@@ -939,16 +1094,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2530803f",
-   "metadata": {},
+   "id": "f457f909",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Bayes' theorem comes to our rescue here since (omitting the normalization constant)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "34940159",
-   "metadata": {},
+   "id": "59447b2a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})\\propto p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})p(\\boldsymbol{\\beta}).\n",
@@ -957,16 +1116,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f497f2c",
-   "metadata": {},
+   "id": "4fe26100",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We have a model for $p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})$ but need one for the **prior** $p(\\boldsymbol{\\beta}$!"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "c780a9b9",
-   "metadata": {},
+   "id": "d73c2d9c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Ridge and Bayes\n",
     "\n",
@@ -979,8 +1142,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68ddd4cc",
-   "metadata": {},
+   "id": "8cdf2c97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n",
@@ -989,16 +1154,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b85ade85",
-   "metadata": {},
+   "id": "7272ef9f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Our posterior probability becomes then (omitting the normalization factor which is just a constant)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6386a328",
-   "metadata": {},
+   "id": "0dc5b2b7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta\\vert\\boldsymbol{D})}=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n",
@@ -1007,8 +1176,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "316194e8",
-   "metadata": {},
+   "id": "b6c8c684",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We can now optimize this quantity with respect to $\\boldsymbol{\\beta}$. As we\n",
     "did for OLS, this is most conveniently done by taking the negative\n",
@@ -1018,8 +1189,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7e39504",
-   "metadata": {},
+   "id": "f681ed50",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{2\\tau^2}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n",
@@ -1028,16 +1201,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c3b01de",
-   "metadata": {},
+   "id": "5c3bc898",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and replacing $1/2\\tau^2$ with $\\lambda$ we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5c4a05c9",
-   "metadata": {},
+   "id": "a3cea046",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n",
@@ -1046,16 +1223,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f26b763",
-   "metadata": {},
+   "id": "68276410",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which is our Ridge cost function!  Nice, isn't it?"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "08efa297",
-   "metadata": {},
+   "id": "dfd55611",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Lasso and Bayes\n",
     "\n",
@@ -1064,8 +1245,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97765f2c",
-   "metadata": {},
+   "id": "83656dd8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n",
@@ -1074,16 +1257,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2e48903",
-   "metadata": {},
+   "id": "b62e29fd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Our posterior probability becomes then (omitting the normalization factor which is just a constant)"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fae174cf",
-   "metadata": {},
+   "id": "1de8855c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n",
@@ -1092,8 +1279,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc3ff171",
-   "metadata": {},
+   "id": "212152f1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Taking the negative\n",
     "logarithm of the posterior probability and leaving out the\n",
@@ -1102,8 +1291,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af3046b7",
-   "metadata": {},
+   "id": "afb042c4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{\\tau}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
@@ -1112,16 +1303,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbf017df",
-   "metadata": {},
+   "id": "ab1fd3c5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and replacing $1/\\tau$ with $\\lambda$ we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "23214eb3",
-   "metadata": {},
+   "id": "43979108",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta}=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n",
@@ -1130,16 +1325,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3c6b69a",
-   "metadata": {},
+   "id": "96622b66",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which is our Lasso cost function!"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "386493f5",
-   "metadata": {},
+   "id": "e17a5b6d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why resampling methods\n",
     "\n",
@@ -1155,8 +1354,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "727bee7f",
-   "metadata": {},
+   "id": "24e35401",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods\n",
     "Resampling methods are an indispensable tool in modern\n",
@@ -1181,8 +1382,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e34ba8e",
-   "metadata": {},
+   "id": "a37f1d06",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling approaches can be computationally expensive\n",
     "\n",
@@ -1205,8 +1408,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc35fdde",
-   "metadata": {},
+   "id": "58f54a23",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Why resampling methods ?\n",
     "**Statistical analysis.**\n",
@@ -1220,8 +1425,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc071fc4",
-   "metadata": {},
+   "id": "6ed7c809",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Statistical analysis\n",
     "\n",
@@ -1238,8 +1445,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef1325b9",
-   "metadata": {},
+   "id": "bed9bb2f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods\n",
     "\n",
@@ -1265,8 +1474,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "340ea11c",
-   "metadata": {},
+   "id": "2cafa0a3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods: Bootstrap\n",
     "Bootstrapping is a [non-parametric approach](https://en.wikipedia.org/wiki/Nonparametric_statistics) to statistical inference\n",
@@ -1288,8 +1499,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74bd7468",
-   "metadata": {},
+   "id": "fefbb980",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The Central Limit Theorem\n",
     "\n",
@@ -1306,8 +1519,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93013ca8",
-   "metadata": {},
+   "id": "4560153d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "z=\\frac{x_1+x_2+\\dots+x_m}{m},\n",
@@ -1316,16 +1531,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92fa2b15",
-   "metadata": {},
+   "id": "ffcbdd5a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "the question we pose is which is the PDF of the new variable $z$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "1031aebe",
-   "metadata": {},
+   "id": "d055ea55",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Finding the Limit\n",
     "\n",
@@ -1337,8 +1556,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc495848",
-   "metadata": {},
+   "id": "004f0161",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n",
@@ -1348,8 +1569,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28b2bcff",
-   "metadata": {},
+   "id": "039f4ad5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where the $\\delta$-function enbodies the constraint that the mean is $z$.\n",
     "All measurements that lead to each individual $x_i$ are expected to\n",
@@ -1359,8 +1582,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d3eb73d",
-   "metadata": {},
+   "id": "413459f1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Rewriting the $\\delta$-function\n",
     "\n",
@@ -1369,8 +1594,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75b47bae",
-   "metadata": {},
+   "id": "bef022c8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
@@ -1380,8 +1607,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a99105b0",
-   "metadata": {},
+   "id": "3d53693d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n",
     "we arrive at"
@@ -1389,8 +1618,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da28e9b0",
-   "metadata": {},
+   "id": "e682c32a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n",
@@ -1401,16 +1632,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bd0da08",
-   "metadata": {},
+   "id": "f44053ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "with the integral over $x$ resulting in"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "8dcbd91d",
-   "metadata": {},
+   "id": "f10de930",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n",
@@ -1421,8 +1656,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ab26352",
-   "metadata": {},
+   "id": "1f91402a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Identifying Terms\n",
     "\n",
@@ -1432,8 +1669,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e232448",
-   "metadata": {},
+   "id": "2d7a8e36",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n",
@@ -1443,16 +1682,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15cdad60",
-   "metadata": {},
+   "id": "4c756ca2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "resulting in"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "7b857d11",
-   "metadata": {},
+   "id": "908f782e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n",
@@ -1462,16 +1705,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7ba76a4",
-   "metadata": {},
+   "id": "f12152da",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and in the limit $m\\rightarrow \\infty$ we obtain"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "27abee5c",
-   "metadata": {},
+   "id": "85dd290d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n",
@@ -1481,8 +1728,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "450fbae6",
-   "metadata": {},
+   "id": "57631d10",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which is the normal distribution with variance\n",
     "$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n",
@@ -1491,8 +1740,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "583a9a42",
-   "metadata": {},
+   "id": "2d4d5ccb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Wrapping it up\n",
     "\n",
@@ -1508,8 +1759,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdd93e78",
-   "metadata": {},
+   "id": "a29c8551",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma_m=\n",
@@ -1519,8 +1772,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dfe218b6",
-   "metadata": {},
+   "id": "6509ba36",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The latter is true only if the average value is known exactly. This is obtained in the limit\n",
     "$m\\rightarrow \\infty$  only. Because the mean and the variance are measured quantities we obtain \n",
@@ -1529,8 +1784,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d3fd1f7",
-   "metadata": {},
+   "id": "733307b1",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sigma_m\\approx \n",
@@ -1540,8 +1797,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b8a47f4",
-   "metadata": {},
+   "id": "a69b7331",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In many cases however the above estimate for the standard deviation,\n",
     "in particular if correlations are strong, may be too simplistic. Keep\n",
@@ -1558,8 +1817,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c57ef602",
-   "metadata": {},
+   "id": "ced659da",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Confidence Intervals\n",
     "\n",
@@ -1579,8 +1840,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdea97fa",
-   "metadata": {},
+   "id": "2c0d0a71",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Standard Approach based on the Normal Distribution\n",
     "\n",
@@ -1592,8 +1855,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc3abe4",
-   "metadata": {},
+   "id": "d3a4d693",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\left(\\mu_{\\beta}\\pm \\frac{z\\sigma_{\\beta}}{\\sqrt{n}}\\right),\n",
@@ -1602,8 +1867,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1679ffac",
-   "metadata": {},
+   "id": "3ed3d852",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $z$ defines the level of certainty (or confidence). For a normal\n",
     "distribution typical parameters are $z=2.576$ which corresponds to a\n",
@@ -1620,8 +1887,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc2481bb",
-   "metadata": {},
+   "id": "e826e70b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods: Bootstrap background\n",
     "\n",
@@ -1638,8 +1907,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a18c7fde",
-   "metadata": {},
+   "id": "10b5d4d5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods: More Bootstrap background\n",
     "\n",
@@ -1660,8 +1931,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4af5f00a",
-   "metadata": {},
+   "id": "1645ce3c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods: Bootstrap approach\n",
     "\n",
@@ -1679,8 +1952,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f40537a7",
-   "metadata": {},
+   "id": "4986483a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Resampling methods: Bootstrap steps\n",
     "\n",
@@ -1707,8 +1982,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6459716",
-   "metadata": {},
+   "id": "fe853f3b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Code example for the Bootstrap method\n",
     "\n",
@@ -1729,8 +2006,11 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "61ebf590",
-   "metadata": {},
+   "id": "81ec18f8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "%matplotlib inline\n",
@@ -1765,16 +2045,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bcfb7ee",
-   "metadata": {},
+   "id": "f0b5b588",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We see that our new variance and from that the standard deviation, agrees with the central limit theorem."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bb8e2e4c",
-   "metadata": {},
+   "id": "262a95e8",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Plotting the Histogram"
    ]
@@ -1782,8 +2066,11 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "4d167410",
-   "metadata": {},
+   "id": "d235b516",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# the histogram of the bootstrapped data (normalized data if density = True)\n",
@@ -1799,8 +2086,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b04a99c",
-   "metadata": {},
+   "id": "c1620bb7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The bias-variance tradeoff\n",
     "\n",
@@ -1815,8 +2104,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df8b5b83",
-   "metadata": {},
+   "id": "fd3bd4b5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n",
@@ -1825,8 +2116,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b1cae6d",
-   "metadata": {},
+   "id": "4a129d86",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n",
     "\n",
@@ -1840,8 +2133,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "347294eb",
-   "metadata": {},
+   "id": "ff57b405",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n",
@@ -1850,16 +2145,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0536e454",
-   "metadata": {},
+   "id": "5a13919e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We can rewrite this as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4edf3a9e",
-   "metadata": {},
+   "id": "45d4a7b6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n",
@@ -1868,8 +2167,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "95b5e144",
-   "metadata": {},
+   "id": "c837442b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "The three terms represent the square of the bias of the learning\n",
     "method, which can be thought of as the error caused by the simplifying\n",
@@ -1883,8 +2184,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4ec0202c",
-   "metadata": {},
+   "id": "4b3c7b8e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n",
@@ -1893,16 +2196,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3729c884",
-   "metadata": {},
+   "id": "7e6f977d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "09d292c0",
-   "metadata": {},
+   "id": "adeab0fd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n",
@@ -1911,16 +2218,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9393b969",
-   "metadata": {},
+   "id": "63b18db5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "which, using the abovementioned expectation values can be rewritten as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "31400952",
-   "metadata": {},
+   "id": "9c7eb00d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n",
@@ -1929,16 +2240,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fab9fd56",
-   "metadata": {},
+   "id": "c3f4530b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f6bbceee",
-   "metadata": {},
+   "id": "90792236",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## A way to Read the Bias-Variance Tradeoff\n",
     "\n",
@@ -1951,8 +2266,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2486e572",
-   "metadata": {},
+   "id": "d73c7cd4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Example code for Bias-Variance tradeoff"
    ]
@@ -1960,8 +2277,11 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "af100ade",
-   "metadata": {},
+   "id": "58124207",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
@@ -2022,105 +2342,23 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4b4ea82",
-   "metadata": {},
+   "id": "4b4e7bf5",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Understanding what happens"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "id": "13bb228b",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 0\n",
-      "Error: 0.32149601703519115\n",
-      "Bias^2: 0.3123314713548606\n",
-      "Var: 0.009164545680330616\n",
-      "0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912\n",
-      "Polynomial degree: 1\n",
-      "Error: 0.08426840630693412\n",
-      "Bias^2: 0.0796891867672603\n",
-      "Var: 0.004579219539673834\n",
-      "0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
-      "Polynomial degree: 2\n",
-      "Error: 0.10398646080125037\n",
-      "Bias^2: 0.10077114273548984\n",
-      "Var: 0.0032153180657605116\n",
-      "0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036\n",
-      "Polynomial degree: 3\n",
-      "Error: 0.06547790180152352\n",
-      "Bias^2: 0.062082386342319454\n",
-      "Var: 0.0033955154592040923\n",
-      "0.06547790180152352 >= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355\n",
-      "Polynomial degree: 4\n",
-      "Error: 0.06844519414009445\n",
-      "Bias^2: 0.06453579006728322\n",
-      "Var: 0.003909404072811221\n",
-      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n",
-      "Polynomial degree: 5\n",
-      "Error: 0.05227921801205679\n",
-      "Bias^2: 0.04818727730430286\n",
-      "Var: 0.004091940707753925\n",
-      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n",
-      "Polynomial degree: 6\n",
-      "Error: 0.03781367141738902\n",
-      "Bias^2: 0.03365768507152769\n",
-      "Var: 0.0041559863458613296\n",
-      "0.03781367141738902 >= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902\n",
-      "Polynomial degree: 7\n",
-      "Error: 0.027609773491022394\n",
-      "Bias^2: 0.022999498260366198\n",
-      "Var: 0.004610275230656182\n",
-      "0.027609773491022394 >= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238\n",
-      "Polynomial degree: 8\n",
-      "Error: 0.017355848195593312\n",
-      "Bias^2: 0.010331721306655165\n",
-      "Var: 0.007024126888938144\n",
-      "0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n",
-      "Polynomial degree: 9\n",
-      "Error: 0.026605727637184558\n",
-      "Bias^2: 0.010018312644139219\n",
-      "Var: 0.016587414993045335\n",
-      "0.026605727637184558 >= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554\n",
-      "Polynomial degree: 10\n",
-      "Error: 0.021592704588021178\n",
-      "Bias^2: 0.010516485576646504\n",
-      "Var: 0.01107621901137467\n",
-      "0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n",
-      "Polynomial degree: 11\n",
-      "Error: 0.07160048164232538\n",
-      "Bias^2: 0.014436800088896381\n",
-      "Var: 0.05716368155342902\n",
-      "0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n",
-      "Polynomial degree: 12\n",
-      "Error: 0.11547777218876518\n",
-      "Bias^2: 0.016285782696017142\n",
-      "Var: 0.09919198949274803\n",
-      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n",
-      "Polynomial degree: 13\n",
-      "Error: 0.2284246870217162\n",
-      "Bias^2: 0.01975416527168255\n",
-      "Var: 0.20867052175003364\n",
-      "0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": 4,
+   "id": "47b138a9",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -2172,8 +2410,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c50c02c2",
-   "metadata": {},
+   "id": "37b66761",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Summing up\n",
     "\n",
@@ -2208,8 +2448,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16a69276",
-   "metadata": {},
+   "id": "5b5c601e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Another Example from Scikit-Learn's Repository"
    ]
@@ -2217,8 +2459,11 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "06c4dbd1",
-   "metadata": {},
+   "id": "9bc32416",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\"\"\"\n",
@@ -2296,8 +2541,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd22f4e5",
-   "metadata": {},
+   "id": "eb934dbe",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Various steps in cross-validation\n",
     "\n",
@@ -2319,8 +2566,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d78f931",
-   "metadata": {},
+   "id": "c65f802b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Cross-validation in brief\n",
     "\n",
@@ -2345,8 +2594,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3e7ddb7",
-   "metadata": {},
+   "id": "9accabd4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Code Example for Cross-validation and $k$-fold Cross-validation\n",
     "\n",
@@ -2356,8 +2607,11 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "d7f6476c",
-   "metadata": {},
+   "id": "d5ed3f5c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import numpy as np\n",
@@ -2453,8 +2707,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29f97a19",
-   "metadata": {},
+   "id": "db1976f4",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## More examples on bootstrap and cross-validation and errors"
    ]
@@ -2462,8 +2718,11 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "ea778a04",
-   "metadata": {},
+   "id": "3c35540c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Common imports\n",
@@ -2548,16 +2807,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5bc26cd",
-   "metadata": {},
+   "id": "e60fabdf",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Note that we kept the intercept column in the fitting here. This means that we need to set the **intercept** in the call to the **Scikit-Learn** function as **False**. Alternatively, we could have set up the design matrix $X$ without the first column of ones."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4bbb49da",
-   "metadata": {},
+   "id": "9b6750d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## The same example but now with cross-validation\n",
     "\n",
@@ -2567,8 +2830,11 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "89f26923",
-   "metadata": {},
+   "id": "5e6b91e1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "# Common imports\n",
@@ -2642,8 +2908,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d39d1c9",
-   "metadata": {},
+   "id": "e83d7b10",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "## Notes on scaling with examples\n",
     "\n",
@@ -2667,8 +2935,11 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "2470e6f1",
-   "metadata": {},
+   "id": "73807393",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
@@ -2737,8 +3008,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e229ae7",
-   "metadata": {},
+   "id": "b09d20a2",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In this example we do not include the intercept and we scale the data by subtracting the mean values. This follows the discussion in the [lecture material](https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#more-on-rescaling-data).\n",
     "see also the weekly slides [for week 36](https://compphysics.github.io/MachineLearning/doc/pub/week36/html/._week36-bs029.html).\n",
@@ -2755,8 +3028,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d43d360",
-   "metadata": {},
+   "id": "ef1cec97",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\beta_0, \\beta_1, ... , \\beta_{p-1}) = \\frac{1}{n}\\sum_{i=0}^{n} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij}\\beta_j\\right)^2,.\n",
@@ -2765,8 +3040,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "777c97c9",
-   "metadata": {},
+   "id": "e43c422b",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Recall also that we use the squared value. This expression can lead to an\n",
     "increased penalty for higher differences between predicted and\n",
@@ -2780,8 +3057,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f464bb58",
-   "metadata": {},
+   "id": "852577bc",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial C}{\\partial \\beta_j} = 0,\n",
@@ -2790,16 +3069,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "624b1d2c",
-   "metadata": {},
+   "id": "4edd229a",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "for all $j$. For $\\beta_0$ we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b872d2db",
-   "metadata": {},
+   "id": "bb93d608",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\frac{\\partial C}{\\partial \\beta_0} = -\\frac{2}{n}\\sum_{i=0}^{n-1} \\left(y_i - \\beta_0 - \\sum_{j=1}^{p-1} X_{ij} \\beta_j\\right).\n",
@@ -2808,16 +3091,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6dd0d07",
-   "metadata": {},
+   "id": "5ef162e3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Multiplying away the constant $2/n$, we obtain"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2f7c34ed",
-   "metadata": {},
+   "id": "b7c5467d",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\sum_{i=0}^{n-1} \\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} \\sum_{j=1}^{p-1} X_{ij} \\beta_j.\n",
@@ -2826,8 +3113,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e06d400",
-   "metadata": {},
+   "id": "493c75d6",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Let us specialize first to the case where we have only two parameters $\\beta_0$ and $\\beta_1$.\n",
     "Our result for $\\beta_0$ simplifies then to"
@@ -2835,8 +3124,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bad7ab31",
-   "metadata": {},
+   "id": "862f2222",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "n\\beta_0 = \\sum_{i=0}^{n-1}y_i - \\sum_{i=0}^{n-1} X_{i1} \\beta_1.\n",
@@ -2845,16 +3136,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b11fd1d0",
-   "metadata": {},
+   "id": "e0d0a4e0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We obtain then"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e18f186d",
-   "metadata": {},
+   "id": "73d327de",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\beta_1\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1}.\n",
@@ -2863,16 +3158,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "002f906f",
-   "metadata": {},
+   "id": "8be27cbd",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If we define"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "4b2ce40a",
-   "metadata": {},
+   "id": "d49a9bac",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mu_{\\boldsymbol{x}_1}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{i1},\n",
@@ -2881,16 +3180,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f6da2aa",
-   "metadata": {},
+   "id": "dd964823",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "and the mean value of the outputs as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "f8705ff4",
-   "metadata": {},
+   "id": "09a87e67",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mu_y=\\frac{1}{n}\\sum_{i=0}^{n-1}y_i,\n",
@@ -2899,16 +3202,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "481c0458",
-   "metadata": {},
+   "id": "9b8797a0",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "de837aab",
-   "metadata": {},
+   "id": "30aeafdb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_0 = \\mu_y - \\beta_1\\mu_{\\boldsymbol{x}_1}.\n",
@@ -2917,16 +3224,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c151900",
-   "metadata": {},
+   "id": "dc867cbb",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "In the general case with more parameters than $\\beta_0$ and $\\beta_1$, we have"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6df6dc61",
-   "metadata": {},
+   "id": "f154321e",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\frac{1}{n}\\sum_{i=0}^{n-1}\\sum_{j=1}^{p-1} X_{ij}\\beta_j.\n",
@@ -2935,16 +3246,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d6150d9",
-   "metadata": {},
+   "id": "6015f267",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "We can rewrite the latter equation as"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "904ad761",
-   "metadata": {},
+   "id": "f181e88f",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\beta_0 = \\frac{1}{n}\\sum_{i=0}^{n-1}y_i - \\sum_{j=1}^{p-1} \\mu_{\\boldsymbol{x}_j}\\beta_j,\n",
@@ -2953,16 +3268,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e427a81",
-   "metadata": {},
+   "id": "a6e6c0e7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where we have defined"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "d40dc5aa",
-   "metadata": {},
+   "id": "708652ea",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\mu_{\\boldsymbol{x}_j}=\\frac{1}{n}\\sum_{i=0}^{n-1} X_{ij},\n",
@@ -2971,8 +3290,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "259f8a07",
-   "metadata": {},
+   "id": "b360788c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "the mean value for all elements of the column vector $\\boldsymbol{x}_j$.\n",
     "\n",
@@ -2981,8 +3302,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be7a32a4",
-   "metadata": {},
+   "id": "8f473602",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "C(\\boldsymbol{\\beta}) = (\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta})^T(\\boldsymbol{\\tilde{y}} - \\tilde{X}\\boldsymbol{\\beta}).\n",
@@ -2991,16 +3314,20 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1723452",
-   "metadata": {},
+   "id": "70f518a7",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "If we minimize with respect to $\\boldsymbol{\\beta}$ we have then"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "a8979b1c",
-   "metadata": {},
+   "id": "674d02d9",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X})^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}},\n",
@@ -3009,8 +3336,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c9b9a4d",
-   "metadata": {},
+   "id": "6715261c",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "where $\\boldsymbol{\\tilde{y}} = \\boldsymbol{y} - \\overline{\\boldsymbol{y}}$\n",
     "and $\\tilde{X}_{ij} = X_{ij} - \\frac{1}{n}\\sum_{k=0}^{n-1}X_{kj}$.\n",
@@ -3020,8 +3349,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6daf72ea",
-   "metadata": {},
+   "id": "17600ee3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "$$\n",
     "\\hat{\\boldsymbol{\\beta}} = (\\tilde{X}^T\\tilde{X} + \\lambda I)^{-1}\\tilde{X}^T\\boldsymbol{\\tilde{y}}.\n",
@@ -3030,8 +3361,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23161172",
-   "metadata": {},
+   "id": "a8c6f068",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Now we try to implement this."
    ]
@@ -3039,8 +3372,11 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "9b9f556f",
-   "metadata": {},
+   "id": "1d89f80d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "\n",
@@ -3109,8 +3445,10 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0a158df",
-   "metadata": {},
+   "id": "522668c3",
+   "metadata": {
+    "editable": true
+   },
    "source": [
     "Finally, instead of using our own function we repeat the same example\n",
     "using the **standardscaler** functionality of the library\n",
@@ -3120,8 +3458,11 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "911c4d30",
-   "metadata": {},
+   "id": "9954bcc1",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
    "outputs": [],
    "source": [
     "from sklearn import linear_model\n",
@@ -3186,25 +3527,7 @@
    ]
   }
  ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.10"
-  }
- },
+ "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/src/week37/week37.do.txt b/doc/src/week37/week37.do.txt
index e6a99ce9d..db84c49b0 100644
--- a/doc/src/week37/week37.do.txt
+++ b/doc/src/week37/week37.do.txt
@@ -1,6 +1,6 @@
 TITLE: Week 37: Statistical interpretations and Resampling Methods
 AUTHOR: Morten Hjorth-Jensen {copyright, 1999-present|CC BY-NC} at Department of Physics, University of Oslo & Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University
-DATE: today
+DATE: September 9, 2024
 
 
 # todo add link to videos and add link to Van Wieringens notes
@@ -10,7 +10,7 @@ DATE: today
 
 
 
-!bblock Material for the lecture on Thursday September 9
+!bblock Material for the lecture on Monday September 9
 #  * "Video of Lecture":"https://youtu.be/YOBBr_toYxc"
 #  * "Whiteboard notes":"https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf"
   * Resampling techniques, Bootstrap and cross validation and bias-variance tradeoff
@@ -25,7 +25,7 @@ DATE: today
 
 !bblock  Material for the active learning sessions on Tuesday and Wednesday
   * Calculations of expectation values
-  * Exercise for week 37
+  * Exercise set for week 37
   * Work on project 1
   * See also additional note on scaling (jupyter-notebook) sent separately. This will be discussed during the first hour of each session. This note is added at the end of these slides.
   * For more discussions of Ridge regression and calculation of averages, "Wessel van Wieringen's":"https://arxiv.org/abs/1509.09169" article is highly recommended.