Distributions_and_Shot_Noise.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating and Plotting Distributions, and the Perils of Small Sample-Sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# all import modules\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# set some global parameters\n",
    "np.set_printoptions(suppress=True)\n",
    "\n",
    "params = {'legend.fontsize': 18,\n",
    "         'axes.labelsize': 18,\n",
    "         'axes.titlesize':24,\n",
    "         'xtick.labelsize':18,\n",
    "         'ytick.labelsize':18,\n",
    "         'font.size': 24}\n",
    "plt.rcParams.update(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "What happens if I were to roll a 10-sided die again and again - what would the distribution of numbers that came up look like?\n",
    "\n",
    "What would happen if I were to roll **two** 10-sided dice again and again and took the average of their results?\n",
    "\n",
    "What if I added more of the same dice into the mix?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist_gen(samples=1e6, draws=4, lowBound=0, upBound=100):\n",
    "    count = []\n",
    "    samples = int(samples)\n",
    "    lowBound = int(lowBound)\n",
    "    upBound = int(upBound)\n",
    "    for i in range(samples):\n",
    "        for j in range(draws):\n",
    "            count.append(np.mean(np.random.randint(lowBound,\n",
    "                                                   upBound + 1,\n",
    "                                                   draws)))\n",
    "    plt.hist(count, bins=range(lowBound, upBound + 2))\n",
    "    plt.show()\n",
    "    lq = np.percentile(count, 25)\n",
    "    uq = np.percentile(count, 75)\n",
    "    mu = np.mean(count)\n",
    "    sig = np.std(count)\n",
    "    tot_N = samples * draws\n",
    "    snr = np.sqrt(tot_N)\n",
    "    std_err = mu/np.sqrt(tot_N)\n",
    "    print(\n",
    "            'For {0} iterations and {4} draws: '\n",
    "            'Mean = {1:.1f}, '\n",
    "            'Sigma = {5:.1f}, '\n",
    "            'LQ = {2:.1f}, '\n",
    "            'UQ = {3:.1f}, '\n",
    "            'SNR = {6:.1f}, '\n",
    "            'Std. Error = {7:.3f}'\n",
    "            .format(samples, mu, lq, uq, draws, sig, snr, std_err))\n",
    "    return samples, draws, mu, sig, lq, uq, snr, std_err"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 1 draws: Mean = 5.5, Sigma = 2.9, LQ = 3.0, UQ = 8.0, SNR = 316.2, Std. Error = 0.017\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 2 draws: Mean = 5.5, Sigma = 2.0, LQ = 4.0, UQ = 7.0, SNR = 447.2, Std. Error = 0.012\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 3 draws: Mean = 5.5, Sigma = 1.7, LQ = 4.3, UQ = 6.7, SNR = 547.7, Std. Error = 0.010\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 4 draws: Mean = 5.5, Sigma = 1.4, LQ = 4.5, UQ = 6.5, SNR = 632.5, Std. Error = 0.009\n"
     ]
    }
   ],
   "source": [
    "# 10-sided\n",
    "\n",
    "for i in range(1, 5):\n",
    "    dist_gen(samples=1e5, draws=i, lowBound=1, upBound=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 1 draws: Mean = 50.4, Sigma = 28.8, LQ = 25.0, UQ = 75.0, SNR = 316.2, Std. Error = 0.160\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 2 draws: Mean = 50.5, Sigma = 20.4, LQ = 36.0, UQ = 65.0, SNR = 447.2, Std. Error = 0.113\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 3 draws: Mean = 50.5, Sigma = 16.7, LQ = 38.7, UQ = 62.3, SNR = 547.7, Std. Error = 0.092\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 4 draws: Mean = 50.5, Sigma = 14.4, LQ = 40.5, UQ = 60.5, SNR = 632.5, Std. Error = 0.080\n"
     ]
    }
   ],
   "source": [
    "# increase resolution: 100-sided\n",
    "\n",
    "for i in range(1, 5):\n",
    "    dist_gen(samples=1e5, draws=i, lowBound=1, upBound=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Shot-Noise\n",
    "\n",
    "If we roll a fair *n*-sided die *n*-times, in **theory** we should get each number once.\n",
    "\n",
    "However, does this happen in **practice**? If not, why, and how do we achieve the theoretical result?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: 10-sided die"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 10 iterations and 1 draws: Mean = 4.9, Sigma = 2.7, LQ = 3.0, UQ = 7.5, SNR = 3.2, Std. Error = 1.550\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZPTexem/g2gT8PfAfwD8C+wJ/AjwR+N2q+tc5ljd1/Z3K19ANYX2SblXdA+mWVl8AXldVH5xbgSuU5Hh+Ojx5It3P86z+8c1Vde6iY48ELqYb8jt70XN+AfitqvrKTIqeMoN/mZJ8lG5q3658qaqOnk0187Xagx8gye/T3aH8TLpf8pcDb6+qL8+1sIEkeTLd1OTn04XcPcC1dHfz7tU37CW5BDhqF7t/5v/b/k7mM4DD6YZ3LgNOqaprBixzUAa/JDXGi7uS1BiDX5IaY/BLUmMMfklqjMEvSY0x+CWpMQa/JDXG4Jekxhj8ktQYg1+SGvN/Wp0wEi8AXyMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100 iterations and 1 draws: Mean = 6.0, Sigma = 3.0, LQ = 3.8, UQ = 8.2, SNR = 10.0, Std. Error = 0.605\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 1000 iterations and 1 draws: Mean = 5.7, Sigma = 2.9, LQ = 3.0, UQ = 8.0, SNR = 31.6, Std. Error = 0.180\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 10000 iterations and 1 draws: Mean = 5.5, Sigma = 2.9, LQ = 3.0, UQ = 8.0, SNR = 100.0, Std. Error = 0.055\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 1 draws: Mean = 5.5, Sigma = 2.9, LQ = 3.0, UQ = 8.0, SNR = 316.2, Std. Error = 0.017\n"
     ]
    }
   ],
   "source": [
    "# Shot-noise demonstration\n",
    "\n",
    "values10 = np.zeros([5,8])\n",
    "\n",
    "for row, i in enumerate(np.logspace(1, 5, num=5, base=10), start=0):\n",
    "    values10[row] = dist_gen(samples=i, draws=1, lowBound=1, upBound=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: 6-sided die"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 6 iterations and 1 draws: Mean = 3.2, Sigma = 1.2, LQ = 2.0, UQ = 4.0, SNR = 2.4, Std. Error = 1.293\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 36 iterations and 1 draws: Mean = 3.4, Sigma = 1.8, LQ = 2.0, UQ = 5.0, SNR = 6.0, Std. Error = 0.574\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 216 iterations and 1 draws: Mean = 3.2, Sigma = 1.6, LQ = 2.0, UQ = 5.0, SNR = 14.7, Std. Error = 0.217\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 1296 iterations and 1 draws: Mean = 3.5, Sigma = 1.7, LQ = 2.0, UQ = 5.0, SNR = 36.0, Std. Error = 0.097\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 7776 iterations and 1 draws: Mean = 3.5, Sigma = 1.7, LQ = 2.0, UQ = 5.0, SNR = 88.2, Std. Error = 0.040\n"
     ]
    }
   ],
   "source": [
    "values6 = np.zeros([5,8])\n",
    "\n",
    "for row, i in enumerate(np.logspace(1, 5, num=5, base=6), start=0):\n",
    "    values6[row] = dist_gen(samples=i, draws=1, lowBound=1, upBound=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: 2-sided coin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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o7UVzd2MCb8zMMqdZFttfEXE0zUXO+Xs8nqP53IN1NCPyN2dmmd9kIuIampD+F5pA3o3mrux30gwwD89mzvjSH19T+t9tU1t4v69N22k722c/72k7ZCvwMPAp4BXT/t97ufUX8Gaa27Xvp7lgvBX4JnAu8JPTfn9j7qvPLNBXL+qvnraH99nPr9PM+30aeIzm9uufnvb7W279RfMo7CtpBgVP0szSuBv4G2D1tN/fBPrrHcANNIPGre2/p9tppimu2U7fLsnx5VMTJamAlXoBVJLUwzCXpAIMc0kqwDCXpAIMc0kqwDCXpAIMc0kqwDCXpAIMc0kqwDCXpAL+D1UvgsLDZ2pkAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 10 iterations and 1 draws: Mean = 1.4, Sigma = 0.5, LQ = 1.0, UQ = 2.0, SNR = 3.2, Std. Error = 0.443\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100 iterations and 1 draws: Mean = 1.4, Sigma = 0.5, LQ = 1.0, UQ = 2.0, SNR = 10.0, Std. Error = 0.143\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 1000 iterations and 1 draws: Mean = 1.5, Sigma = 0.5, LQ = 1.0, UQ = 2.0, SNR = 31.6, Std. Error = 0.047\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 10000 iterations and 1 draws: Mean = 1.5, Sigma = 0.5, LQ = 1.0, UQ = 2.0, SNR = 100.0, Std. Error = 0.015\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For 100000 iterations and 1 draws: Mean = 1.5, Sigma = 0.5, LQ = 1.0, UQ = 2.0, SNR = 316.2, Std. Error = 0.005\n"
     ]
    }
   ],
   "source": [
    "values2 = np.zeros([5,8])\n",
    "\n",
    "for row, i in enumerate(np.logspace(1, 5, num=5, base=10), start=0):\n",
    "    values2[row] = dist_gen(samples=i, draws=1, lowBound=1, upBound=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,3)\n",
    "fig.set_size_inches(16, 8)\n",
    "\n",
    "ax[0].scatter(values10[:, 0], values10[:,7], label='10-sided')\n",
    "ax[1].semilogx(values10[:, 0], values10[:,7])\n",
    "ax[2].loglog(values10[:, 0], values10[:,7])\n",
    "\n",
    "ax[0].scatter(values6[:, 0], values6[:,7], label='6-sided')\n",
    "ax[1].semilogx(values6[:, 0], values6[:,7])\n",
    "ax[2].loglog(values6[:, 0], values6[:,7])\n",
    "\n",
    "ax[0].scatter(values2[:, 0], values2[:,7], label='2-sided')\n",
    "ax[1].semilogx(values2[:, 0], values2[:,7])\n",
    "ax[2].loglog(values2[:, 0], values2[:,7])\n",
    "\n",
    "ax[0].legend(loc=0)\n",
    "ax[0].set_ylabel(r'Standard Error on $\\mu$')\n",
    "ax[1].set_xlabel(r'Number of Samples ($N$)')\n",
    "\n",
    "ax[0].set_title(r'Linear Axes')\n",
    "ax[1].set_title(r'Semi-Log X-axis')\n",
    "ax[2].set_title(r'Log-log axes')\n",
    "\n",
    "plt.show()"
   ]
  }
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