Lectures/Lecture03/3dasm_Lecture3.ipynb

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    "<img src=../figures/Brown_logo.svg width=50%>\n",
    "\n",
    "## Data-Driven Design & Analyses of Structures & Materials (3dasm)\n",
    "\n",
    "## Lecture 3\n",
    "\n",
    "### Miguel A. Bessa | <a href = \"mailto: miguel_bessa@brown.edu\">miguel_bessa@brown.edu</a>  | Associate Professor"
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    "**What:** A lecture of the \"3dasm\" course\n",
    "\n",
    "**Where:** This notebook comes from this [repository](https://github.com/bessagroup/3dasm_course)\n",
    "\n",
    "**Reference for entire course:** Murphy, Kevin P. *Probabilistic machine learning: an introduction*. MIT press, 2022. Available online [here](https://probml.github.io/pml-book/book1.html)\n",
    "\n",
    "**How:** We try to follow Murphy's book closely, but the sequence of Chapters and Sections is different. The intention is to use notebooks as an introduction to the topic and Murphy's book as a resource.\n",
    "* If working offline: Go through this notebook and read the book.\n",
    "* If attending class in person: listen to me (!) but also go through the notebook in your laptop at the same time. Read the book.\n",
    "* If attending lectures remotely: listen to me (!) via Zoom and (ideally) use two screens where you have the notebook open in 1 screen and you see the lectures on the other. Read the book."
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    "**Optional reference (the \"bible\" by the \"bishop\"... pun intended 😆) :** Bishop, Christopher M. *Pattern recognition and machine learning*. Springer Verlag, 2006.\n",
    "\n",
    "**References/resources to create this notebook:**\n",
    "* [Car figure](https://korkortonline.se/en/theory/reaction-braking-stopping/)\n",
    "\n",
    "Apologies in advance if I missed some reference used in this notebook. Please contact me if that is the case, and I will gladly include it here."
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    "## **OPTION 1**. Run this notebook **locally in your computer**:\n",
    "1. Confirm that you have the '3dasm' mamba (or conda) environment (see Lecture 1).\n",
    "2. Go to the 3dasm_course folder in your computer and pull the last updates of the [repository](https://github.com/bessagroup/3dasm_course):\n",
    "```\n",
    "git pull\n",
    "```\n",
    "    - Note: if you can't pull the repo due to conflicts (and you can't handle these conflicts), use this command (with **caution**!) and your repo becomes the same as the one online:\n",
    "```\n",
    "git reset --hard origin/main\n",
    "```\n",
    "3. Open command window and load jupyter notebook (it will open in your internet browser):\n",
    "```\n",
    "jupyter notebook\n",
    "```\n",
    "5. Open notebook of this Lecture and choose the '3dasm' kernel."
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    "## **OPTION 2**. Use **Google's Colab** (no installation required, but times out if idle):\n",
    "\n",
    "1. go to https://colab.research.google.com\n",
    "2. login\n",
    "3. File > Open notebook\n",
    "4. click on Github (no need to login or authorize anything)\n",
    "5. paste the git link: https://github.com/bessagroup/3dasm_course\n",
    "6. click search and then click on the notebook for this Lecture."
   ]
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    "# Basic plotting tools needed in Python.\n",
    "\n",
    "import matplotlib.pyplot as plt # import plotting tools to create figures\n",
    "import numpy as np # import numpy to handle a lot of things!\n",
    "from IPython.display import display, Math # to print with Latex math\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\" # render higher resolution images in the notebook\n",
    "plt.rcParams[\"figure.figsize\"] = (8,4) # rescale figure size appropriately for slides"
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    "## Outline for today\n",
    "\n",
    "* Probability: multivariate models\n",
    "    - Introduction to joint pdfs\n",
    "    - Marginal pdfs\n",
    "    - Conditional pdfs\n",
    "\n",
    "**Reading material**: This notebook + Chapter 3 (until Section 3.3)"
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    "# This cell is hidden during presentation. It's just to define a function to plot the governing model of\n",
    "# the car stopping distance problem. Defining a function that creates a plot allows to repeatedly run\n",
    "# this function on cells used in this notebook.\n",
    "def car_fig(ax):\n",
    "    x = np.linspace(3, 83, 1000)\n",
    "    mu_z = 1.5; sigma_z = 0.5;  # parameters of the \"true\" p(z)\n",
    "    mu_y = mu_z*x + 0.1*(x**2) # Recall: E[z*x+0.1*x^2] = E[z]*E[x]+0.1*E[x^2]\n",
    "    sigma_y = np.sqrt( sigma_z**2*x**2 ) # Recall: V[z*x+x^2] = V[z*x]+V[x^2]=...=sigma_z^2+mu_x^2\n",
    "    ax.set_xlabel(\"x (m/s)\", fontsize=20) # create x-axis label with font size 20\n",
    "    ax.set_ylabel(\"y (m)\", fontsize=20) # create y-axis label with font size 20\n",
    "    ax.set_title(\"Car stopping distance problem\", fontsize=20); # create title with font size 20\n",
    "    ax.plot(x, mu_y, 'k:', label=\"Governing model $\\mu_y$\")\n",
    "    ax.fill_between(x, mu_y - 1.9600 * sigma_y,\n",
    "                    mu_y + 1.9600 * sigma_y,\n",
    "                    color='k', alpha=0.2,\n",
    "                    label='95% confidence interval ($\\mu_y \\pm 1.96\\sigma_y$)') # plot 95% credence interval\n",
    "    ax.legend(fontsize=15)"
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    "## Consider an even simpler car distance problem\n",
    "\n",
    "<img src=\"../figures/reaction-braking-stopping.svg\" title=\"Car stopping distance\" width=\"25%\" align=\"right\">\n",
    "<br></br>\n",
    "For now, let's focus on the case where every driver is going at the same velocity $x=75$ m/s.\n",
    "\n",
    "Then, the governing model is even simpler:\n",
    "\n",
    "${\\color{red}y} = {\\color{blue}z}\\cdot 75 + 0.1\\cdot 75^2 = 75 {\\color{blue}z} + 562.5$\n",
    "\n",
    "- ${\\color{red}y}$ is the **output**: the car stopping distance (in meters)\n",
    "- ${\\color{blue}z}$ is a hidden variable: an <a title=\"random variable\">rv</a> representing the driver's reaction time (in seconds)\n",
    "\n",
    "where $z \\sim \\mathcal{N}(\\mu_z=1.5,\\sigma_z^2=0.5^2)$"
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stopping distance for x=75 m/s is: [715.51472401]\n"
     ]
    }
   ],
   "source": [
    "# Let's make different observations\n",
    "from scipy.stats import norm # import the normal dist, as we learned before!\n",
    "# Define our car stopping distance function\n",
    "def samples_y(N_samples,x): # observations/measurements/samples of car stop. dist. prob.\n",
    "    mu_z = 1.5; sigma_z = 0.5;  # parameters of the \"true\" p(z)\n",
    "    samples_z = norm.rvs(mu_z, sigma_z, size=N_samples) # randomly draw samples from the normal dist.\n",
    "    samples_y = samples_z*x + 0.1*x**2 # compute the stopping distance for samples of z\n",
    "    return samples_y # return samples of y\n",
    "\n",
    "print(\"Stopping distance for x=75 m/s is:\",samples_y(N_samples=1,x=75)) # drawing random samples of y"
   ]
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   "source": [
    "### Let's estimate the confidence interval for $x=75$ m/s\n",
    "\n",
    "- Let's estimate the confidence interval (error bar) using samples of different sizes.\n",
    "\n",
    "- We will also overlay this with the plot for the governing model (shown in Lecture 2)"
   ]
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empirical mean[y] is 676.3637594389137 (real mean[y]=675)\n",
      "Empirical std[y] is 36.99648339461671 (real std[y]=37.5)\n"
     ]
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KbZcfNEXLli2Lr7/+Om666abYY489kn+QnHfeeSn9vvrqqyguLo4I+UHm+umnn+Lcc8+NiIjrr78+eVfJNXH+oKl4/PHHY/PNN49WrVpFmzZtYuONN44RI0bEuHHjKtxHfpDp3n333YhYdTGyTZs28a9//Su23HLL6NChQ/Tv3z86dOgQm2yySfz1r39N+ZF1KTlCU7RkyZJ46qmnIiKiV69eaX/gKTfIdEcddVS0bds2Ilb97VH693ZZkyZNiueeey4iIo4++uhk/wg5AgBNSVU+PwNVV5s5taZrz9BUrG1ezZs3LyZMmBAnn3xyXHfddRER0bFjxzjmmGNqO1RoFKqbU6NHj47nn38+1ltvvbjxxhvrIUJofGpyrjrxxBOja9eukZeXFx07dowdd9wxfv/73ydnY4SmrCo59dFHHyUL5rfccstYtGhRnHfeedGxY8fo2bNn9OnTJ9q1axdDhgyJ119/vR6jh3VTbXxf8cQTT8SyZcsiIuK4446LrKys2gwRGpWq5tRvfvObiFhVBHznnXem7XPNNdeU6w9NUVXyKj8/P7n8888/VzhWIpGIRYsWRcSqGzFNmTKldoOthoorkmEds2LFiuQdXrp3715p3/XWWy9at24dS5cujWnTptVHeLBOmz59enJ5TfnTo0eP5LL8obErKSmJP//5z8n1I444olwf+UFT8eCDD8aJJ55Y4fZLLrkkjj766JQ2+UFTcNFFF8WsWbNil112iZNPPrnK+8kPmoqyhVsREVOmTIkpU6bEww8/HMOHD48HH3ww2rVrl9JHfpDJSkpK4osvvoiIVT/wPPfcc+PWW28t1++rr76K3/3ud/HUU0/Fc889F+3bt09ukyM0Rf/5z39i6dKlERFx7LHHpr2QLzfIdB07doxRo0bFUUcdFW+//XYMGjQozjvvvOjfv38sWbIk3n777bjxxhujoKAgfvGLX5T7MbQcAYCmoyqfn4Gqq62c+uijj5I3wNpyyy0V1NOk1SSv9txzz5SbUpTVsWPHeOqpp1K+R4WmpDo5tXDhwuRkCX/+85+jU6dO9REiNDo1OVeVLfCdP39+zJ8/P95777248cYb4+abb47TTz+9rsKFdV5Vcqrs70tKSkpiu+22i6+//jqlT0FBQbz66qvx2muvxciRI+Piiy+u28BhHVYb31es7Qz3kEmqmlMnnXRSvPXWW/Hwww/HWWedFR988EEcfPDB0aVLl/jhhx9i1KhRMWbMmIiIuPzyy2Pvvfeur0OAdU5V8qrs9+RvvPFGDBw4MO1YkyZNiiVLliTXf/jhhzVOJlFXzFBPo7F48eLkctm7V1SkdevWEREpyQZNVXXypzR3IuQPjd/f/va3mDhxYkREHHrooWk/nMkPmrptttkmJk6cGCNHjiz3R478INONHz8+7r333sjJyYk777yzWl9Kyw8yXatWreLXv/513HPPPTF+/PiYNGlSvPzyy3H55ZdHhw4dIiJizJgxMWzYsCgsLEzZV36QyX7++ecoKSmJiIhPPvkkbr311ujSpUs88sgjsWDBgli2bFm88cYbseOOO0ZExDvvvBMnnXRSyhhyhKaoKhfy5QZNwcEHHxwffPBBnHLKKfHhhx/GiBEjYqeddoohQ4bEVVddFa1atYqbb745xo8fHxtssEHKvnIEAJoOP4SF2lUbObVy5co45ZRTori4OCIiOaM2NFW1ea767W9/G5MnT45dd911bcOCRqs6OfW73/0uZs+eHTvttFOceuqpdR0aNFrVyau+ffvG//f//X/xn//8JyZOnBgTJ06M0aNHx+GHHx5ZWVmxYsWK+M1vfhN33313XYcN66yq5NSCBQuSy9dff318/fXXsd9++8XEiRNjxYoVMWfOnLjjjjuiXbt2kUgk4pJLLomxY8fWeeywrlrbv6t++OGH5E3Ldt5559hoo41qLTZojKqaU82aNYuHHnooHn/88dh6663j3nvvjYMPPjgGDRoUhx12WIwZMyYGDx4cr7zySlx77bX1ETqss6qSV/vvv3/k5Kya8/2mm25KTqZdVklJSVx++eUpbWV/A1PfFNTTaKxYsSK5nJeXt8b+zZs3j4iI5cuX11lM0FhUJ39KcydC/tC4vfHGG3HJJZdERETnzp3jjjvuSNtPftBUDB8+PD755JP45JNPYuLEifHvf/87DjnkkPjwww/jqKOOimeffbbcPvKDTFZQUBCnnXZaJBKJOP/882PAgAHV2l9+kOlmzJgR//73v+OUU06JXXfdNbbZZpsYMmRIXHvttfHZZ5/FtttuGxGrPnOt/jlLfpDJSu+4GrHqvd6qVasYN25cHHPMMbHeeutFy5YtY/fdd4///ve/sfXWW0dExFNPPRXvvfdeyn6l5AhNwfTp05Ozuuy4447Rv3//tP3kBk1BQUFBPPzwwzF27NhIJBLlts+ePTseeeSRePXVV8ttkyMA0DRU9fMzUDW1lVNnn312vP/++xERMWLEiDjooINqK0RodGqaVw888EB88skn8fHHH8ebb74ZN910U2y88cZx2223xYknnhizZ8+uw6hh3VWdnHrzzTfj/vvvr9EN46EpqU5eHXLIITFlypT4y1/+EoceemgMGjQoBg0aFEceeWQ89thj8fTTT0dubm5ERJx//vkxa9as+jgEWKdUNadWv5Y+ZMiQePbZZ2PQoEHRvHnz6NSpU/zmN7+JZ599NrKzV5UxXXrppWmvl0Cmq43vKx555JFk/rgpJ01ddXNq8uTJ8fDDD8cnn3ySdvuECRPivvvuixkzZtR2qNBoVDWvevToEb/5zW8iYtXvjnfZZZcYO3ZsLFq0KFasWBHvvvtuHHDAAfHiiy+m/NalIX/LoqCeRqNFixbJ5YKCgjX2X7lyZUREtGzZss5igsaiOvlTmjsR8ofG67PPPotDDjkkioqKokWLFvH4449H586d0/aVHzQV7du3jwEDBsSAAQNi0KBB8etf/zqefPLJePjhh+Obb76JYcOGxYMPPpiyj/wgk/3pT3+KL774Inr27BlXXnlltfeXH2S69u3bV7htgw02iCeeeCL5w4G///3vKdvlB5ms7Ps7IuKUU06JTTbZpFy/li1bpsxU9uijj6YdQ47QFDzyyCNRUlISEauKDioiN8h0S5cujb333jtGjhwZCxYsiIsuuigmT54cK1eujJ9//jlefvnl2HXXXeP999+P4cOHx0033ZSyvxwBgKahqp+fgaqpjZwaOXJk3HvvvRERMWjQoPjHP/5Ra/FBY1TTvOrTp08MGDAgttxyy9htt93i/PPPj48//jgOOOCAZKHV9OnT6ypsWGdVNadWrlyZvGH8ueeeG1tttVV9hQiNTnXOVe3atav05hQHHnhgXHHFFRERsWzZsrjvvvtqL1BoJGpyrS9i1Sz1zZo1K9dv1113jUMPPTQiVhU0VlTMCJmsNr6vGDVqVESsutH2kUceWWuxQWNUnZwaP3587LTTTvHMM89Et27dYtSoUTFr1qwoKCiIadOmxT/+8Y9o1apVjB49Orbffvv47LPP6uMQYJ1Tnbz661//GgcccEBERHz11VcxfPjwaNeuXbRs2TJ22mmneOmll2K77baLk08+OblPmzZt6i74NVBQT6NRNlGWLFmyxv6ldznLz8+vs5igsahO/pS9Q6D8oTH69ttvY5999omFCxdGs2bNYvTo0bH77rtX2F9+0NQdd9xxcfjhh0dJSUmcffbZsWDBguQ2+UGm+uKLL2LkyJERsaoQuHXr1tUeQ37Q1PXt2zeGDBkSERFTpkyJmTNnJrfJDzLZ6l/k7rPPPhX2/eUvfxk5OTkREfG///0v7RhyhKagqhfy5QaZ7qqrrorx48dHRMR9990X119/fWy66aaRl5cXbdu2jSFDhsS4ceNi8ODBkUgk4ne/+1189NFHyf3lCAA0DX4IC7VrbXPqrrvuissuuywiIjbddNN4/vnna3RNATJJbZ6rWrRoEQ888EC0atUqpk2bFhdddFFthAiNSlVz6rrrrosvv/wyevToEVdffXV9hQeNUm3/XXXaaacli+7feOONtR4PGpuaXOvr1KlTbLvtthX23XfffZPLZa+lQ1OxtueqiRMnxhdffBEREQcffHClE6dAU1DVnFq5cmUcddRR8fPPP8eGG24Y7777bhx77LGxwQYbRG5ubnTv3j3OPPPMePPNN6NFixYxc+ZMN76lyarOuap58+bxzDPPxD333BPbbLNNyk3LOnfuHJdffnmMHz8+EolEsn299darm8CrIKfBnhmqqUWLFtGhQ4eYP3/+Gu9Gu3DhwuQPxnr06FEf4cE6rXv37snlNeXPtGnTksvyh8Zm5syZsffee8fMmTMjKysr7r///hg2bFil+8gPiBg2bFg89thjsXTp0njxxRfj6KOPjgj5Qeb629/+FgUFBdG3b99YtmxZjB49ulyfTz/9NLn83//+N2bNmhUREQcddFC0bt1afkBEbL755vH8889HRMSMGTOia9euEeH8QWZr3rx5dOrUKebOnRsRlb9vW7RoER07doxZs2Yl+0fIEZqW999/Pz7//POIWDWLS2UXQ+QGmSyRSMT9998fERH9+/ev8KJ7Tk5OXHPNNbHrrrtGSUlJPPjgg/G3v/0tIuQIADQF1fn8DKzZ2ubUv//97zjzzDMjIqJXr17xyiuvRMeOHWs9TmhM6uJc1bFjx9hll13ilVdeibFjx0ZhYWHk5uau9bjQGFQnp66//vqIiNh7773jmWeeSdun9DezS5cuTV4D79y5c+y11161GTas0+riXNW5c+fo0KFDzJs3L2bMmLHW40FjUp2cKns9ouw1jTX1LXstHZqC2jhXPfzww8nl448/vtZig8aoOjn14osvJj/PnXPOObHhhhum7bfFFlvEscceG/fee2988MEH8dFHH8XWW29d+8HDOqom56rs7Ow45ZRT4pRTTonFixfH7Nmzo1WrVrHhhhtGdvaqOeG//vrrZP/NN9+8boK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      "text/plain": [
       "<Figure size 2500x500 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 490,
       "width": 2026
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# vvvvvvvvvvv this is just a trick so that we can run this cell multiple times vvvvvvvvvvv\n",
    "fig_car_new, ax_car_new = plt.subplots(1,2); plt.close() # create figure and close it\n",
    "if fig_car_new.get_axes():\n",
    "    del ax_car_new; del fig_car_new # delete figure and axes if they exist\n",
    "    fig_car_new, ax_car_new = plt.subplots(1,2) # create them again\n",
    "# ^^^^^^^^^^^ end of the trick ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n",
    "N_samples = 300 # CHANGE THIS NUMBER AND RE-RUN THE CELL\n",
    "x = 75; empirical_y = samples_y(N_samples,x); # Empirical measurements of N_samples\n",
    "empirical_mu_y = np.mean(empirical_y); empirical_sigma_y = np.std(empirical_y); # empirical mean and std\n",
    "car_fig(ax_car_new[0]) # a function I created to include the background plot of the governing model\n",
    "for i in range(2): # create two plots (one is zooming in on the error bar)\n",
    "    ax_car_new[i].errorbar(x , empirical_mu_y,yerr=1.96*empirical_sigma_y, fmt='*m', markersize=15);\n",
    "    ax_car_new[i].scatter(x*np.ones_like(empirical_y),empirical_y, s=40,\n",
    "                          facecolors='none', edgecolors='k', linewidths=2.0)\n",
    "print(\"Empirical mean[y] is\",empirical_mu_y, \"(real mean[y]=675)\")\n",
    "print(\"Empirical std[y] is\",empirical_sigma_y,\"(real std[y]=37.5)\")\n",
    "fig_car_new.set_size_inches(25, 5) # scale figure to be wider (since there are 2 subplots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 414,
       "width": 722
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_hist, ax_hist_y = plt.subplots()\n",
    "# Plot the histogram obtained by sampling p(y) with data\n",
    "empirical_y = samples_y(N_samples=300,x=75) # CHANGE NUMBER OF SAMPLES AND RE-RUN CELL\n",
    "ax_hist_y.hist(empirical_y, bins='auto', \n",
    "               density=True, label='Histogram of $p(y)$')  \n",
    "ax_hist_y.set_title(\"$p(y)$ [for fixed x=75]\", fontsize=20)\n",
    "\n",
    "# Plot the actual p(y|z) pdf:\n",
    "yrange = np.linspace(500, 850, 200) # to show the real Gaussian distribution\n",
    "ax_hist_y.plot(yrange, norm.pdf(yrange, 675, 37.5), 'k--', linewidth = 3, label='$p(y)$')\n",
    "ax_hist_y.set_xlabel(\"y\", fontsize=20)\n",
    "ax_hist_y.set_ylabel(\"probability density\", fontsize=20)\n",
    "ax_hist_y.legend(fontsize=15, loc='upper left');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusions about $y$ and $z$\n",
    "\n",
    "* We conclude that $y$ is also an <a title=\"random variable\">rv</a> because $z$ is an <a title=\"random variable\">rv</a>.\n",
    "\n",
    "* In this case, we empirically found that $p(y)$ is also a Gaussian distribution, just like $z$ but with different parameters. This makes sense because $y$ is just linearly dependent on $z$.\n",
    "\n",
    "* In **Homework 2** you will calculate the expected value (mean) and variance of $y$.\n",
    "\n",
    "These observations lead to the conclusion:\n",
    "\n",
    "$$\n",
    "p(y) = \\mathcal{N}(\\mu_{y}=675,\\sigma_{y}^2=37.5^2)\n",
    "$$\n",
    "\n",
    "with $p(z) = \\mathcal{N}(\\mu_z=1.5,\\sigma_z^2=0.5^2)$ and for $x=75$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transformation of random variables\n",
    "\n",
    "This empirical conclusion can be reached analytically from the **change of variables formula**.\n",
    "\n",
    "This formula says that if $y=f(z)$ and if this function is invertible, i.e. $z=f^{-1}(y)=g(y)$, then:\n",
    "\n",
    "$$\n",
    "p_y(y) = p_z\\left( g(y) \\right) \\left| \\frac{d}{dy}g(y)\\right|\n",
    "$$\n",
    "\n",
    "where $g(y) = f^{-1}(z)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Homework 2 (Exercise 3)\n",
    "\n",
    "Use the change of variables formula to demonstrate that $p(y)$ is a Gaussian distribution with the expected value and variance determined previously. In other words, that $p(y)=\\mathcal{N}(y|\\mu_{y}=x\\mu_z+0.1x^2, \\sigma_y^2 = \\sigma_z^2 x^2)$ when $y=z + 0.1x^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transformation of random variables (multivariate)\n",
    "\n",
    "For more information about transformation of random variables read Section 2.8 of the book.\n",
    "\n",
    "The multivariate change of variables formula is:\n",
    "\n",
    "$$\n",
    "p_y(\\mathbf{y}) = p_z\\left( \\mathbf{g}(\\mathbf{y}) \\right) \\left| \\text{det}\\left[\\mathbf{J}_g(\\mathbf{y})\\right]\\right|\n",
    "$$\n",
    "\n",
    "where $\\mathbf{J}_g(\\mathbf{y})=\\frac{d\\mathbf{g}(\\mathbf{y})}{d\\mathbf{y}^T}$ is the jacobian of $\\mathbf{g}$ and $\\text{det}\\left[\\mathbf{J}_g(\\mathbf{y})\\right]$ is the absolute value of the determinant of $\\mathbf{J}_g$ evaluated at $\\mathbf{y}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Introducing joint probability density of $y$ and $z$\n",
    "\n",
    "Just like in Lecture 1 where we talked about **joint probability** of two events, $\\text{Pr}(A \\wedge B)= \\text{Pr}(A, B)$, the **joint probability density** is:\n",
    "\n",
    "$$\n",
    "p(y \\wedge z)= p(y, z)\n",
    "$$\n",
    "\n",
    "- But how do we **calculate** $p(y,z)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**If** the two rv's were independent, then it would be: $p(y,z)=p(y)p(z)$\n",
    "\n",
    "**But...** We know that $y$ is dependent on $z$... So now what do we do?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is the joint probability density of $y$ and $z$?\n",
    "\n",
    "As we saw in Lecture 1, \n",
    "\n",
    "$$\n",
    "p(y, z) = p(y|z)p(z) = p(z|y)p(y) = p(z, y)\n",
    "$$\n",
    "\n",
    "Here, we already know $p(y)$ and $p(z)$.\n",
    "\n",
    "* But what is the **conditional pdf** $p(y|z)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Remember that for now we are assuming that we know the governing model: $y=z x+0.1x^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So, what is the **conditional pdf** $p(y|z)$? <font color='blue'>Tell me what you think!</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "## The conditional pdf $p(y|z)$ if we know the model... Dirac delta!\n",
    "\n",
    "$p(y|z)=\\delta\\left(y-(z x+0.1x^2)\\right)$\n",
    "\n",
    "This is the Dirac delta pdf, assigning zero probability everywhere except when $y=z x+0.1x^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "If we want to consider this for a fixed $x$ at 75 m/s:\n",
    "\n",
    "$p(y|z)=\\delta\\left(y-(75 z+562.5)\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "This was not a trick question, although a lot of people do not think about this answer when first thinking about the problem 😉"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Then, what is the **joint pdf** $p(y,z)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## What is the joint probability density of $y$ and $z$?\n",
    "\n",
    "Since $y$ and $z$ are dependent, the joint pdf $p(y,z)$ is\n",
    "\n",
    "$$\n",
    "p(y, z) = \\delta\\left(y-(75 z+562.5)\\right) p(z)\n",
    "$$\n",
    "\n",
    "where $p(y|z)=\\delta\\left(y-(75 z+562.5)\\right)$ is the above-mentioned Dirac delta pdf, assigning zero probability everywhere except when $y=75 z+562.5$ for a fixed $x=75$ m/s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Recall that $p(z) = \\mathcal{N}(\\mu_z=1.5,\\sigma_z^2=0.5^2)$, also for a fixed $x=75$ m/s.\n",
    "\n",
    "* Note: $p(y,z)$ and $p(y|z)$ are pdf's that depend on *both* $y$ and $z$, but the joint pdf $p(y,z)$ has two rv's while the conditional pdf $p(y|z)$ is conditioned to a value of $z$ (it's like \"removing\" the stochasticity of $z$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Why do we care about joint pdfs?\n",
    "\n",
    "In general, from a joint pdf $p(y,z)$ we can obtain $p(y)$ and $p(z)$ simply by **integrating out** wrt the other variable. This is called **marginalizing**:\n",
    "\n",
    "$$\n",
    "p(y) = \\int p(y,z) dz\n",
    "$$\n",
    "\n",
    "$$\n",
    "p(z) = \\int p(y,z) dy\n",
    "$$\n",
    "\n",
    "Therefore, $p(y)$ and $p(z)$ are also called **marginal distributions** of $p(y,z)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Homework 2 (Exercise 4)\n",
    "\n",
    "Knowing that $p(y, z) = \\delta\\left(y-(z x+0.1x^2)\\right)  \\mathcal{N}(z|\\mu_z,\\sigma_z^2)$, calculate $p(y)$ and $p(z)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## In general, do we know the true conditional distribution $p(y|z)$?\n",
    "\n",
    "Unfortunately, we usually don't know the true conditional pdf $p(y|z)$ because $z$ is hidden!\n",
    "\n",
    "(Remember: we are cheating with the *car stopping distance problem* because we already know that $y=zx+0.1x^2$\n",
    "\n",
    "In general, we don't know the true relationship between $y$ and $z$..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* So, what can we do?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can **observe** the effect caused by the hidden $z$ in $y$ by taking measurements of $y$.\n",
    "\n",
    "In other words, within the measurements of $y$ (which we call data $\\mathcal{D}_y$) lies the *effect* of the hidden $z$.\n",
    "\n",
    "* The Bayes' rule provides a way to estimate the distribution of the hidden rv $z$ given data $\\mathcal{D}_y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "### Side note: conditional moments (book Section 2.2.5.4)\n",
    "\n",
    "On purpose, I skipped talking about conditional moments in Lecture 1...\n",
    "\n",
    "But now that we talked about conditional pdf's, it's a good time to introduce this.\n",
    "\n",
    "We can calculate the expected value and variance of an rv that is dependent on another rv with the following two laws.\n",
    "\n",
    "#### Law of iterated expectations\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[y] = \\mathbb{E}\\left[\\mathbb{E}[y|z]\\right]\n",
    "$$\n",
    "\n",
    "#### Law of total variance (or conditional variance formula)\n",
    "\n",
    "$$\n",
    "\\mathbb{V}[y] = \\mathbb{E}\\left[\\mathbb{V}[y|x]\\right]+\\mathbb{V}\\left[\\mathbb{E}[y|z]\\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Remember the amazing Bayes' rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Bayes’ rule: a formula for computing the probability distribution over possible values of an unknown (or hidden) quantity $z$ given some observed data $y$:\n",
    "\n",
    "$$\n",
    "p(z|y) = \\frac{p(y|z) p(z)}{p(y)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Bayes' rule follows automatically from the identity: $p(z|y) p(y) = p(y|z) p(z) = p(y,z) = p(z,y)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' rule\n",
    "$\\require{color}$\n",
    "The pdfs we have been discussing in this lecture are what enable us to create ML models via the Bayes' rule when we apply it on **observed data** $\\mathcal{D}_y$:\n",
    "\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$\n",
    "\n",
    "* ${\\color{red}p(z)}$ is the **prior** distribution: this term represents what we know (or what we believe we know!) about possible values of the unknown (hidden) <a title=\"random variable\">rv</a> $z$ before we see any data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' rule\n",
    "$\\require{color}$\n",
    "The pdfs we have been discussing in this lecture are what enable us to create ML models via the Bayes' rule when we apply it on **observed data** $\\mathcal{D}_y$:\n",
    "\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$\n",
    "\n",
    "* $\\require{color}{\\color{blue}p(y | z)}$ is the **observation** distribution (not yet the likelihood!): represents the distribution over the possible outcomes $y$ we expect to see given a particular hidden variable $z$.\n",
    "    - When we evaluate the observation distribution $p(y | z)$ at a point corresponding to the actual observations, $y=\\mathcal{D}_y$, we get the function $p(y=\\mathcal{D}_y|z)$:\n",
    "        * ${\\color{blue}p(y=\\mathcal{D}_y|z)}$ is the **likelihood** function: it is a function of $z$, since $y$ is *fixed* to the observations $\\mathcal{D}_y$, but **it is not a probability distribution** (it does not sum to one)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' rule\n",
    "$\\require{color}$\n",
    "The pdfs we have been discussing in this lecture are what enable us to create ML models via the Bayes' rule when we apply it on **observed data** $\\mathcal{D}_y$:\n",
    "\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$\n",
    "\n",
    "* $p(y=\\mathcal{D}_y)$ is the **marginal likelihood**, which is obtained by *marginalizing* over the unknown $z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayes' rule\n",
    "$\\require{color}$\n",
    "The pdfs we have been discussing in this lecture are what enable us to create ML models via the Bayes' rule when we apply it on **observed data** $\\mathcal{D}_y$:\n",
    "\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$\n",
    "\n",
    "* ${\\color{green}p(z|y=\\mathcal{D}_y)}$ is the **posterior**, which represents our *belief state* about the possible values of the unknown $z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "### A note about the term \"distribution\"\n",
    "\n",
    "The term distribution can mean two things:\n",
    "1. For **continuous** <a title=\"random variables\">rv's</a>, the term *distribution* means *probability density function* (<a title=\"probability density function\">pdf</a>).\n",
    "\n",
    "2. For **discrete** <a title=\"random variables\">rv's</a> the term *distribution* means *probability mass function* (<a title=\"probability mass function\">pmf</a>), as we will see later in the course.\n",
    "\n",
    "We won't talk about categorical distributions or <a title=\"probability mass functions\">pmf's</a> for a while. So, for now, when you see the term *distribution* it is the same as saying <a title=\"probability density function\">pdf</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Summary of Bayes' rule\n",
    "$\\require{color}$\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)} = \\frac{ {\\color{magenta}p(y=\\mathcal{D}_y, z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$\n",
    "\n",
    "* ${\\color{red}p(z)}$ is the **prior** distribution\n",
    "* ${\\color{blue}p(y=\\mathcal{D}_y|z)}$ is the **likelihood** function\n",
    "* ${\\color{magenta}p(y=\\mathcal{D}_y, z)}$ is the **joint likelihood** (product of likelihood function with prior distribution)\n",
    "* $p(y=\\mathcal{D}_y)$ is the **marginal likelihood**\n",
    "* ${\\color{green}p(z|y=\\mathcal{D}_y)}$ is the **posterior**\n",
    "\n",
    "We can write Bayes' rule as <font color='green'>posterior</font> $\\propto$ <font color='blue'>likelihood</font> $\\times$ <font color='red'>prior </font>, where we are ignoring the denominator $p(y=\\mathcal{D}_y)$ because it is just a **constant** independent of the hidden variable $z$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  }
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