diff --git a/notebook.ipynb b/notebook.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib as mpl\n",
+    "import matplotlib.pyplot as plt\n",
+    "# PLOTTING OPTIONS\n",
+    "fig_width_pt = 3*246.0  # Get this from LaTeX using \\showthe\\columnwidth\n",
+    "inches_per_pt = 1.0/72.27               # Convert pt to inch\n",
+    "golden_mean = (np.sqrt(5)-1.0)/2.0         # Aesthetic ratio\n",
+    "fig_width = fig_width_pt*inches_per_pt  # width in inches\n",
+    "fig_height = fig_width*golden_mean      # height in inches\n",
+    "fig_size =  [fig_width,fig_height]\n",
+    "\n",
+    "params = { 'axes.labelsize': 24,\n",
+    "          'font.family': 'serif',\n",
+    "          'font.serif': 'Computer Modern Raman',\n",
+    "          'font.size': 24,\n",
+    "          'legend.fontsize': 20,\n",
+    "          'xtick.labelsize': 24,\n",
+    "          'ytick.labelsize': 24,\n",
+    "          'axes.grid' : True,\n",
+    "          'text.usetex': True,\n",
+    "          'savefig.dpi' : 100,\n",
+    "          'lines.markersize' : 14,\n",
+    "          'figure.figsize': fig_size}\n",
+    "\n",
+    "mpl.rcParams.update(params)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Do:\n",
+    "1) Basic statistics and Pulse detection: Work out the Neyman-Pearson detection statistic for testing if a certain data vector d(t) of length 100, is either:\n",
+    "H0: pure gaussian noise (can generate using d(t) = np.random.normal(0,1,100))\n",
+    "\n",
+    "or  \n",
+    "\n",
+    "H1: A gaussian shaped pulse located at position 50, with known height A, sigma (width) of 5 samples, embedded in white gaussian noise stream of length 100 \n",
+    "\n",
+    "can generate using\n",
+    "\n",
+    "T(t) = A * np.exp(-((np.arange(100) - 50)**2) / (2*5**2))\n",
+    "\n",
+    "d(t) = T(t) + np.random.normal(0,1,100) where )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n = np.random.normal(0,1,100)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A = 1\n",
+    "sigma = 5\n",
+    "x = np.arange(100)\n",
+    "s = A * np.exp(-(x-50)**2/(2*sigma**2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x12c59e8d0>"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(n,marker='.',label='noise')\n",
+    "plt.plot(s,marker='.',label='sigal')\n",
+    "plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5, 1.0, 'Noise+Signal')"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(s+n,marker='.')\n",
+    "plt.title('Noise+Signal')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### a) Write the statistical model for the two competing hypothesis (H0, H1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "H0: There is only noise in the data $d_i = n_i$, where $n_i\\sim\\mathcal{N}(0,1)$ and $i=(1,2,...,100)$\n",
+    "\n",
+    "H1: There are signal and noise in the data $d=n_i+s_i$, where $n_i\\sim\\mathcal{N}(0,1)$,  and $s_i= A\\exp(-\\frac{(i-50)^2}{2\\sigma^2})$, $\\sigma=5$, $i=(1,2,...,100)$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "$\\log\\mathcal{L}(d|H_0) \\propto \\sum_{i} -\\frac{1}{2}(d_i)^2$\n",
+    "\n",
+    "$\\log\\mathcal{L}(d|H_1) \\propto \\sum_{i} -\\frac{1}{2}(d_i-s_i)^2$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Test statistic $\\mathcal{T}(d) = \\log \\frac{\\mathcal{L}(d|H_1)}{\\mathcal{L}(d|H_0)} = \\sum_i (d_is_i - \\frac{1}{2}s_i^2)$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### b) Assume A is known, given a data-stream that contains this signal with probability half,  what would be the minimal A that you can detect with probability greater than 90%, while maintaining a false alarm probability (FAP) less than 1 in 10^6?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "A is known, hence $s_i = A\\exp(-\\frac{(x_i-50)^2}{2\\times5^2})$\n",
+    "\n",
+    "maintaining a false alarm probability < $1/10^6 \\to \\int_\\eta^\\infty \\mathcal{T}(d|H_0) < 1/10^6$, solve $\\eta$ accordingly. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def test_A(A):\n",
+    "    sigma = 5\n",
+    "    x = np.arange(100)\n",
+    "    #signal model\n",
+    "    s = A * np.exp(-(x-50)**2/(2*sigma**2))\n",
+    "    stat_h0 = []\n",
+    "    stat_h1 = []\n",
+    "\n",
+    "    for i in range(1000):\n",
+    "        n = np.random.normal(0,1,100)\n",
+    "        d = n+s\n",
+    "        stat_h0.append(np.sum(n*s-0.5*s*s))\n",
+    "        stat_h1.append(np.sum(d*s-0.5*s*s))\n",
+    "    return stat_h0,stat_h1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for A in [1,0.1,0.01]:\n",
+    "    stat_h0,stat_h1 = test_A(A)\n",
+    "    plt.figure()\n",
+    "    plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "    plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "    plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### c) Suppose that the height of the pulse is unknown, what would you do? Is it the test optimal? What is the minimal A now? [for the same conditions as (1b) is it the same?]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "compute the partical derivative for A first. My guess is it's much higher than 1b because we'll have look else-where effect"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Test statistic $\\mathcal{T}(d) = \\log \\frac{\\mathcal{L}(d|H_1)}{\\mathcal{L}(d|H_0)} = \\sum_i (Ad_i\\hat{s}_i -A^2 \\frac{1}{2}\\hat{s}_i^2)$, where $s = A\\hat{s}$\n",
+    "\n",
+    "Let $\\frac{\\partial{\\mathcal{T}(d)}}{\\partial A} =\\sum_i (d_i\\hat{s}_i -A\\hat{s}_i^2) = 0$, hence $A=\\frac{\\sum_id_i\\hat{s}_i}{\\sum\\hat{s}_i^2}$, this is the condition to achieve the maximized $\\mathcal{T}(d)$ for an unknown A\n",
+    "\n",
+    "Substitute A to the test statistic, we get $\\mathcal{T}(d) = \\frac{1}{2}\\frac{(\\sum_id_i\\hat{s}_i)^2}{\\sum_i\\hat{s}_i^2}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def t_unknownA(d,shat):\n",
+    "    return 0.5*np.sum(d*shat)**2/np.sum(shat*shat)\n",
+    "\n",
+    "def dist_unknownA(A):\n",
+    "    sigma = 5\n",
+    "    x = np.arange(100)\n",
+    "    shat = np.exp(-(x-50)**2/(2*sigma**2))\n",
+    "    s = A*shat\n",
+    "    \n",
+    "    stat_h0 = []\n",
+    "    stat_h1 = []\n",
+    "    for i in range(1000):\n",
+    "        n = np.random.normal(0,1,100)\n",
+    "        d = n+s\n",
+    "        stat_h0.append(t_unknownA(n,shat))\n",
+    "        stat_h1.append(t_unknownA(d,shat))\n",
+    "    return stat_h0,stat_h1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAGbCAYAAABEeK1/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8li6FKAAAc50lEQVR4nO3dz2+c52En8O+zju2ghmKK9sI1imodCvA5pVQgRwVLnXqlor/Aw3MWCxG+9CpQwGLPpBGgh15s+dqTGIQ3B4hE9FasAU+yPhRF1qZYy0ZtN8azh3kpjyiONDPkcPiYnw8gyHzfh+88ekgPv3x+llprAABox3+ZdwUAAJiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHggDOtlLJRSunNux4AZ0mxDxxwlpVSHibp11qvzLsuSVJKuZXkcpJPkryWJLXW9Xk8r5SymuR6rXVt2tcH2vSjeVcAYJRSykqShSTLpZSlWmt/zvW5l+TucGAqpayUUh5MEzCneV4pZSnJcpKbSVaTbE36ukD7DKECZ9mNJAe9UavzrEgpZSNJaq1PBKZa63aS+6WUu7N+XtfjtpFkKck7E/0DgB8UQ6jAmdWFnNtJDoZRL8+xLjXJjVrrh0fcW07yIMnFWuv+aT2ve8aWIVQ4f/TAAWdSt3Dh/S7AbCdZ6oLNPOpy0Pu3O6LIwdDuWIstTvp5wPkjwAFn1ZVa60HA2ez+nldP0/UkGTUHb6iX7PqcngecMwIccOaUUhYyWJWZJBkaZvzlfGqUpTHK9McsN4vnAeeMAAecRb0kh+eGfZhkoVuZetoWz3g54JwR4ICz6PIRw4vzHEZdSDLO4oSFOT0POGcEOOBM6fY5e3D4ere9xn6es51IKeVWKaWewJ/h8DROT9hYq09n9DzgnBHggLNm7fDeaEO2kidWcT6l1nqn1lpO4M+kAeqke8v0vgEjOYkBOGtWn7FdyMGk/rU8PUdulvYy3oKCcUPfST8POGcEOODM6BYorB+1ue1QmU+SrJRSFqboJZvWOK+zmEEwm8fzgHPGECpwlhx5MsEhB4sZTnOT2/vJ4+1NRlnI6I15Z/084JwR4IDWHMyPu3nUzRktYjhYVHHksOdQ2Xtj/htO+nnAOSPAAWdCtzDhuQfCd8Omu0mWuxWrh+/PYhHDB93fV0dU62Bvuu0x/7kn/TzgnBHggLPiZrdVyDhOdU+4Lszdecbr3czgUPmnjsY6akHGcZ53BJv9wjkkwAFz1x1cv/qcOWHD7nd/n9o8uFrrevK4ro91PYfLSdYPf04p5VaSB6WUzcP3pnneoXIHbWW7ETiHrEIF5qZbdXo334eQP5RS3nnOKtR7+X7ocaGU8jCDc0NvjNljNbVa65Vujt1mBme1vtZdvzziU3YzWHH61MbE0zzvYJVuBnPnDoaPV4baYK/Wen2qfxzQlFJrnXcdAACYgCFUAIDGCHAAAI0R4AAAGiPAAQA0pulVqK+//np96623Zv46X331VV555ZWZv855pG1nQ7vOjradHW07G9p1dmbdtg8ePPis1vpfj7rXdIB76623cv/+/ecXPKadnZ1cu3Zt5q9zHmnb2dCus6NtZ0fbzoZ2nZ1Zt20p5f+OumcIFQCgMQIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQmKY38gUApvfNN99kb28vjx49ynfffTfv6jTn1Vdfzb/8y7+MVfaFF17IhQsXsri4mJdffvnYry3AAcA59M033+TTTz/NxYsX89Zbb+XFF19MKWXe1WrKo0ePcuHCheeWq7XmP//zP/PFF1/k008/zaVLl44d4gyhAsA5tLe3l4sXL+b111/PSy+9JLzNUCklL730Ul5//fVcvHgxe3t7x36mAAcA59CjR4/yk5/8ZN7VOHd+8pOf5NGjR8d+jgAHAOfQd999lxdffHHe1Th3XnzxxROZbyjAAcA5Zdj09J1UmwtwAACNsQp1DH969E3+972P512NE/Or62/PuwoAwDHogQMAaIweOADgKWd95Om8jyYJcGN45Zv/l5//6d68q3EifnepN+8qAMDcra+vZ3t7O7u7u+n1erlx40ZWVlaSJFtbW7l79262t7ezurqa69evp9c7Wz8/BTgA4NzZ2NjI1tZW1tfXs7m5+cS9Xq+Xq1ev5sqVK3nvvfeysLDwxP3d3d1sb2/nzTffzH/8x39kaWnpcfg7LQIcAMCY+v1+bt++nbt37z4+SuvGjRtZXFzM8vLyqdXDIgYAgDFtbGxkbW3tiWvvvvtu1tfXT7UeAhwAwJg++OCDLC0tPXFtaWkp29vbp1oPAQ4AYAz9fj/7+/tPBbiDOXK7u7unVhdz4ACAc2t/fz937tx56vonn3xyZNln2dvbO7F6PY8ABwCcWwsLC7l169ZT13d3d7O1tTWHGo3HECoAwASe1xN3GgQ4AIAxHMx1OzxUehDoFhcXT60uAhwAwBiWlpaysLDwVA/cQaCzDxwAwBm0srKSfr//xLV+v3/qJzEIcAAAY9rY2Mjt27efuLa5uZmNjY1TrYdVqADAU351/e15V2GmDg6z39/fz9ra2pGH2SfJO++8k5s3b2Z1dTXJYBj14BzVv/zLv8y//du/ZW1t7VSHTxMBDgA4h57VY9br9dLr9UbePwh6B2ehzoMhVACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGjMj+ZdAQDgDPrt7XnX4Nl+8e68azBXeuAAgHNnfX09V65cSSkla2tr2d7efnxva2sr169fTyklN27cyNbW1hxrejQBDgA4dzY2NrK2tpaFhYVsbm5mZWXl8b1er5eNjY0kyXvvvZder3fkM/7+7/8+u7u7p1LfwwyhAgCMqd/vZ2NjIwsLC/mHf/iH/N3f/d1c6iHAAQCMaWlpKZubm0mSDz74YG71MIQKANAYAQ4AoDGGUAGAc2t/fz937tx56vonn3wyh9qMT4ADAM6thYWF3Lp166nru7u7Z3L7kAOGUAEAGiPAAQA0RoADAGiMAAcA0BgBDgCgMVahAgBP+8W7867BTK2vr2d7ezv7+/tZW1vLjRs3Hp+HurW1lbt37yZJ3nnnndy8eTOrq6tJBtuO3L59O/1+P3/84x+zvr6elZWVXL9+/YnzVGdtogBXSukluTx06fNa61Obp3TlFpLsd3/3a60fPuOZY5UFADgJB4fVH6XX6408wH5hYeHx5z569CgXLlyYSf2eZ+wAV0q5m+T3tdb14WullF6tdWvo2kYOBbtSykYpZelw2JukLAAAA2MFuC5o7R0RqlaSvD9UbilJr9Z6cbhQrXW9lPKwlLJVa92ftCwAAN977iKGLmjdSvJUX2Ot9eKh4c61JNsjHtVP0puyLAAAnXFWoa5lMC+tP0bZlQzC11H6Sa5PWRYAgM44AW4lyW6SlFIWSimrXa/cUZaTfD7iXj/J1SnLAgDQGSfALSfZK6WsZhDmtpMsdAsYRgW5URZmVBYA4NwYdxXqYpL9WuvBnLXdUsp6kgellJ/WWvdLKQeB67kLDyYpe8Tn9tLNj3vjjTeys7Mz6SMm9ucX/iJ7r/5s5q9zGv7q6z9kZ+df512Nx7788stT+RqeN9p1drTt7Gjb2RjVrq+++mq++OKLlFJOv1I/EN99910ePXo00efUWvP1118f+3v9mQFuKGgtD4W3gwr0Syn9JO8mWX/qk2ek27JkK0muXr1ar127NvPX/KcP/zGL//7PM3+d0/DxpV5+ee3teVfjsZ2dnZzG1/C80a6zo21nR9vOxqh2/fjjj/PjH/84L7300ulX6gdimn3gvv3227zyyiv5m7/5m2O99jOHUIe28dgdUaSfZPVQ2ecOfU5SFgA4eRcuXMgXX3wx72qcO1988cWJbP47zhy4/SR7I+7tJRl3HtzBaQsnXRYAmNDi4mIePnyYzz77LN9++21qrfOu0g9WrTXffvttPvvsszx8+DCLi4vHfuY4c+D6GcyBG2U4aG3nyaO2hi0muT9lWQDgBL388su5dOlS9vb28sc//jHffffdvKvUnK+//jo//vGPxyr7wgsv5MKFC7l06VJefvnlY7/2OAHu/Qz2gjvKUp4MWrsZrFodVXZzyrIAwAl7+eWX8+abb+bNN9+cd1WatLOzc+y5bNMaZwh1K8nSiC1DVvLkCQ2bOWL/tm4xxHKSD6YsCwBA57kBrltwsJ5DPWKllM0kW8OrU7vTGra6s1OHbSRZHz7bdJKyAAB8b6x94Gqtd0op+11oO/Cg29LjcNn1UkqvlHIrg/lxl5PcO3Rm6sRlAQAYGHcj3xwV1k67LAAA482BAwDgDBHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAa86NpP7GUcq/Wen3EvV6ShST73d/9WuuHxy0LAMCUAa6UsppkZcS9jSSf11rvDF8rpSwNX5u0LAAAAxMHuFLKQpKbI+4tJenVWi8OX6+1rpdSHpZStmqt+5OWBQDge9PMgesleX/EvbUk2yPu9bvPnaYsAACdiQJcKWU5g9A1qmdsJYPwdZR+kutTlgUAoDNpD9xKrXX3GfeXk3w+4l4/ydUpywIA0Bk7wHWrRbeO+XoLMyoLAHBujLWIoVtwsPesRQXd4oZk9PDqVGWP+Nxeuvlxb7zxRnZ2diZ9xMT+/MJfZO/Vn838dU7DX339h+zs/Ou8q/HYl19+eSpfw/NGu86Otp0dbTsb2nV25tm2465CXT0r23rUWrfS9QRevXq1Xrt2beav+U8f/mMW//2fZ/46p+HjS7388trb867GYzs7OzmNr+F5o11nR9vOjradDe06O/Ns2+cOoXZ7vj13Y92h3rnnDn1OUhYAgCc9M8B1Q52LtdZRq0UncXDawkmXBQA4V543hNpL8rellCuHri8lSSlls/v4bq11O4MtRi6PeNZikvtDH09SFgCAzjMD3Kh5bwdHadVa1w7d2s1ge5CjLCXZnLIsAACdqQ+zH2EzyYPDF7uh2OUkH0xZFgCAzjRHaSWDIc7h7UCSJN1cua3ukPphG0nWh7chmaQsAADfm6gHrhs6vZnBMVhJ8ptSSj/JOweBqzuMvldKuZXBQoTLSe7VWp9ayTpJWQAABiYKcF2wGmdLkbFPbJikLAAA0w+hAgAwJwIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjfjRuwVLKrSSvJVnuLm3WWj8cUbaXZCHJfvd3/yTKAgAwZoArpWwkuV1r3e8+Xk7ym1LKzVrrjSPKfl5rvTN8rZSyNHxt0rIAAAw8N8B1PWSbB+EtSWqtu6WUG0nulVJWD3rMSilLSXq11ovDz6i1rpdSHpZStoZC4NhlAQD43jhz4C7XWvuHL9ZatzMY9lwburyWZHvEc/pJelOWBQCgM06Au1VKuTvi3v0kV4c+XskgfB2ln+T6lGUBAOiME+BG9ZIlyWKSvaGPl5N8PqJsP0+GvUnKAgDQee4cuFrrs3rClpNsTfB6CzMqCwBwboy9jchh3eKGJNnoPj4IXM9deDBJ2RGv20uSN954Izs7O5M+YmJ/fuEvsvfqz2b+Oqfhr77+Q3Z2/nXe1Xjsyy+/PJWv4XmjXWdH286Otp0N7To782zbqQJcF8A2ktw4aoHDLNVat9L1+l29erVeu3Zt5q/5Tx/+Yxb//Z9n/jqn4eNLvfzy2tvzrsZjOzs7OY2v4XmjXWdH286Otp0N7To782zbaU9iuJtkfXjD3aEtP5479DlJWQAAnjRxgOs2373b9YRN4uC0hZMuCwBwrkwU4LrjtD55RnjbTnJ5xL3FDLYdmaYsAACdsQNcKWU1yf7h8FZKWRn6cDfJ0ohHLGUw9DpNWQAAOmMFuIOQNqLnbXibkc0csX9bt+hhOckHU5YFAKAzzlmoyxkce/V+1wt3YDGDuWqPFyLUWvullK1SykatdX2o7EYGix72pykLAMD3xtlG5DcZhLTVEfeHw9fBYfS9br7cfgbz3O4Nr1idpiwAAAPjnMRwcdKHTrJCdYrVrAAA59q0+8ABADAnAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAY8Y5C5UfkJ9/upX89rV5V+N7X/40+e3t6T73F++ebF0AoBF64AAAGiPAAQA0xhDqOfRR//N5V+Gxr17963z0p+nq87s/f5wk+dX1t0+ySgBw5umBAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAaI8ABADRGgAMAaIwABwDQGAEOAKAxAhwAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMYIcAAAjRHgAAAa86N5VwCm9fNPt5IkH/16zhU5Ab+71EuS/Or623OuCQAt0AMHANAYAQ4AoDECHABAYwQ4AIDGCHAAAI0R4AAAGiPAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjBDgAgMY4zB7OgJ9/upUk+ejXJ/O8r179WT769f88mYdN6HeXeo//+1fX355LHQB+6PTAAQA0RoADAGiMAAcA0BgBDgCgMQIcAEBjrEIFTtTBitrk5FbVzsvwitrEqlrg7NADBwDQGAEOAKAxcx9CLaX0kiwk2e/+7tdaP5xvrQAAzq65BrhSykaSz2utd4avlVKWhq8BAPC9uQW4UspSkl6t9eLw9VrreinlYSllq9a6P6fqAQCcWfPsgVtLsj3iXj9JL4leOGBuhlfUJkl++1ry5U+T396eT4Wm9Yt3510D4ITNM8Ct5NkB7noEOOAM+aj/eb569a/z0Z8+n3dVJvK7P3985HXbokC75hnglpO8P+LeQQ8cAMf0VE9i56zt0/fVqz/LR7/+n/Ouxqk5vM/gMOGa55n7KtRnWJh3BQCAMTxnWsFH/XZ6rZ8VrA+chYA9lwBXSjkIZxMvUui2HTlo3S9LKf/nxCo22utJPjuF1zmPtO1saNfZ0bazc87a9n+NvPM/TvaFzlm7Htfor8uBoa/PrNv2v426cZZ74I5Ua91KcvR4wIyUUu7XWq+e5mueF9p2NrTr7Gjb2dG2s6FdZ2eebTuXkxiGtgcxTAoAMKGzepTWwckMAAAcMs8At53k8oh7i0nun2JdnudUh2zPGW07G9p1drTt7Gjb2dCuszO3ti211vm88OAYreVa6/Uj7j1IstnNdwMAYMg8A9xSkgeHj9LqVqg+THLRUVoAAE+bW4BLHvfCpda6PnRtM8knDrMHADjaXANc8nhft4NFC5eT/L7W+uFcK9U5VLeFJP2zUrdWdT2sG0nuacuTV0q5leS1DE46SQZTEbTzMXXft70M3qP2kyxlcGLMbSMFJ6uUcu+oqTVMppRyN4Pv0c1aa78b9VpJcqXWujbf2v0wdBlheC7/56fZ+TT3AHdWdb2DT3wxjrrGeLqe1cUkv88gwN0QLE5W9/35OFCUUpaT/CbJdq31xlwr17AuvL07PFLQXb+bQVC+IsSdjFLKapK7tdYy77q0rptLvnzo8rZwfDK6//9/fygj3M2gc+JU5u8LcEcYNT+vu/cwyU+9YU+vlFIjwJ2o7jfB7Vpr/9D1lST3or2n1vVq3kzy34f/v+8C8oMkaxZcHV8XlN9LsirAHV/3C929DHqLk+R+rXV3jlX6wejaduFwT2aXD945rffa5k5iOCVrGWxzcpR+BkMpeuE4Sy4fFSJqrdullP0MvqcFuOn08/0PQWanl+T9JKvzrsgPxOe11lE/x5hS18FzK0dsg3ZUp88sndWNfOdtJYM37aP0k+iC5qy51XXfH+V+EsfoTKnW+mGt9ahV8Qdt6ofkMXW9mduxgTtn31oG8+FHZYRTI8AdbTnJ5yPu9eOHIWfPs0LEYpK906rIObKeZOssvJH/AKwY3puNUspCKWWl6zni+FaS7CaP23Z1Xm0rwE3HGa6cKbXW689YqHDQu8EJKKUsdb2dH1rNd3zd/E1zCE/ea13bXs2gF36hlHKvm2vI9JaT7HULblYyeG9dKKXcPe0gZw7cIUPf3LryaV73Bp4MVv5yDENbibyWwWpqPW/H1P3A27MobGY+GGrb3W7y/YOMPsaS8Swm2R+aY7hbSllP8qCUcmqLHPXAwQ/U0J57NwzzHV+tdb/WeqfWut5tHXC9lHJv3vVq3KrV0bPRfZ/uH7q2nWRx6Bc7JjDUwbN8eIFI9x7bT/LuadVHgDtk6BteNzOtu5tk3Q/ImVlPsnJwogyT6YagfG+evn4S+0JOYbg3c0SRfk5xFbUAN7mDkxngzOpCxV37k81O92a+m8GwKhPoejIW9QzPhW1xjmc/oxeF7eUU29YcuKNtZ/QcgcUMJoTCmdRtPPuJ8HYySimfZLBgYf2I23tJlkspC+ZxTaSX5G9LKVcOXV9KHp/ckgx+CbEAZ0LdKQzbI75nOZ5+BjlglFN7HxDgjrabp48gObCUZHPEPZirblhq/3B4K6Ws+EE4ua6n6Fm/US9l0N7C2wRGHUd4sLLP6t5jW0jyyYh7Sxk9BMjzvZ/BXnBHWcopdvAYQj3aZo7Y6617M19O8sGp1wieozs2KyN63mw+PYUumG0d1ZMxFO68H3DWbB71PtCt+l2OTojj2EqyNGLLkJWc4op/Ae4I3byMrSMmJ29kMCncb9vH96wuaCbU7WS/1v336tCfXjekalHO9DaGhvSGvZdkV2/RiVpMnljtx3SO+vmVDILbHb3x0+t+/q/nUAju3iO2TrNtHWb/DN1S64NFC5eT/N6Kvul0IeJvM/jtbymDNr2fwXwCofiYukOUn/VDb33UsBXP1wWK4e0BljJ4P9CmJ6AbOr2ZQQ/GQgZDfP0MDgb33jCFQ9+zCxmE403h7WR0+WB4DueD0553LMABADTGECoAQGMEOACAxghwAACNEeAAABojwAEANEaAAwBojAAHANAYAQ4AoDECHABAYwQ4AIDG/H+nqYthRs17GQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for A in [2,1,0.1,0.01]:\n",
+    "    stat_h0,stat_h1 = dist_unknownA(A)\n",
+    "    plt.figure()\n",
+    "    plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "    plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "    plt.legend()\n",
+    "    plt.title('A='+str(A))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### d) Suppose that this pulse sits on a baseline with unknown height. (BTW, this is the standard in gamma-ray astronomy) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "introduce one more variable, the height"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The signal model is changed from the above to $s_i= A\\exp(-\\frac{(i-50)^2}{2\\sigma^2})+B$, $\\sigma=5$, $i=(1,2,...,100)$. Now both A and B are unknown parameters\n",
+    "\n",
+    "Test statistic $\\mathcal{T}(d) = \\log \\frac{\\mathcal{L}(d|H_1)}{\\mathcal{L}(d|H_0)} = \\sum_i (d_is_i - \\frac{1}{2}s_i^2)$\n",
+    "\n",
+    "Subsitute A into $\\mathcal{T}(d)$, and take $\\frac{\\partial\\mathcal{T}}{\\partial A} = 0$, we get $A = \\frac{\\sum_i(d_i-B)\\exp(-\\frac{(i-50)^2}{2\\sigma^2})}{\\sum_i\\exp^2(-\\frac{(i-50)^2}{2\\sigma^2})}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def t_unknownAB(d,shat,B):\n",
+    "    A = np.sum((d-B)*shat)/np.sum(shat*shat)\n",
+    "    s = A*shat+B\n",
+    "    return np.sum(d*s-0.5*s*s)\n",
+    "\n",
+    "def dist_unknownAB(A,B):\n",
+    "    sigma = 5\n",
+    "    x = np.arange(100)\n",
+    "    shat = np.exp(-(x-50)**2/(2*sigma**2))\n",
+    "    s = A*shat+B\n",
+    "    \n",
+    "    stat_h0 = []\n",
+    "    stat_h1 = []\n",
+    "    \n",
+    "    Bguess = B#assume we know B, in practice we'll build a template bank for B\n",
+    "    for i in range(1000):\n",
+    "        n = np.random.normal(0,1,100)\n",
+    "        d = n+s\n",
+    "        stat_h0.append(t_unknownAB(n,shat,Bguess))\n",
+    "        stat_h1.append(t_unknownAB(d,shat,Bguess))\n",
+    "    return stat_h0,stat_h1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for A in [2,1,0.1,0.01]:\n",
+    "    for B in [2,1,0]:\n",
+    "        stat_h0,stat_h1 = dist_unknownAB(A,B)\n",
+    "        plt.figure()\n",
+    "        plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "        plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "        plt.legend()\n",
+    "        plt.title('A='+str(A)+' B='+str(B))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### e) Suppose that the position of the pulse is unknown (that is, it can be at any position with uniform probability). How would you detect it then?\n",
+    "What would be the minimal A for you to detect? [for the same conditions as in (Q1 b)? Use monte-carlo to get A]\n",
+    "What is the equivalent \"look-elsewhere-effect\" of the positional uncertainty?\n",
+    "(look-elsewhere-effect is the ratio between the FAP of the known position statistic and the unknown position statistic evaluated at the detection threshold of the known position statistic)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The signal model is changed from the above to $s_i= A\\exp(-\\frac{(i-x)^2}{2\\sigma^2})$, $\\sigma=5$, $i=(1,2,...,100)$. x is an unknown position parameter\n",
+    "\n",
+    "Test statistic $\\mathcal{T}(d) = \\log \\frac{\\mathcal{L}(d|H_1)}{\\mathcal{L}(d|H_0)} = \\sum_i (Ad_i\\hat{s}_i -A^2 \\frac{1}{2}\\hat{s}_i^2)$, where $s = A\\hat{s}$\n",
+    "\n",
+    "Let $\\frac{\\partial{\\mathcal{T}(d)}}{\\partial A} =\\sum_i (d_i\\hat{s}_i -A\\hat{s}_i^2) = 0$, hence $A=\\frac{\\sum_id_i\\hat{s}_i}{\\sum\\hat{s}_i^2}$, this is the condition to achieve the maximized $\\mathcal{T}(d)$ for an unknown A\n",
+    "\n",
+    "Substitute A to the test statistic, we get $\\mathcal{T}(d) = \\frac{1}{2}\\frac{(\\sum_id_i\\hat{s}_i)^2}{\\sum_i\\hat{s}_i^2}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def t_unknownAx(d,shat):\n",
+    "    '''\n",
+    "    This is a matched-filtering.\n",
+    "    d is data.\n",
+    "    shat is a template.\n",
+    "    '''\n",
+    "    return 0.5*np.sum(d*shat)**2/np.sum(shat*shat)\n",
+    "\n",
+    "def signal(A,pos):\n",
+    "    '''\n",
+    "    A is the amplitude\n",
+    "    pos is the unknown position of the pulse\n",
+    "    '''\n",
+    "    sigma = 5\n",
+    "    x = np.arange(100)\n",
+    "    return A*np.exp(-(x-pos)**2/(2*sigma**2))\n",
+    "\n",
+    "def dist_unknownAx(A,pos,temp_offset=0):\n",
+    "    '''\n",
+    "    A is the amplitude\n",
+    "    pos is the unknown position of the pulse\n",
+    "    '''\n",
+    "    s=signal(A,pos)\n",
+    "    template = signal(A,pos+temp_offset)/A\n",
+    "    \n",
+    "    stat_h0 = []\n",
+    "    stat_h1 = []\n",
+    "    for i in range(1000):\n",
+    "        n = np.random.normal(0,1,100)\n",
+    "        d = n+s\n",
+    "        stat_h0.append(t_unknownA(n,template))\n",
+    "        stat_h1.append(t_unknownA(d,template))\n",
+    "    return stat_h0,stat_h1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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v63HKAgBQOTbADXvu7fAorZzz5pFbe9HbHmSQZkRsT1gWAIDKxIfZD7EdEY+PXqymYlcj4t6EZQEAqExylFZEb4qzfzuQiIionpXrVIfU99uKiHb/NiTjlAUA4GdjjcBVU6c3o3cMVkTEtymlbkR8dRi4qsPoWymlW9FbiHAlIh7mnN9ZyTpOWQAAesYKcFWwGmVLkZFPbBinLAAAk0+hAgBQEwEOAKAwAhwAQGEEOACAwghwAACFEeAAAAojwAEAFEaAAwAojAAHAFAYAQ4AoDACHABAYQQ4AIDCCHAAAIUR4AAACiPAAQAURoADACiMAAcAUBgBDgCgMAIcAEBhBDgAgMIIcAAAhRHgAAAKI8ABABRGgAMAKIwABwBQGAEOAKAwAhwAQGEEOACAwghwAACFEeAAAAojwAEAFEaAAwAojAAHAFAYAQ4AoDACHABAYQQ4AIDCCHAAAIUR4AAACiPAAQAURoADACiMAAcAUBgBDgCgMAIcAEBhBDgAgMIIcAAAhRHgAAAKI8ABABRGgAMAKIwABwBQGAEOAKAwH9RdAXhv390ZrdzLL0YvW6cvb9ddAwDmnAC3jEoIMQDAUKZQAQAKI8ABABRGgAMAKIwABwBQGAEOAKAwAhwAQGEEOACAwghwAACFEeAAAAojwAEAFEaAAwAojAAHAFAYAQ4AoDACHABAYQQ4AIDCCHAAAIUR4AAACiPAAQAURoADACjMB6MWTCndiohPImK1urSdc34wpGwrIhoRcVD93p1G2br84tX/if/2x4eTv8F3n0yvMgDA0hspwKWUtiLiTs75oPp6NSK+TSndzDlvDCj7NOd8t/9aSqnZf23csgAA9JwY4KoRsu3D8BYRkXPeSyltRMTDlNL64YhZSqkZEa2c88X+98g5t1NKz1JKnb4QOHJZAAB+NsozcFdyzt2jF3POO9Gb9tzsu7wZETtD3qcbEa0JywIAUBklwN1KKd0fcu9RRFzr+3oteuFrkG5E3JiwLAAAlVEC3LBRsoiIlYjY7/t6NSKeDinbjbfD3jhlAQConPgMXM75uJGw1YjojPF5jVMqCwCwNEbeRuSoanFDRMRW9fVh4Dpx4cE4ZYd8bisi4tNPP43d3d1x32Js/+/MX8X+x3878et3X078v5kpevmX87H78ou6q3GyGXxPl+zly5cz6fecLu24OLRlPSZKFlUA24qIjUELHE5TzrkT1ajftWvX8vXr10/9M//pwT/Eyv/9XxO//tdN+8DNg92XX8T1//z7uqtxsuv/ve4azLXd3d2YRb/ndGnHxaEt6zHpSQz3I6Ldv+Fu35YfJ059jlMWAIC3jR3gqs1371cjYeM4PG1h2mUBAJbKWAGuOk7ryTHhbScirgy5txK9bUcmKQsAQGXkAJdSWo+Ig6PhLaW01vflXkQ0h7xFM3pTr5OUBQCgMlKAOwxpQ0be+rcZ2Y4B+7dVix5WI+LehGUBAKiMchbqavSOvfqmGoU7tBK9Z9XeLETIOXdTSp2U0lbOud1Xdit6ix4OJikLAMDPRtlG5NvohbT1Iff7w9fhYfSt6nm5g+g95/awf8XqJGUBAOgZ5SSGi+O+6TgrVCdYzQoAsNQm3QcOAICaCHAAAIUR4AAACiPAAQAURoADACiMAAcAUBgBDgCgMKNs5AvM0nd36q7B9Hx5u+4aACwkAW4Gvu8+fa/X/7r5yZRqAgAsAlOoAACFEeAAAAojwAEAFEaAAwAojAAHAFAYAQ4AoDACHABAYQQ4AIDCCHAAAIUR4AAACiPAAQAURoADACiMAAcAUBgBDgCgMAIcAEBhBDgAgMIIcAAAhRHgAAAKI8ABABRGgAMAKIwABwBQGAEOAKAwAhwAQGEEOACAwghwAACFEeAAAAojwAEAFEaAAwAojAAHAFAYAQ4AoDACHABAYQQ4AIDCCHAAAIUR4AAACiPAAQAURoADACiMAAcAUBgBDgCgMAIcAEBhPqi7AsAC++7O9N/z5Ren876j+PJ2PZ8LcIQROACAwghwAACFEeAAAArjGbgCfN99+l6v/3XzkynVBACYB0bgAAAKI8ABABRGgAMAKIwABwBQGAEOAKAwAhwAQGEEOACAwghwAACFEeAAAAojwAEAFEaAAwAojAAHAFAYAQ4AoDACHABAYQQ4AIDCfFB3BQCK8d2dumswXV/errsGwIQEuCXwfffpe7/Hr5ufTKEmAMA0mEIFAChM7SNwKaVWRDQi4qD6vZtzflBvrQAA5letAS6ltBURT3POd/uvpZSa/deo3/tOw5qCBYDpqS3ApZSaEdHKOV/sv55zbqeUnqWUOjnng5qqBwAwt+ocgduMiJ0h97oR0YoIo3AAp6XOVbUvv5j+51tVyxKpcxHDWvSC2iDdiLgxw7oAABSjzhG41Yj4Zsi9wxE4mIrvu0/jTx//l/j+j5M9y+cZPgDmSe2rUI/RqLsCTM809qKrU931FyBhBIu20XIpTmM6fN7NwXR9LQEupXQYzsZepFBtO3I4OvcypfQvU6vYcJci4j9m8DmcLu24GLTjYtCOi2MJ2/J/zOqD/uuwG/M8AjdQzrkTEZ1ZfmZK6VHO+dosP5Pp046LQTsuBu24OLRlPWpZxNC3PYhpUgCAMc3rUVqHJzMAAHBEnQFuJyKuDLm3EhGPZliXk8x0ypZTox0Xg3ZcDNpxcWjLGqSccz0f3DtGazXn/M5+bymlxxGxXT3vBgBAnzoDXDMiHh89SqtaofosIi46SgsA4F21BbiIN6NwkXNu913bjognDrMHABis1gAX8WZft8NFC1ci4rc55we1VqpypG6NiOjOS90YTUrpfvRO9tjOOXerkd+1iLiac96st3YcVY3Ab0XEw+P6mr45/0ZpS/2zDCmlWxHxSfROUIrotdewNtU3Z6T2ADevqtHBp/0jgYOuMd+q5ylXj1zeGfTsJfWpRt5XIuK30ftLf+OYvyD0zTk2Zlvqn3Ou6lt3Dh9pSimtRsS30WunjQFl9c0ZEeAGGPZ8XnXvWUR84fm8MlQ/PB5GRLO69CjnvFdjlThBSinHkL/09c2yHNeW1X39c45Vo2k7Oefuketr0Wu3N22rb85ecScxzMhm9LY5GaQbvaO8/GuiDE9zzsPakvLom4tF/5xvVwbtBpFz3kkpHUSvPx6Gc31zxuZ1I9+6rUXvG26QbkQY3od66JswO7eq5xQHeRQR/cdn6ZszJsANthoRT4fc68bb37QUIKXUSCmtVcP8lEvfXED659w6bnR0JSL2+77WN2dMgJuMM1zL8Un1HMe16P2LsZFSelitkGPxaNey6J9zLOd84+hChT6rcXzAO0qbTpln4I7o+8HhYcvFca/v4dm96sHpxzH8KDfmkL65sPTPwlShO6K3yljfrIkROBZazrl9dOVT9dD0St8PIaAG+md5+vb32zi6OpXZEuCO6PthYrh3sXUjYtjUAHNI31wq+uf8uh8R7f6tYfTNeghw4zvcYZqydePnvadYDPrm4tA/51A1vX1/0NYiJ9A3T4EAN9hODH/+YiV6D9sy51JKjw/P22Vh6JsLQv8sS3Wc1pNjwpu+OWMC3GB7Mfxff83oDSEz/xoR8WTIvWb02pmy6JuLQ/8sREppPSIOjoa36kSGQ/rmjAlwg23HgD1rqoc3VyPi3sxrxCS2B/1rsdprajV67UxZ9M3FoX8W4DCkDRl569+cV9+cMQFugGplTWfA8P5W9B7eNJdfhkFtGNH7QXPXET5zbWXQRX2zSAPbMvTPuVcdXL9Z/Xm971ermlJ9s2hB35w9h9kfo1rGfvjw5ZWI+O2wQ5mZT9W//m5XXzai95fJtr8c5kv1l8HfRe9f6s3o9blH0XuY/Z0f/vrm/BqnLfXP+VYdQn/cytJ2zvmt8031zdkR4AAACmMKFQCgMAIcAEBhBDgAgMIIcAAAhRHgAAAKI8ABABRGgAMAKIwABwBQGAEOAKAwAhwAQGH+P798OQ0nqRMOAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for A in [2,1,0.1,0.01]:\n",
+    "    stat_h0,stat_h1 = dist_unknownAx(A,30)\n",
+    "    plt.figure()\n",
+    "    plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "    plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "    plt.legend()\n",
+    "    plt.title('A='+str(A))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Scan the template bank and choosing the maximum match"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 76,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for offset in [0,3,10]:\n",
+    "    stat_h0,stat_h1 = dist_unknownAx(A=1,pos=30,temp_offset=offset)\n",
+    "    plt.figure()\n",
+    "    plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "    plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "    plt.legend()\n",
+    "    plt.title('offset='+str(offset))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### f) What would you do if the width of the pulse is unknown, and can take any width between 2 bins and 30 bins? Use monte-carlo to determine the minimal A for detection [for the same conditions as (1b)]. What is the equivalent look-elsewhere-effect?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The signal model is changed from the above to $s_i= A\\exp(-\\frac{(i-50)^2}{2\\sigma^2})$, $i=(1,2,...,100)$. $\\sigma$ is an unknown variance parameter, $\\sigma\\in[2,30]$\n",
+    "\n",
+    "Test statistic $\\mathcal{T}(d) = \\log \\frac{\\mathcal{L}(d|H_1)}{\\mathcal{L}(d|H_0)} = \\sum_i (Ad_i\\hat{s}_i -A^2 \\frac{1}{2}\\hat{s}_i^2)$, where $s = A\\hat{s}$\n",
+    "\n",
+    "Let $\\frac{\\partial{\\mathcal{T}(d)}}{\\partial A} =\\sum_i (d_i\\hat{s}_i -A\\hat{s}_i^2) = 0$, hence $A=\\frac{\\sum_id_i\\hat{s}_i}{\\sum\\hat{s}_i^2}$, this is the condition to achieve the maximized $\\mathcal{T}(d)$ for an unknown A\n",
+    "\n",
+    "Substitute A to the test statistic, we get $\\mathcal{T}(d) = \\frac{1}{2}\\frac{(\\sum_id_i\\hat{s}_i)^2}{\\sum_i\\hat{s}_i^2}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def t_unknownAsigma(d,shat):\n",
+    "    '''\n",
+    "    This is a matched-filtering.\n",
+    "    d is data.\n",
+    "    shat is a template.\n",
+    "    '''\n",
+    "    return 0.5*np.sum(d*shat)**2/np.sum(shat*shat)\n",
+    "\n",
+    "def signal_unknownAsigma(A,sigma):\n",
+    "    '''\n",
+    "    A is the amplitude\n",
+    "    sigma is the unknown width of the pulse\n",
+    "    '''\n",
+    "    x = np.arange(100)\n",
+    "    return A*np.exp(-(x-50)**2/(2*sigma**2))\n",
+    "\n",
+    "def dist_unknownAsigma(A,sigma,temp_offset=0):\n",
+    "    '''\n",
+    "    A is the amplitude\n",
+    "    sigma is the unknown width of the pulse\n",
+    "    '''\n",
+    "    s=signal(A,sigma)\n",
+    "    template = signal(A,sigma+temp_offset)/A\n",
+    "    \n",
+    "    stat_h0 = []\n",
+    "    stat_h1 = []\n",
+    "    for i in range(1000):\n",
+    "        n = np.random.normal(0,1,100)\n",
+    "        d = n+s\n",
+    "        stat_h0.append(t_unknownA(n,template))\n",
+    "        stat_h1.append(t_unknownA(d,template))\n",
+    "    return stat_h0,stat_h1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for A in [2,1,0.1,0.01]:\n",
+    "    stat_h0,stat_h1 = dist_unknownAsigma(A,5)\n",
+    "    plt.figure()\n",
+    "    plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "    plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "    plt.legend()\n",
+    "    plt.title('A='+str(A))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 735.243x454.405 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for offset in [0,3,10]:\n",
+    "    stat_h0,stat_h1 = dist_unknownAsigma(A=1,sigma=5,temp_offset=offset)\n",
+    "    plt.figure()\n",
+    "    plt.hist(stat_h0,alpha=0.5,label='H0')\n",
+    "    plt.hist(stat_h1,alpha=0.5,label='H1')\n",
+    "    plt.legend()\n",
+    "    plt.title('offset='+str(offset))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### g) What if we have two identical pulses (still, with unknown width and height), but both their positions are unknown? What is the best strategy now? Are you more sensitive than in the one pulse version? By how much?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The signal model is changed from the above to $s_i= A\\exp(-\\frac{(i-x_1)^2}{2\\sigma^2})+A\\exp(-\\frac{(i-x_x)^2}{2\\sigma^2})$, $i=(1,2,...,100)$. $\\sigma$ is an unknown variance parameter, $\\sigma\\in[2,30]$. A is an unknown amplitude parameter. $x_1$ and $x_2\\in[1,100]$ are two unknown position parameters\n",
+    "\n",
+    "Test statistic $\\mathcal{T}(d) = \\log \\frac{\\mathcal{L}(d|H_1)}{\\mathcal{L}(d|H_0)} = \\sum_i (Ad_i\\hat{s}_i -A^2 \\frac{1}{2}\\hat{s}_i^2)$, where $s = A\\hat{s}$\n",
+    "\n",
+    "Let $\\frac{\\partial{\\mathcal{T}(d)}}{\\partial A} =\\sum_i (d_i\\hat{s}_i -A\\hat{s}_i^2) = 0$, hence $A=\\frac{\\sum_id_i\\hat{s}_i}{\\sum\\hat{s}_i^2}$, this is the condition to achieve the maximized $\\mathcal{T}(d)$ for an unknown A\n",
+    "\n",
+    "Substitute A to the test statistic, we get $\\mathcal{T}(d) = \\frac{1}{2}\\frac{(\\sum_id_i\\hat{s}_i)^2}{\\sum_i\\hat{s}_i^2}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def t_unknownAsigma(d,shat):\n",
+    "    '''\n",
+    "    This is a matched-filtering.\n",
+    "    d is data.\n",
+    "    shat is a template.\n",
+    "    '''\n",
+    "    return 0.5*np.sum(d*shat)**2/np.sum(shat*shat)\n",
+    "\n",
+    "def signal_twopulse(A,sigma,x1,x2):\n",
+    "    '''\n",
+    "    A is the amplitude\n",
+    "    sigma is the unknown width of the pulse\n",
+    "    '''\n",
+    "    x = np.arange(100)\n",
+    "    return A*np.exp(-(x-x1)**2/(2*sigma**2))+A*np.exp(-(x-x2)**2/(2*sigma**2))\n",
+    "\n",
+    "def dist_unknownAsigma_twopulse(A,sigma,x_1,x_2,offset1=0,offset2=0):\n",
+    "    '''\n",
+    "    A is the amplitude\n",
+    "    sigma is the unknown width of the pulse\n",
+    "    '''\n",
+    "    s=signal_twopulse(A,sigma,x_1,x_2)\n",
+    "    template = signal(A,sigma,x_1+offset1,x_2+offset2)/A\n",
+    "    \n",
+    "    stat_h0 = []\n",
+    "    stat_h1 = []\n",
+    "    for i in range(1000):\n",
+    "        n = np.random.normal(0,1,100)\n",
+    "        d = n+s\n",
+    "        stat_h0.append(t_unknownA(n,template))\n",
+    "        stat_h1.append(t_unknownA(d,template))\n",
+    "    return stat_h0,stat_h1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "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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+ "nbformat_minor": 2
+}