Lectures/Lecture7/3dasm_Lecture7.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 7\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",
    "* Understanding the Posterior Predictive Distribution (PPD)\n",
    "    - Similar example to Lecture 6 but now with a Gaussian prior.\n",
    "\n",
    "**Reading material**: This notebook"
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    "## In this Lecture...\n",
    "\n",
    "### Summary of the model\n",
    "\n",
    "1. The **observation distribution**:\n",
    "\n",
    "$$\n",
    "p(y|z) = \\mathcal{N}\\left(y | \\mu_{y|z}=w z+b, \\sigma_{y|z}^2\\right) = \\frac{1}{C_{y|z}} \\exp\\left[ -\\frac{1}{2\\sigma_{y|z}^2}(y-\\mu_{y|z})^2\\right]\n",
    "$$\n",
    "\n",
    "where $C_{y|z} = \\sqrt{2\\pi \\sigma_{y|z}^2}$ is the **normalization constant** of the Gaussian pdf, and where $\\mu_{y|z}=w z+b$, with $w$, $b$ and $\\sigma_{y|z}^2$ being constants.\n",
    "\n",
    "2. <font color='blue'>but now assuming a different **prior distribution**</font>: $p(z) = \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle <}{\\mu}_z=3, \\overset{\\scriptscriptstyle <}{\\sigma}_z^2=2^2\n",
    "\\right)$"
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    "As in Lecture 6, we start by using Bayes' rule applied to data to determine the <font color='green'>posterior</font>:\n",
    "\n",
    "$\\require{color}$\n",
    "$$\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} = \\frac{ {\\color{blue}p(y=\\mathcal{D}_y|z)}{\\color{red}p(z)} } {p(y=\\mathcal{D}_y)}\n",
    "$$"
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    "The <font color='blue'>likelihood</font> is the same as in Lecture 6:\n",
    "\n",
    "$$\n",
    "{\\color{blue}p(y=\\mathcal{D}_y | z)} = \\frac{1}{|w|^N} \\cdot C \\cdot \\frac{1}{\\sqrt{2\\pi \\sigma^2}} \\exp\\left[ -\\frac{1}{2\\sigma^2}(z-\\mu)^2\\right]\n",
    "$$\n",
    "\n",
    "where $\\mu = \\frac{w^2\\sigma^2}{\\sigma_{y|z}^2} \\sum_{i=1}^N \\mu_i = \\frac{\\sum_{i=1}^N y_i}{w N}-\\frac{b}{w}$\n",
    "\n",
    "$\\sigma^2 = \\frac{\\sigma_{y|z}^2}{w^2 N}$, and\n",
    "\n",
    "$C = \\frac{1}{2\\pi^{(N-1)/2}} \\sqrt{\\frac{\\sigma^2}{\\left( \\frac{\\sigma_{y|z}^2}{w^2}\\right)^N}}\n",
    "$"
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    "But now the marginal likelihood is different from Lecture 6 because we have a different prior:\n",
    "\n",
    "$$\n",
    "p(y=\\mathcal{D}_y) = \\frac{C\\cdot C_M}{|w|^N}\n",
    "$$\n",
    "\n",
    "where $C_M = \\frac{1}{\\sqrt{2\\pi\\left(\\sigma^2+\\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right)}} \\exp\\left[-\\frac{1}{2\\left(\\sigma^2+\\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right)}\\left(\\mu - \\overset{\\scriptscriptstyle <}{\\mu}_z\\right)^2 \\right]$.\n",
    "\n",
    "(Algebra to get this result is in the notes below.)"
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    "#### Note: calculation of the marginal likelihood\n",
    "\n",
    "$$\\begin{align}\n",
    "p(y=\\mathcal{D}_y) &= \\int p(y=\\mathcal{D}_y | z) p(z) dz \\\\\n",
    "&= \\int \\frac{1}{|w|^N} C \\cdot \\mathcal{N}(z|\\mu, \\sigma^2)\\cdot \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle <}{\\mu}_z, \\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right) dz\\\\\n",
    "&= \\frac{C}{|w|^N} \\int C_M\\mathcal{N}\\left(z\\left|\\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}} \\left( \\frac{\\mu}{\\sigma^2} + \\frac{\\overset{\\scriptscriptstyle <}{\\mu}_z}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}\\right), \\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}}\\right.\\right) dz = \\frac{C\\cdot C_M}{|w|^N} \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $C_M = \\frac{1}{\\sqrt{2\\pi\\left(\\sigma^2+\\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right)}} \\exp\\left[-\\frac{1}{2\\left(\\sigma^2+\\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right)}\\left(\\mu - \\overset{\\scriptscriptstyle <}{\\mu}_z\\right)^2 \\right]$"
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    "Therefore, the <font color='green'>posterior</font> will also be different:\n",
    "\n",
    "$$\\require{color}\\begin{align}\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} &= \\frac{ p(y=\\mathcal{D}_y|z)p(z) } {p(y=\\mathcal{D}_y)} \\\\\n",
    "&= \\frac{|w|^N}{C\\cdot C_M} \\cdot \\frac{1}{|w|^N} C \\cdot \\mathcal{N}(z|\\mu,\\sigma^2) \\cdot \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle <}{\\mu}_z, \\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right) \\\\\n",
    "&= \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle >}{\\mu}_z, \\overset{\\scriptscriptstyle >}{\\sigma}_z^2\\right)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $\\overset{\\scriptscriptstyle >}{\\mu}_z = \\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}} \\left( \\frac{\\mu}{\\sigma^2} + \\frac{\\overset{\\scriptscriptstyle <}{\\mu}_z}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}\\right)$\n",
    "\n",
    "and $\\overset{\\scriptscriptstyle >}{\\sigma}_z^2 = \\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}}$\n",
    "\n",
    "are the parameters of the <font color='green'>posterior</font> distribution, symbolized by the superscript $\\overset{\\scriptscriptstyle >}{(\\cdot)}$."
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    "Reflection on the differences between the posterior we obtain for the two different priors we considered.\n",
    "\n",
    "* When using the noninformative Uniform prior $p(z) = \\frac{1}{C_z}$ (Lecture 6):\n",
    "\n",
    "$$\\require{color}\\begin{align}\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)}\n",
    "&= \\mathcal{N}(z|\\mu, \\sigma^2)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "* When using a Gaussian prior $p(z) = \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle <}{\\mu}_z, \\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\right)$ (this Lecture):\n",
    "\n",
    "$$\\require{color}\\begin{align}\n",
    "{\\color{green}p(z|y=\\mathcal{D}_y)} &= \\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle >}{\\mu}_z, \\overset{\\scriptscriptstyle >}{\\sigma}_z^2\\right) = \\mathcal{N}\\left(z\\left|\\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}} \\left( \\frac{\\mu}{\\sigma^2} + \\frac{\\overset{\\scriptscriptstyle <}{\\mu}_z}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}\\right), \\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}}\\right.\\right)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The posterior is still a Gaussian but its mean and variance have been updated by the influence of the prior!"
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    "Finally, the goal of calculating the posterior is to use it to determine the <font color='orange'>Posterior Predictive Distribution (<a title=\"Posterior Predictive Distribution\">PPD</a>)</font>:\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\int \\underbrace{p(y^*|z)}_{\\text{observation}\\\\ \\text{distribution}} \\overbrace{p(z|y=\\mathcal{D}_y)}^{\\text{posterior}} dz\n",
    "$$\n",
    "\n",
    "where $y^*$ highlights that we can make a prediction for any $y$ value (just to highlight that it has nothing to do with the training data)."
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    "Considering the terms we found before, we get:\n",
    "\n",
    "$$\\begin{align}\n",
    "p(y^*|\\mathcal{D}_y) &= \\int \\underbrace{\\frac{1}{|w|}\\frac{1}{\\sqrt{2\\pi \\left(\\frac{\\sigma_{y|z}}{w}\\right)^2}} \\exp\\left\\{ -\\frac{1}{2\\left(\\frac{\\sigma_{y|z}}{w}\\right)^2}\\left[z-\\left(\\frac{y^*-b}{w}\\right)\\right]^2\\right\\} }_{\\text{observation}\\\\ \\text{distribution}} \\overbrace{\\mathcal{N}\\left(z| \\overset{\\scriptscriptstyle >}{\\mu}_z, \\overset{\\scriptscriptstyle >}{\\sigma}_z^2\\right)}^{\\text{posterior}} dz\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "The calculation of this integral is similar to what we did in Lecture 6! The difference is that the posterior has a different mean and variance (indicated with the superscript) that originated from the choice of different prior!"
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    "So, we can fast forward to the result we obtained before! We just need to replace the symbols $\\mu_z$ by $\\overset{\\scriptscriptstyle >}{\\mu}_z$, and $\\sigma_z^2$ for $\\overset{\\scriptscriptstyle >}{\\sigma}_z^2$:"
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    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\frac{\\tilde{C}}{|w|} \n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\\tilde{C} = \\frac{1}{\\sqrt{2\\pi \\left( \\overset{\\scriptscriptstyle >}{\\sigma}_z^2 + \\frac{\\sigma_{y|z}^2}{w^2} \\right)}}\\exp\\left[ - \\frac{\\left(\\overset{\\scriptscriptstyle >}{\\mu}_z - \\frac{y^*-b}{w}\\right)^2}{2\\left( \\overset{\\scriptscriptstyle >}{\\sigma}_z^2+\\frac{\\sigma_{y|z}^2}{w^2}\\right)}\\right]$$\n",
    "\n",
    "is the same constant as $C^*$ in Lecture 6, but replacing $\\mu_z$ by $\\overset{\\scriptscriptstyle >}{\\mu}_z$, and $\\sigma_z^2$ for $\\overset{\\scriptscriptstyle >}{\\sigma}_z^2$."
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    "After a bit of algebra, we get to the following expression for the PPD:\n",
    "\n",
    "$$\\require{color}\n",
    "\\begin{align}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} &= \\frac{1}{\\sqrt{2\\pi \\left( \\sigma_{y|z}^2 + w^2\\overset{\\scriptscriptstyle >}{\\sigma}_z^2\\right)}}\\exp\\left\\{ - \\frac{1}{2\\left( \\sigma_{y|z}^2 + w^2\\overset{\\scriptscriptstyle >}{\\sigma}_z^2\\right)}\\left[y^*-\\left(w\\overset{\\scriptscriptstyle >}{\\mu}_z+b\\right)\\right]^2\\right\\} \\\\\n",
    "&= \\mathcal{N}\\left(y^* \\left| w\\overset{\\scriptscriptstyle >}{\\mu}_z+b , \\sigma_{y|z}^2 + w^2\\overset{\\scriptscriptstyle >}{\\sigma}_z^2 \\right.\\right) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where all of the terms have been defined before (for convenience, see them in the next cell as notes)."
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    "#### Note: PPD when using a Gaussian prior\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\mathcal{N}\\left(y^* \\left| w\\overset{\\scriptscriptstyle >}{\\mu}_z+b , \\sigma_{y|z}^2 + w^2\\overset{\\scriptscriptstyle >}{\\sigma}_z^2 \\right.\\right)$$\n",
    "\n",
    "$b = 0.1 \\cdot 75^2 = 562.5$\n",
    "\n",
    "$w = x = 75$\n",
    "\n",
    "$\\sigma_{y|z}^2 = 80^2$ (**NOTE**: This is an assumption that we made when we defined the observation distribution! This number was our own choice!)\n",
    "\n",
    "$\\overset{\\scriptscriptstyle >}{\\mu}_z = \\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}} \\left( \\frac{\\mu}{\\sigma^2} + \\frac{\\overset{\\scriptscriptstyle <}{\\mu}_z}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}\\right) = \\frac{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2 \\sigma^2}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2+\\sigma^2} \\left( \\frac{\\mu}{\\sigma^2} + \\frac{\\overset{\\scriptscriptstyle <}{\\mu}_z}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}\\right) = \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2+\\sigma^2}\\left( \\mu \\overset{\\scriptscriptstyle <}{\\sigma}_z^2 + \\overset{\\scriptscriptstyle <}{\\mu}_z \\sigma^2\\right)$\n",
    "\n",
    "$\\overset{\\scriptscriptstyle >}{\\sigma}_z^2 = \\frac{1}{\\frac{1}{\\sigma^2} + \\frac{1}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2}} = \\frac{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2 \\sigma^2}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2+\\sigma^2}$\n",
    "\n",
    "$\\sigma^2 = \\frac{\\sigma_{y|z}^2}{w^2 N} = \\frac{\\sigma_{y|z}^2}{x^2 N}$\n",
    "\n",
    "$\\mu = \\frac{w^2 \\sigma^2}{\\sigma_{y|z}^2} \\sum_{i=1}^{N} \\mu_i = \\cdots = \\frac{\\sum_{i=1}^N y_i}{w N}-\\frac{b}{w}$"
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    "In order to see the explicit dependence on the observed data $\\mathcal{D}_y$, we can also rewrite the PPD as:\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\mathcal{N}\\left(y^* \\left| \\mu^*, \\sigma^* \\right.\\right)\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$\n",
    "\\mu^* = \\frac{1}{1+\\frac{\\sigma_{y|z}^2}{w^2N \\overset{\\scriptscriptstyle <}{\\sigma}_z^2}}\\left[\\frac{\\sum_{i=1}^N y_i}{N} + \\frac{\\sigma_{y|z}^2}{w^2 N \\overset{\\scriptscriptstyle <}{\\sigma}_z^2}\\left( w \\overset{\\scriptscriptstyle <}{\\mu}_z + b\\right) \\right]\n",
    "\\quad$ (**Note** that $y_i$ is the training data point $i$, not the new predicted value $y^*$) \n",
    "\n",
    "$\n",
    "\\left(\\sigma^*\\right)^2 = \\sigma_{y|z}^2 + w^2 \\overset{\\scriptscriptstyle >}{\\sigma}_z^2 = \\sigma_{y|z}^2 + \\frac{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2\\frac{\\sigma_{y|z}^2}{N}}{\\overset{\\scriptscriptstyle <}{\\sigma}_z^2 + \\frac{\\sigma_{y|z}^2}{w^2 N}} \n",
    "$\n",
    "\n",
    "* What happens when $N \\rightarrow \\infty$ ?"
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    "When $N \\rightarrow \\infty$ the mean and variance of the PPD become:\n",
    "\n",
    "$$\n",
    "\\mu^* = \\frac{\\sum_{i=1}^N y_i}{N} \\equiv \\text{Empirical mean}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\left(\\sigma^*\\right)^2 = \\sigma_{y|z}^2 \\equiv \\text{Variance assumed by us for the observation distribution}\n",
    "$$\n",
    "\n",
    "So, in this limit the PPD is simply:\n",
    "\n",
    "$$\\require{color}\n",
    "{\\color{orange}p(y^*|\\mathcal{D}_y)} = \\mathcal{N}\\left(y^* \\left| \\frac{\\sum_{i=1}^N y_i}{N}, \\sigma_{y|z}^2 \\right.\\right) \\quad \\text{when } N\\rightarrow \\infty\n",
    "$$\n",
    "\n",
    "* <font color='blue'>This means that in the limit of $N \\rightarrow \\infty$ we have exactly the same result obtained when we used the noninformative Uniform prior!</font> Were you expecting this? Let's debate!"
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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 # From Homework of Lecture 4\n",
    "    sigma_y = np.sqrt( (x*sigma_z)**2 ) # From Homework of Lecture 4\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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "# This cell is also hidden during presentation.\n",
    "from scipy.stats import norm # import the normal dist, as we learned before!\n",
    "def samples_y(N_samples,x): # observations/measurements/samples for car stop. dist. prob.\n",
    "    mu_z = 1.5; sigma_z = 0.5;\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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "# This cell is hidden during presentation\n",
    "def PPD_comparison(N_samples): # PLOT PPD for Homework and compare it to data and PPD of Lecture 6\n",
    "    fig_car_PPD, ax_car_PPD = plt.subplots(1,2)\n",
    "    x = 75\n",
    "    # Observation of N_samples from the true data:\n",
    "    empirical_y = samples_y(N_samples, x) # Empirical measurements of N_samples at x=75\n",
    "    # Empirical mean and std directly calculated from observations:\n",
    "    empirical_mu_y = np.mean(empirical_y); empirical_sigma_y = np.std(empirical_y); \n",
    "    #\n",
    "    # Now define all the constants needed in the calculation of the PPD's obtained with each prior.\n",
    "    w = x\n",
    "    b = 0.1*x**2\n",
    "    sigma_yGIVENz = 80\n",
    "    sigma = np.sqrt(sigma_yGIVENz**2/(w**2*N_samples)) # std arising from the likelihood\n",
    "    mu = empirical_mu_y/w - b/w # mean arising from the likelihood (product of Gaussian densities for the data)\n",
    "    #\n",
    "    # Now, calculate PPD when using a UNIFORM prior (Lecture 6):\n",
    "    PPD_mu_y_UniformPrior = mu*w + b # same result if using: np.mean(empirical_y)\n",
    "    PPD_sigma_y_UniformPrior = np.sqrt(sigma_yGIVENz**2*(1/N_samples + 1))\n",
    "    \n",
    "    # Now, calcualte PPD when using the GAUSSIAN prior (Homework of Lecture 6):\n",
    "    mu_prior_z = 3; sigma_prior_z = 2 # parameters of the Gaussian prior distribution \n",
    "    sigma_posterior_z = np.sqrt( (sigma_prior_z**2*sigma**2)/(sigma_prior_z**2+sigma**2) )# std of posterior\n",
    "    #mu_posterior_z = sigma_posterior_z**2*( mu/(sigma**2) + mu_prior_z/(sigma_prior_z**2) ) # mean of posterior\n",
    "    mu_posterior_z = 1/(sigma_prior_z**2+sigma**2)*( mu*sigma_prior_z**2 + mu_prior_z*sigma**2 ) # mean of posterior\n",
    "    PPD_mu_y_GaussianPrior = mu_posterior_z*w + b\n",
    "    PPD_sigma_y_GaussianPrior = np.sqrt(w**2*sigma_posterior_z**2+sigma_yGIVENz**2)\n",
    "    #\n",
    "    car_fig(ax_car_PPD[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_PPD[i].errorbar(x , empirical_mu_y,yerr=1.96*empirical_sigma_y, fmt='m*',\n",
    "                               markersize=30, elinewidth=9);\n",
    "        ax_car_PPD[i].errorbar(x , PPD_mu_y_UniformPrior,yerr=1.96*PPD_sigma_y_UniformPrior,\n",
    "                               color='#F39C12', fmt='*', markersize=15, elinewidth=6);\n",
    "        ax_car_PPD[i].errorbar(x , PPD_mu_y_GaussianPrior,yerr=1.96*PPD_sigma_y_GaussianPrior,\n",
    "                               fmt='b*', markersize=10, elinewidth=3);\n",
    "        ax_car_PPD[i].scatter(x*np.ones_like(empirical_y),empirical_y, s=150,facecolors='none',\n",
    "                              edgecolors='k', linewidths=2.0)\n",
    "    print(\"Ground truth                   : mean[y] = 675    & std[y] = 37.5\")\n",
    "    print(\"Empirical values (purple)      : mean[y] = %.2f & std[y] = %.2f\" % (empirical_mu_y,empirical_sigma_y) )\n",
    "    print(\"PPD with Uniform Prior (orange): mean[y] = %.2f & std[y] = %.2f\" % (PPD_mu_y_UniformPrior, PPD_sigma_y_UniformPrior))\n",
    "    print(\"PPD with Gaussian Prior (blue) : mean[y] = %.2f & std[y] = %.2f\" % (PPD_mu_y_GaussianPrior,PPD_sigma_y_GaussianPrior))\n",
    "    fig_car_PPD.set_size_inches(15, 6) # scale figure to be wider (since there are 2 subplots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ground truth                   : mean[y] = 675    & std[y] = 37.5\n",
      "Empirical values (purple)      : mean[y] = 661.04 & std[y] = 16.71\n",
      "PPD with Uniform Prior (orange): mean[y] = 661.04 & std[y] = 92.38\n",
      "PPD with Gaussian Prior (blue) : mean[y] = 671.99 & std[y] = 91.37\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 402,
       "width": 902
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "PPD_comparison(N_samples=3) # Plot data and the two PPD's considering different priors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### See you next class\n",
    "\n",
    "Have fun!"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "hide_code_all_hidden": false,
  "kernelspec": {
   "display_name": "Python [conda env:3dasm]",
   "language": "python",
   "name": "conda-env-3dasm-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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