Update documentation

Author: abikesa

_sources/index.ipynb

@@ -40,8 +40,6 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "\n",
-    "\n",
     "<Details>\n",
     "    <Summary></Summary>\n",
     "\n",
@@ -68,7 +66,39 @@
     "        <p>Is the nextoken groove-based or emotional/harmonic/narrative-based? Teddy Riley or Kenny Edmonds?</p>\n",
     "        <p>You might have guessed it already: groove-based tokens have more predictive accuracy of the overall arc</p>\n",
     "        <p>But for more personalized, resonant, and intimate arcs, look no further than Mr. Face</p>\n",
-    "</Details>\n",
+    "</Details>"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Life as `raw` noise is chaotic and unstructured—just random inputs, static, or things that happen without inherent meaning. Art, by contrast, takes that rawness and `filters` it, shaping it into something intentional, structured, and expressive, much like turning noise into music. \n",
+    "\n",
+    "Natural static could be seen as the undifferentiated flow of events, the overwhelming barrage of sensory information, emotions, and experiences. Humans, through art and creativity, organize that chaos, applying rhythm, harmony, or form to produce something coherent and impactful—like music that arises from dissonance and finds resolution. \n",
+    "\n",
+    "This makes art an act of imposing order on the universe's randomness, a way of finding meaning in the overwhelming noise of existence. It's not just about control, though—sometimes art embraces the chaos, too, letting it pulse through the music or the painting or the writing. It’s the interplay between that noise and the human impulse to make sense of it that creates the most powerful expressions.\n",
+    "\n",
+    "Similarly, real-world data is just variance—random, scattered points, much like the raw noise of life. But information, as defined in statistical terms, is the structure or meaning we extract from that variance. The Fisher Information $\\mathcal{I}(\\theta)$ quantifies how much information a dataset contains about a parameter $\\theta$, where:\n",
+    "\n",
+    "$$\n",
+    "\\mathcal{I}(\\theta) = -\\mathbb{E} \\left[ \\frac{\\partial^2 \\log L(\\theta)}{\\partial \\theta^2} \\right]\n",
+    "$$\n",
+    "\n",
+    "This information isn't readily apparent in the raw data but must be \"Coxed-out\" (a nod to Cox regression and proportional hazards models) by first curating the data—cleaning, selecting, and organizing it—and then analyzing it through statistical models. After this curation and analysis, we can make inferences about the underlying parameters that govern the system we're studying. It's an iterative process of refining the signal from the noise, much like transforming static into music, to reveal meaningful patterns and insights.\n",
+    "\n",
+    "We then tranform these parameters into an absolute or relative risk to inform thresholds in algorithms or lines of further research based on effect-sizes.\n",
+    "\n",
+    "For now we'll focus on informing thresholds for decision making -- at an individualized level"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "\n",
+    "\n",
     "\n",
     "```{tip}\n",
     "In the mountains the shortest way is from peak to peak, but for that route thou must have long legs. Proverbs should be peaks, and those spoken to should be big and tall.{cite}`nietzsche1883zarathustra`\n",

index.html

@@ -456,7 +456,17 @@ <h2>Imputation, not Imitation<a class="headerlink" href="#imputation-not-imitati
         <p>Is the nextoken groove-based or emotional/harmonic/narrative-based? Teddy Riley or Kenny Edmonds?</p>
         <p>You might have guessed it already: groove-based tokens have more predictive accuracy of the overall arc</p>
         <p>But for more personalized, resonant, and intimate arcs, look no further than Mr. Face</p>
-</Details>
+</Details><p>Life as <code class="docutils literal notranslate"><span class="pre">raw</span></code> noise is chaotic and unstructured—just random inputs, static, or things that happen without inherent meaning. Art, by contrast, takes that rawness and <code class="docutils literal notranslate"><span class="pre">filters</span></code> it, shaping it into something intentional, structured, and expressive, much like turning noise into music.</p>
+<p>Natural static could be seen as the undifferentiated flow of events, the overwhelming barrage of sensory information, emotions, and experiences. Humans, through art and creativity, organize that chaos, applying rhythm, harmony, or form to produce something coherent and impactful—like music that arises from dissonance and finds resolution.</p>
+<p>This makes art an act of imposing order on the universe’s randomness, a way of finding meaning in the overwhelming noise of existence. It’s not just about control, though—sometimes art embraces the chaos, too, letting it pulse through the music or the painting or the writing. It’s the interplay between that noise and the human impulse to make sense of it that creates the most powerful expressions.</p>
+<p>Similarly, real-world data is just variance—random, scattered points, much like the raw noise of life. But information, as defined in statistical terms, is the structure or meaning we extract from that variance. The Fisher Information <span class="math notranslate nohighlight">\(\mathcal{I}(\theta)\)</span> quantifies how much information a dataset contains about a parameter <span class="math notranslate nohighlight">\(\theta\)</span>, where:</p>
+<div class="math notranslate nohighlight">
+\[
+\mathcal{I}(\theta) = -\mathbb{E} \left[ \frac{\partial^2 \log L(\theta)}{\partial \theta^2} \right]
+\]</div>
+<p>This information isn’t readily apparent in the raw data but must be “Coxed-out” (a nod to Cox regression and proportional hazards models) by first curating the data—cleaning, selecting, and organizing it—and then analyzing it through statistical models. After this curation and analysis, we can make inferences about the underlying parameters that govern the system we’re studying. It’s an iterative process of refining the signal from the noise, much like transforming static into music, to reveal meaningful patterns and insights.</p>
+<p>We then tranform these parameters into an absolute or relative risk to inform thresholds in algorithms or lines of further research based on effect-sizes.</p>
+<p>For now we’ll focus on informing thresholds for decision making – at an individualized level</p>
 <div class="admonition tip">
 <p class="admonition-title">Tip</p>
 <p>In the mountains the shortest way is from peak to peak, but for that route thou must have long legs. Proverbs should be peaks, and those spoken to should be big and tall.<span id="id2"><sup><a class="reference internal" href="act3/part3/part3_3.html#id11" title="Friedrich Nietzsche. Thus spoke zarathustra: a book for all and none. 1883. Chapter VII, Reading and Writing. “In the mountains the shortest way is from peak to peak, but for that route thou must have long legs. Proverbs should be peaks, and those spoken to should be big and tall.”. URL: https://www.gutenberg.org/files/1998/1998-h/1998-h.htm.">2</a></sup></span></p>