week05/2021F_Week05.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "## Week05\n",
    "\n",
    "Lets continue discussing the detials of Regression. In particular, we can write down the maximum likelhood estimators for $\\beta_{0}$, $\\beta_{1}$, and $\\sigma^{2}$.\n",
    "Next we will write down the Fisher Infromation **Matrix** for a 2X1 vector that contains $\\beta_{0}$ and $\\beta_{1}$.\n",
    "\n",
    "With our MLE and Fisher Infromation Matrix we can compute confidence intervals for $\\beta$ and setup hypothesis tests. \n",
    "\n",
    "Our goal this week is to:\n",
    "1. Write down the solution to the loglikelihood\n",
    "2. Write down and understand how to use the Fisher Information\n",
    "3. Learn how to build Confidnece intervals for $\\beta$\n",
    "4. Learn how to compute fitted values $\\hat{\\mu(x)}$\n",
    "5. Briefly discuss the \"true\" model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The solution to the loglikelihood (ie the MLEs for $\\beta_{0}$, $\\beta_{1}$, and $\\sigma^{2}$)\n",
    "\n",
    "The MLE of $\\beta_{1}$ ($\\hat \\beta_{1}$) is \n",
    "\n",
    "\\begin{align}\n",
    "    \\hat \\beta_{1} = \\dfrac{ \\sum_{i=1}^{N}(x_{i} - \\bar{x})(y_{i} - \\bar{y}) }{ \\sum_{i=1}^{N} (x_{i} - \\bar{x})^{2}  }\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "The MLE of $\\beta_{0}$  ($\\hat \\beta_{0}$) is \n",
    "\n",
    "\\begin{align}\n",
    "    \\hat \\beta_{0} = \\bar{y} - \\hat{\\beta_{1}}\\bar{x}\n",
    "\\end{align}\n",
    "\n",
    "The MLE for $\\sigma^{2}$ is worth some discussion of the model form for SLR.\n",
    "Recall SLR model form is \n",
    "\n",
    "\\begin{align}\n",
    "    y_{i} &= \\beta_{0} + \\beta_{1}x_{i} + \\epsilon_{i} \\\\ \n",
    "          \\epsilon_{i} & \\sim \\mathcal{N}\\left(0,\\sigma^{2}\\right)\n",
    "\\end{align}\n",
    "\n",
    "In model form we see that given estimates for $\\beta_{0}$ and $\\beta_{1}$ we can compute $\\epsilon_{i}$ values.\n",
    "Lets plug in our MLE estimates for $\\beta_{0}$ and $\\beta_{1}$ and solve for  $\\epsilon_{i}$:\n",
    "\n",
    "\\begin{align}\n",
    "    y_{i} &= \\beta_{0} + \\beta_{1}x_{i} + \\epsilon_{i} \\\\ \n",
    "    y_{i} &= \\hat \\beta_{0} + \\hat \\beta_{1}x_{i} + \\epsilon_{i} \\\\ \n",
    "    \\epsilon_{i} &= y_{i} - \\left(\\hat \\beta_{0} + \\hat \\beta_{1}x_{i} \\right)\n",
    "\\end{align}\n",
    "\n",
    "We can consider each \\epsilon_{i} as a data point.\n",
    "Our data is $\\epsilon = [\\epsilon_{1},\\epsilon_{2},\\cdots,\\epsilon_{N}]$ and our model is \n",
    "\n",
    "\\begin{align}\n",
    "    E_{i} \\sim \\mathcal{N}\\left(0,\\sigma^{2} \\right)\n",
    "\\end{align}\n",
    "\n",
    "We know from previous work that the MLE for $\\sigma^{2}$ of this model is \n",
    "\n",
    "\\begin{align}\n",
    "    \\hat \\sigma^{2} = \\dfrac{ (\\epsilon_{i} - \\bar{\\epsilon})^{2} }{N}\n",
    "\\end{align}\n",
    "\n",
    "and by assumption, and the Law of Large Numbers, we expect $\\bar{\\epsilon} \\approx 0$ sp \n",
    "\n",
    "\\begin{align}\n",
    "    \\hat \\sigma^{2} &= \\dfrac{ (\\epsilon_{i} - 0)^{2} }{N} \\\\ \n",
    "    \\hat \\sigma^{2} &= \\dfrac{ \\epsilon_{i}^{2} }{N} \\\\ \n",
    "\\end{align}\n",
    "\n",
    "Though the above is the MLE for \\hat \\sigma^{2} it is more traditional to estimate $\\hat \\sigma^{2}$ as \n",
    "\n",
    "\\begin{align}\n",
    "    \\hat \\sigma^{2} &= \\dfrac{ \\epsilon_{i}^{2} }{N-2} \\\\ \n",
    "\\end{align}\n",
    "\n",
    "### Fitted values\n",
    "\n",
    "Assume data $\\mathcal{D} = [ (x_{1},y_{1}),(x_{2},y_{2}),\\cdots,(x_{N},y_{N})]$\n",
    "and the following model \n",
    "\n",
    "\\begin{align}\n",
    "    Y_{i} | x_{i} \\sim \\mathcal{N}\\left(\\mu(x_{i}), \\sigma^{2} \\right)\n",
    "\\end{align}\n",
    "\n",
    "where \n",
    "\n",
    "\\begin{align}\n",
    "    \\mu(x_{i}) =  \\beta_{0} + \\beta_{1}x_{i}\n",
    "\\end{align}\n",
    "\n",
    "Then $E(Y_{i}|x_{i}) = \\mu(x_{i}) =  \\beta_{0} + \\beta_{1}x_{i}$ and the MLE estimate of $\\mu(x_{i})$, denoted $\\hat \\mu(x_{i})$ is called a **fitted value** for $Y_{i}$.\n",
    "A **fitted value** for $Y_{i}$ assuming a SLR model is \n",
    "\n",
    "\\begin{align}\n",
    "    \\hat \\mu(x_{i}) = \\hat \\beta_{0} + \\hat \\beta_{1} x_{i}\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Treating parameters as a vector and the Fisher Information Matrix\n",
    "\n",
    "Up until now we have specificed our data and model for individual data points/random variables. \n",
    "Let us reformulate our data and model using Matrix algebra (because it is awesome). \n",
    "\n",
    "Assume data $\\mathcal{D} = [ (x_{1},y_{1}),(x_{2},y_{2}),\\cdots,(x_{N},y_{N})]$\n",
    "Our model says that each random variable $Y_{i}$ has the following distribution \n",
    "\n",
    "\\begin{align}\n",
    "    Y_{1}  = 1\\beta_{0} + x_{1}\\beta_{1} + \\epsilon_{1}\\\\\n",
    "    Y_{2}  = 1\\beta_{0} + x_{2}\\beta_{1} + \\epsilon_{2}\\\\\n",
    "    Y_{3}  = 1\\beta_{0} + x_{3}\\beta_{1} + \\epsilon_{3}\\\\\n",
    "    Y_{4}  = 1\\beta_{0} + x_{4}\\beta_{1} + \\epsilon_{4}\\\\\n",
    "    Y_{5}  = 1\\beta_{0} + x_{5}\\beta_{1} + \\epsilon_{5}\n",
    "\\end{align}    \n",
    "\n",
    "where each $\\epsilon_{i} \\sim \\mathcal{N}\\left(0,\\sigma^{2}\\right)$.\n",
    "\n",
    "This model can be rewritten as \n",
    "\n",
    "\\begin{align}\n",
    "    Y = X\\beta + \\epsilon\n",
    "\\end{align}\n",
    "\n",
    "where \n",
    "\n",
    "\\begin{align}\n",
    "    Y  = \\left[\\begin{matrix}\n",
    "               Y_{1}\\\\\n",
    "               Y_{2}\\\\\n",
    "               Y_{3}\\\\\n",
    "               Y_{4}\\\\\n",
    "               Y_{5}\n",
    "          \\end{matrix}\\right]\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "    \\epsilon  = \\left[\\begin{matrix}\n",
    "               \\epsilon_{1}\\\\\n",
    "               \\epsilon_{2}\\\\\n",
    "               \\epsilon_{3}\\\\\n",
    "               \\epsilon_{4}\\\\\n",
    "               \\epsilon_{5}\n",
    "          \\end{matrix}\\right]\n",
    "\\end{align}\n",
    "\n",
    "where each $\\epsilon_{i}$ is normally distributed with parameter $\\sigma^{2}$ or \n",
    "$\\epsilon_{i} \\sim \\mathcal{N}\\left(0,\\sigma^{2}\\right)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "    X  = \\left[\\begin{matrix}\n",
    "               1 & x_{1} \\\\ \n",
    "               1 & x_{2} \\\\ \n",
    "               1 & x_{3} \\\\ \n",
    "               1 & x_{4} \\\\ \n",
    "               1 & x_{5} \\\\  \n",
    "          \\end{matrix}\\right]\n",
    "\\end{align}\n",
    "\n",
    "and finally\n",
    "\n",
    "\\begin{align}\n",
    "    \\beta = \\left[\\begin{matrix}\n",
    "                    \\beta_{0} \\\\ \n",
    "                    \\beta_{1}\\\\\n",
    " \\end{matrix}\\right]\n",
    "\\end{align}                "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Multivariate Normal distribution and probabilities over vectors\n",
    "\n",
    "Because we have re-expressed our Simple linear regression using matrices and vectors, we need a way to talk about probabilities over vectors. To be clear, we rewrote our SLR  \n",
    "\n",
    "\\begin{align}\n",
    "    Y \\sim \\text{Some Distribution}( X\\beta, \\Sigma )\n",
    "\\end{align}\n",
    "\n",
    "But how should we characterize a vector where each entry in the vector has a Normal Distribution? \n",
    "\n",
    "#### The Multivariate Normal Distribution (MVN)\n",
    "\n",
    "The multivariate distribution uses a probability density over vectors to assign with assigning probabilities over intervals. For a **random vector** $x = [x_{1},x_{2},\\cdots,x_{N}]'$ the MVN Normal distribution is denoted \n",
    "\n",
    "\\begin{align}\n",
    "    x \\sim MVN\\left( \\mu, \\Sigma \\right)\n",
    "\\end{align}\n",
    "\n",
    "where $\\mu = [\\mu_{1},\\mu_{2},\\cdots,\\mu_{N}]$ is a mean vector and \n",
    "\n",
    "\\begin{align}\n",
    "    \\Sigma = \\left [ \\begin{matrix}\n",
    "                           \\sigma_{x_{1}}^{2}    & \\sigma_{x_{1},x_{2}} &\\cdots &\\sigma_{x_{1},x_{N}}\\\\\n",
    "                           \\sigma_{x_{1},x_{2} } & \\sigma_{x_{2}}^{2}   &\\cdots &\\sigma_{x_{2},x_{N}}\\\\\n",
    "                           \\vdots\n",
    "                      \\end{matrix} \\right ]\n",
    "\\end{align}\n",
    "\n",
    "is called the covariance matrix where agonal entries in this matrix $\\Sigma_{ii}$ are equal to the variance of $x_{i}$ and entries $\\Sigma_{ij}$ are equal to the covariance between $x_{i}$ and $x_{j}$.\n",
    "\n",
    "##### PDF\n",
    "The probability density for the multivariate normal distribution over vectors of length $k$ is \n",
    "\n",
    "\\begin{align}\n",
    "    f(x,\\mu,\\Sigma) = (2\\pi)^{-k/2}|\\Sigma|^{-1/2} \\exp -\\frac{1}{2}\\left[ (x-\\mu)'\\Sigma^{-1}(x-\\mu) \\right]\n",
    "\\end{align}\n",
    "\n",
    "##### The Expected value and Coviariance\n",
    "For a random vector $X$ of length $k$ with a $MVN(\\mu,\\Sigma)$ distribution the expected value is \n",
    "\n",
    "\\begin{align}\n",
    "    E(X) = \\mu\n",
    "\\end{align}\n",
    "\n",
    "where $\\mu = [ \\mu_{1},\\mu_{2},\\cdots,\\mu_{k}]'$ is a vector of length $k$.\n",
    "\n",
    "The covariance matrix (rather than variance) of a random variable $X$ as above is \n",
    "\n",
    "\\begin{align}\n",
    "    Cov(X) = \\Sigma\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "For a vector of length two we can visualize the probability density function of the MVN for different parameter values. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1296x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "y = np.linspace(-5, 5, 100)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "def MVN(pos,m,s):\n",
    "    return scipy.stats.multivariate_normal(mean=m,cov=s).pdf(pos)\n",
    "\n",
    "pos = np.empty(X.shape + (2,))\n",
    "pos[:, :, 0] = X\n",
    "pos[:, :, 1] = Y\n",
    "\n",
    "Z= MVN(pos,m=[0,0],s=[[2,0],[0,4]])\n",
    "\n",
    "fig,axs = plt.subplots(1,3)\n",
    "\n",
    "ax = axs[0]\n",
    "ax.contour(X, Y, Z, colors='black');\n",
    "\n",
    "ax.text(0.99,0.99,r\"Cov=0\",transform=ax.transAxes,ha=\"right\",va=\"top\",fontsize=12)\n",
    "ax.set_xlabel(\"X1\")\n",
    "ax.set_ylabel(\"X2\")\n",
    "\n",
    "\n",
    "Z= MVN(pos,m=[0,0],s=[[2,2],[2,4]])\n",
    "\n",
    "ax = axs[1]\n",
    "ax.contour(X, Y, Z, colors='black');\n",
    "\n",
    "ax.text(0.99,0.99,r\"Cov>0\",transform=ax.transAxes,ha=\"right\",va=\"top\",fontsize=12)\n",
    "ax.set_xlabel(\"X1\")\n",
    "ax.set_ylabel(\"X2\")\n",
    "\n",
    "Z= MVN(pos,m=[0,0],s=[[2,-2],[-2,4]])\n",
    "\n",
    "ax = axs[2]\n",
    "ax.contour(X, Y, Z, colors='black');\n",
    "\n",
    "ax.text(0.99,0.99,r\"Cov<0\",transform=ax.transAxes,ha=\"right\",va=\"top\",fontsize=12)\n",
    "ax.set_xlabel(\"X1\")\n",
    "ax.set_ylabel(\"X2\")\n",
    "\n",
    "fig.set_size_inches(18,4)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the far left is a MVN density with 0 covariance between X1 and X2, where \n",
    "\n",
    "\\begin{align}\n",
    "    \\left[\\begin{matrix}\n",
    "        X_{1}\\\\\n",
    "        X_{2}\n",
    "    \\end{matrix}\\right] \\sim MVN\\left( \\left[\\begin{matrix}\n",
    "        0\\\\\n",
    "        0\n",
    "    \\end{matrix}\\right],  \\left[\\begin{matrix}\n",
    "        2 & 0\\\\\n",
    "        0 & 4\n",
    "    \\end{matrix}\\right]  \\right)\n",
    "\\end{align}\n",
    "\n",
    "The middle figure is a MVN distribution with a positive covariance\n",
    "\\begin{align}\n",
    "    \\left[\\begin{matrix}\n",
    "        X_{1}\\\\\n",
    "        X_{2}\n",
    "    \\end{matrix}\\right] \\sim MVN\\left( \\left[\\begin{matrix}\n",
    "        0\\\\\n",
    "        0\n",
    "    \\end{matrix}\\right],  \\left[\\begin{matrix}\n",
    "        2 & 2\\\\\n",
    "        2 & 4\n",
    "    \\end{matrix}\\right]  \\right)\n",
    "\\end{align}\n",
    "\n",
    "and the figure on the far right is MVN with a negative covariance\n",
    "\n",
    "\\begin{align}\n",
    "    \\left[\\begin{matrix}\n",
    "        X_{1}\\\\\n",
    "        X_{2}\n",
    "    \\end{matrix}\\right] \\sim MVN\\left( \\left[\\begin{matrix}\n",
    "        0\\\\\n",
    "        0\n",
    "    \\end{matrix}\\right],  \\left[\\begin{matrix}\n",
    "        2 & -2\\\\\n",
    "        -2 & 4\n",
    "    \\end{matrix}\\right]  \\right)\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
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    "### Applying the MVN distributoin to our linear regression\n",
    "\n",
    "Recall that our linear regression model can be written \n",
    "\n",
    "\\begin{align}\n",
    "    Y = X\\beta + \\epsilon\n",
    "\\end{align}\n",
    "\n",
    "where $X$ is a matrix and $Y$, $\\beta$, and $\\epsilon$ are vectors.\n",
    "\n",
    "#### Distribution for MLE of $\\beta$\n",
    "\n",
    "The distribution over $\\hat \\beta$ is \n",
    "\n",
    "\\begin{align}\n",
    "     \\beta = \\left[ \\begin{matrix} \n",
    "                           \\beta_{0}\\\\\n",
    "                           \\beta_{1}\n",
    "                         \\end{matrix}\n",
    "                \\right ] \\sim MVN\\left(\\hat \\beta, \\hat \\sigma^{2} \\left(X'X\\right)^{-1} \\right)\n",
    "\\end{align}\n",
    "\n",
    "where $\\hat \\beta$, the MLE for $\\beta_{0}$ and for $\\beta_{1}$ can be written using matrices\n",
    "\n",
    "\\begin{align}\n",
    "    $\\hat \\beta$ = (X'X)^{-1}X'y\n",
    "\\end{align}\n",
    "\n",
    "Because $X\\hat\\beta$ is the $\\mu$ we can write our fitted values $\\hat y$ as \n",
    "\n",
    "\\begin{align}\n",
    "       \\hat y &= X \\left[(X'X)^{-1}X'y \\right]\\\\\n",
    "              &=X \\left[(X'X)^{-1}X' \\right] y\\\\\n",
    "              &=P_{x} y \\\\ \n",
    "\\end{align}"
   ]
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