Lectures/Lecture3/3dasm_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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   "source": [
    "# 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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   "source": [
    "# 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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   "execution_count": 12,
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stopping distance for x=75 m/s is: [631.02841186]\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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   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empirical mean[y] is 672.1835692705513 (real mean[y]=675)\n",
      "Empirical std[y] is 39.28016913637344 (real std[y]=37.5)\n"
     ]
    },
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",
      "text/plain": [
       "<Figure size 1800x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 348,
       "width": 1459
      },
      "needs_background": "light"
     },
     "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": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 294,
       "width": 408
      },
      "needs_background": "light"
     },
     "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": {
    "slideshow": {
     "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": {
    "slideshow": {
     "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": {
    "slideshow": {
     "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": {
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   "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": {
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     "slide_type": "fragment"
    }
   },
   "source": [
    "* So, what can we do?"
   ]
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    "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": {
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     "slide_type": "notes"
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   "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": {
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     "slide_type": "slide"
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   "source": [
    "## Remember the amazing Bayes' rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "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": {
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   "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": {
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   "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": {
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     "slide_type": "slide"
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   },
   "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",
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     "slide_type": "slide"
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   },
   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  }
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