Part1_Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Compare the following methods of Monte Carlo integration: A) Regular Monte Carlo ; B) Importance Sampling ; C) Stratified Sampling\n",
    "\n",
    "First we need to find an example/ an appropriate function to be integrated through different methods:\n",
    "\n",
    "First example function: f(x) = 3x^4 + 2x exp(x) + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-25T05:59:41.210587Z",
     "start_time": "2018-11-25T05:59:41.134Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6 with absolute error < 4e-14"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SmQps5qhQQIECBAYKgCzRUz8qsnjiAN9VdgRuNWIM0I1movIaBAugSJBwgQIECA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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.width=7, repr.plot.height=6)\n",
    "\n",
    "# plotting the chosen function using built-in function curve()\n",
    "curve(3*x^4 + 2*x*exp(x) + 1 , xlim=c(-2,2), ylim=c(0,40), col=\"blue\")\n",
    "abline(h=0, col=\"black\")\n",
    "abline(v=0, col=\"black\")\n",
    "abline(v=1, col=\"red\")\n",
    "\n",
    "# The true value of the integral we are interested in, evaluated over interval (0, 1)\n",
    "integrate(function(x){3*x^4 + 2*x*exp(x) + 1}, 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We proceed with this example to perform our simulations, i.e. our function 'f' is : f(x) = 3*x^4 + 2*x*exp(x) +1 and we would like to find its integral over: (0, 1) for example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-25T06:00:02.296583Z",
     "start_time": "2018-11-25T05:59:58.401Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.58495737573558"
      ],
      "text/latex": [
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       "[1] 3.584957"
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     },
     "metadata": {},
     "output_type": "display_data"
    },
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     "data": {
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       "3.73379273385925"
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       "[1] 3.733793"
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       "[1] 3.598703"
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       "3.6 with absolute error < 4e-14"
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z42V1wWxn0S\nJVNa4pPCjsuK33tV3YVLyomVz2UyuZ7qAhtzmf169Yhck2IvL9midSuTrTMZ9yMlV7vZtJWs\nd8vuWZ7o65nctqU5+tcnJEgVDEYQQAABBBBAAAEEpkugelPc2h7fqdUGFGcrDlXsolALwbiw\n3u0oM1xAj9Ktig6xei3kS+8V2TJfGffVjhtsgWvQg5wPCZLbJuP8uG7v+np7drBN68vYqtyr\n/ercQH5V/7dzSe92lkzVrlPYes5IUtvxg3P9D1ySzK1djykEEEAAAQQQQAABBDZNoO5GdNKd\n/VprbK94lcJak+5Q2Mv79XGy5lFmvkD8rlj1WgitRnb85XGtOFpTHe/GtUj5xF9fXMf5uc4V\n6lqQ1BKUyTTsWCGTuH/RB/Xp0bzXZArZBq1M7indmZxakGrLvK36LDmnIIAAAggggAACCCAw\nbQLWA107ZaVWvqeFDf7awjqsssUFhpXk9IajKD7iZhMFP3p7Jumy5Gl0ZGzwrvIKNQmSFl5b\nnl8duGRtacJlMpnsguqC0pgenfukxs6on584b+8p2ctPW2WziXXEULOKEqfts935eaUOE6uL\nuhJnPSneUZ3DGAIIIIAAAggggAACmybQboL0nk37OLaeIQKh5SgM7bAqLUg9+42uHlmeLPPO\nDc49MLmveMwarxy784Wf3zR4WmU6jFiHDuXcRh1A6FG5+uJ2eezqZOFWByeP1Czxbuvids5l\nnfefrllmE5YgZTP7189XBw4NH9mrX49pBBBAAAEEEEAAAQRaFWg3QWp1v6w3CwSUHVUek9N4\nzTtDPctGV9RUwfsBPW5XmlVIbit+N1LNCtZvgt+oxKg4V28RjUtobEGut393vcZWSZBGVnUv\nVQuSWodCZuWydbu1ye2dz9h3INWVwtZ1M5hEAAEEEEAAAQQQQGCTBCZLkOwxKbtxthta69lM\nj0IljW5gNbumWHfPxS6fa+YyseUEGnTzrYOpJEhKb2o7Qag/Up+MhASl4AofrF9s0955+26s\nYnHOv6iS9ISZGrpMvtL73Ojqvudnk8xF0eK6UX+5tjhUMxdpf0fW78+5zHO07Id1GzGJAAII\nIIAAAggggMCUBSqPVTXZwyWaf79iSXn5deVpmzdRfLi8PoMZLKBWI/1XKRMnSImrvIOUz/tb\nK1vFI4XM+mgyXDPRLKU4LlN5NylTyOxdszCe8H6N98XeEjVXTVcuXINe3Y374hfSusQvjTdh\nHAEEEEAAAQQQQACBTRWYrAXp9/qAWxTryh90nobWi91k5f8mW4HlM0IgakFyuQmPKFNQYlLK\np33e5RutOzqcrM1W9uIaJlzOJ4dr27OK2ztrtRr33Fxxkff+u4XErchWFrs9SgvcYxqu1mYv\n1HDHs85Kso0e9yuu+wT9M3x9z9Nv8CN/W7asrqe/J+jz+RgEEEAAAQQQQACB6ROYLEGqbwn6\ngj7ablAfbnIIdgd9SHmdJqswe6YIqPmokiApDxnXLXftcbqQJFtncpXt4nWuHRy877BcbqOS\nnqbfT6R3k7bNr+5/jy/4h9QudFi8fTx++q+G/u3EI5Ot5s+v693b+Y1qWbpJTUovVMPSTq9Z\nlDv7rLMGX3Pcotzn8vn8lV37j5wT72dzj+dX9Z2iVrFP7pd0nat3q47e3J/H/hFAAAEEEEAA\nAQQ2r0CpSaD1z7AWpfdNsLr1GX2p4l0TrMOiGSJQ94jdxNeCd2pBKpexxi1IRxyh99R88Tux\nwpoaKp0pFl9KqnxytJKxb6jLb7UiuWdHK1ZHvR897bSksNUhyaPavjYZ88Xe9G6rrOySlyhJ\nukw97p2U6c7+j79E6dsmluEVPfuMrc697pIW9qVE7cWlj/NH5VfnvjSysrvho4WbeEhsjgAC\nCCCAAAIIIPAECUx2M7mXjuPQ6FjU21iyn+Lt0bwwajfY4eaw0ktZWMhw5gnELUg6ugkTJJ8U\nBlx5lUJ3lCyNq5a6+q4tl+eTwilZ7z6hx+KOUKtP3CTUrJvuB20XSqQsO7LOPuy6KxXnBwuF\nwp+zlc7uXK9WfG5xoXeZwQU57XPw7rD6VIbdma5LtN32h26de5L29eVG+xhZ0b+sK5P8a+Wz\n1f2EjvfErkz3iaOrMy/pXjx8fqPtmIcAAggggAACCCAwswUmS5CsI4bTFU+OqvEKjVs0K3ZD\n+4tmC5k/owTKrTvFY5owQRosDJ0/J9N/vhKlNf1LhponIM5viN8rUjLzue6lw1cUVuWqj+hN\nTnBTZRWf3KskpJog+WTD+uHhaxfk+ldoHUvWa0pXwdm12vz4atYePzG6su9wfV7xPTs9AniM\n1hiXII2s7D+gy/lrlOw17NExk2SO0nYkSON5mYMAAggggAACCMx4gckSJOuV7GWKfco1+aKG\nVygaJUD2KNSAwm5c1yooM0mgq9pjnbXM2KG104I0b79ErToDL2mhSnYNVIr3TgmTfZZbr89t\nUqyhSG8nVUulFarg3clqmqlcb9rPz7Y5KFk/uNy/qrc7USJV2xlEJuv31G6WV3c1+Zh9ee28\n/v7LtOaovpOp2gGFc4cPr+p5Ru+Skb+Evdi0KP+rWXJk66kjil3D+gwRQAABBBBAAAEEZpfA\nZAmS1cYSHgsryxSXK86xCcrsFlCCVEyUSrXwcYIy9Yp5JckhE1Lrz/qRoVXFnTl90WxlQe3u\nCwX/bj2gtps2+6gt0UE9Gta44tGB3xy2oP8hbbqtltyaXTL4bVuWWza4Vq1SasXRY3tRUSXO\nHF2ZW9u9dPDqaPaEo3Pm9Nsjes8srRQOvjTVlWRfpLFigjS8uueZ3Un2M6rHotLS8r8+Wams\nyOpXetTPucP0DtOxXYsHf16zHhMIIIAAAggggAACM16g3ZviE1WjRsmRJVpPU9TeXc746qf7\nANU8OKikI7SYtHstNMRTcqN9qnh/+x3rBvaw1p7Siq6S9JSmq//mM4VrkoIvvndUnOuq7zhZ\nxw96rO+rypoeLOSTj1S3SvTNtYV3x9OlcZfJ2rtB7RRf2Hr86qXOJfSY3QeViN2knvd+2J10\n3aD1xvVUp+O7dsQX3qZjXFnez4KMT/67sKp/XX5V7qTx+2YOAggggAACCCCAwEwVmMpN8bGq\nTPGv+OVKvVzDhxU3Kuzdj1Yew9JqlC0tsLOSGSU0/1U+jqlcCw2q4C62mepV7qLdj0iGKisU\nvHUP36g8tPbukVt84tdVF/qR6niSZJcMnZ5ZMrB9136DZ8fz+5YM36ztvmzJk1pwqp/V4N2k\neLt4fOAPuadkEvfKeF55/M7S0D1Fj9MtUuZ/Qnk6+iOAv6uQFN7x2NjQR+xYNP4flf0416U/\nF2ytBOsL669Ntgnzx1bkXp9f2X/G6Oreo6yjhzCfIQIIIIAAAggggMDMEGj3pthuJO0m9S0K\nu1HcSvFjhb1Ef6FijuKniqcqKLNCwD9UPsx2r4WGtcsuGfj2usGBrbKLB94Zr+Az/r54Oozr\n7aPT9nppMjyYGTpPrU6l1iyf/C0sn2yYXTx4kiVP2k+UPLl5Y6v7LXGftPT1ue8pAXp17YqW\noLnKe0e1y2xK3+Lkkx/kC4W3dS0e+t7CZcXvBkvOuXnoR1ryzdr11W1fX18xAVu+POnOZJLv\n6W2rt2ST7HldWX+tdSleuz5TCCCAAAIIIIAAAltSoN2b4lN1sLcrnq1Q40Oxly9Lkj6vsO+D\nWaqw6UZ/kddsykwTUKcH4RG77HQdW/WxuuoelfqsqU5Vx/R4WrG1aN7i5AFlHSd477/wyMbB\n/6yu0fLYtfGa6ijhgHi6fnxsdd9b9PjbBzV/v/plmr5fCdDyBvNLs5y7SYng29Q73+/idY4/\nPsk/8vjgyUr0Ho/nq4XqO/mVff+8tKvvq0rGctVlLtOVzfAIXhWEMQQQQAABBBBAYIsLtJMg\n2bp7K6yF6E/lI39pefjz8vA2Df+qaHTTWV6FwQwTUA9yxdLOtdB2FXySb/aIXaXXu66lQ2eq\nE4YPb/e8ZEO7H7Bhw+CZytntMc9iUfOmJfENy+DKvt3UFfcZzrkv6NG8hZWVfKKEx9+p5OjL\njw4NfL7SolVZwUb8NQ/4gabJlx17wReO14r6OfDDpU3VBUUm86/OZca9M6Uvmj1h/XLrgIKC\nAAIIIIAAAgggMBME2rkptsfo+hThUSlrcbAevh5RXKcIxdbpCRMMZ7zAtLcgNapx3mUbJ0g+\n03Yy1Gj/Wx+SrBsYHjxCSU0p4XLJiwZX9+1ev+5ZZyXZbJLZrjq/1L24mkO/65YMvDizeHAX\nJWlfLLaCuXKrl/drtN81to2Sp6uftLj45bXVXdSNdS0dPjezeGCfsbGxUq92dctrJ1333K7c\nVaedNvEX9dZuwxQCCCCAAAIIIIDA5hJoJ0GyG1xLhg4pH8wLNVygOF8RWiGWatxuSq0liTKT\nBLLFRyKLR2TPRkYlnLt2roVo89ZGc0uHLMkYrF9bj9g9Wj9vqtNzD1Ty7txlYfsefWHrX86q\nJutjK3PHvWZRbqjLJT8I64ShXn/6tVqdamm8u6W8fNXIaOEovef0vkeHBj8Ztpls2LP/6PWq\nc5P3qaJ3stQJxL8c09o7U5N9JssRQAABBBBAAAEENk2g3Zti6/HsOMWlChu3G8rvKKycorhS\nYTfcP1RQZoGALoByC1LNF7VuriNfWb9jn3FD9fM2ZbpQyH89bK+E5xt7L+qv9LioB92OVgJl\nvcs9I6wThnlXaiEK0zYc8fkPqMXokyOj/kN9BwzflF068PVG71fF29SPFwrJP+vHRD8T2lMo\n6nXvr12Du2rSHkctFn0Zbk2nFmE+QwQQQAABBBBAAIEnVqDdBOlkHZ71WvdshSVC71eEv9gf\npnHdkxa7Q67c+GmaMrMFwiN2yVnqUXtzHuoDbvBFhbx/g9KFH5WThqGRkcG10/mZwz5bk4S5\nxL+usDr3P8pO1OO2H5cYFT/b+2t7F4/8uf44+pYO36LOGE7tO2DotvplrU5b1+R69G+n4YLf\nQ3X+Q3E75//6jGckI7fePWAtrteX9uVfPLSyd6+xFf2v4J2kVnVZDwEEEEAAAQQQmH6BdhMk\n+2v/WxTWU90Oispf6zX+wfI8a1mizB6BSoKk7GGzJkj27o4Shp+qJeaEscLY/iNjhWcVH4ub\nRqs5+w3co0TkxsoundM7ce41XkmS5u1bmR+N6DubQqcj0dzpG7U62iOG+bz9jPiz83n/cdu7\ndW+uZPEHxU9Sy1ZPJnNjJpv8Su8k3Te2Onfs9B0Be0IAAQQQQAABBBBoVaDdBCns17pmts4Y\nnqWw1iQrtyqm5YX74t7454kSqCRI8zdzghRXqGfp6Kq+/YebvJ8Tr9n+uLoKD62a0cZOCYer\n7TzE+xGt+/XhYX96tOJmG+3eb/AadQJxXPd+Q5XjU6J4sZKmSm93xQ93LqsfzI9bhxKb7WDY\nMQIIIIAAAggggEBDgakkSLtoT3oaq9iTl/3l3b4DyYq1HH1K0WsTlNkiUPkeJDtxHXFDPpYv\nfGVC/XLHCT7xn1KPde/rP3DwzgnX34wLe/cf+aveTtJ7SvXF7XvsotyXRlf0HXqaergrrMqd\nrbhLcVF+de4D9shg/RZTmX70imTBLecmvWMr+95h3w11ySVJ11T2wzYIIIAAAggggECnCLSb\nID1ZFV+hsI4a7DGmOxSh2A3bxxT2ToW1LlFmgYButCstSLoz7ogEqZh0JIXTmvHnC/7tdz8+\n0J9dMnR6s3WeyPlr1w1+s1EPf/qepvdns5nLTnlV7n16g+pYxU6K5+u7k75SWNn/nk09Rn1R\n7mfmz+9/5Kk75f6SyWS+a98NdeiCnL1XSEEAAQQQQAABBFIr0G6C9FVJ5RSHKPZRWLIUir0z\n8WmFvQh/QpjJcAYKqLeC6KgKYVzZUUckSFafzOKhT+oLW9+WFPzZoX6lof/VzX8b+sPOByeD\ntfO33NTuRyRDvqbr8ajHOx2W/vLwufqjU5+Dp6vV553WuhSW5Vf2fUwdUvxy4I+5ncM8+1Jc\nzbuusLr/vuEVPfs8cEky15ZZC5R9SW1pPffUsL7mnaqWpLeH6TDMr+x/r1qv/qgHI48I85oN\n7dFAHg9spsN8BBBAAAEEEJjpApWbqxYP9EitZx0zXNlgfWuJ+ITiMcVBDZYza0sKdNUkRdGR\nFCotSLoRb/d6iPYzs0ZVF9+1ZOgHBed/HR/ZaD7/0Wccn9g7dDOqjI4UvqpWpHsUVxcSX9fl\nd927U6UjX6hWn++c8srcSTY5srJ7ictkPqW855i+Hne+zbPvgOrNuAs0b5kmd+jOdF297cLc\nY2o5+qKSnS8o87IW4drikq3UkvSpdSuTrcOCYjKVST6ulOqArMucM7S8t5JQhXXCML8y90/6\nrqn1ijs2rEi2C/MZIoAAAggggAACs0VAT1W1XPQOf/GLYW+aYItRLftLeb0JVmPRDBKotCB1\nUoIUfL13t8Vv6xSymRnTchSO0Yb2PUsa7GTj9h7QoQv7D3Lev1FJibXYlou/XL3e/UWtR29R\n0jPHZuqcvX94dc8FXT57dVhLM/exJKa7y71BayyK5qv3SbURuaSYVFXm24glZ/bzXfq8J22V\nyT2cX5V87PRfDv77yMt7ntld6rXS1ty6pzv7R723tOPOO/bumi1ktrHOJ2zB4Iq+XfVdUx/R\naL9Ffyb3Re3j0YIr/LZ78XAxabP1KAgggAACCCCAwEwWaKfFYL0qcp/igAkqZEmUPWJ34wTr\nsGhmCXR0gjTkB2+2u/8SuR/Z8MjQgzOLf/zRHHFEMpZdPPDO0bH8fvHSvC98Ort08L2FgnuT\n5t9fXObcrt0+e0ltIpUkSmJ+plTolHj7xuN+NO/zR122bnDX0SSvn+1gpVTHuc/8y6v6j+7K\nZJ9ft+3Cp+7Y//OeJLMqm3VXF1b1r1KL1BW9mcy5Wm9BWFfbv0nxvmySPU+tVj/jsbsgwxAB\nBBBAAAEEZrJAOwmS1eM8xTsU71MU32XQMBR7JOdHCvuOpN+FmQxnvEAlQdLFkJ3xR9vmAc7b\nL3nQJ86uS7v1/8X2RyQb29zFFlu9Z9nITXow8oHiAXh/TveS4QttvGvpwC/HxvwrKwfm3LaV\n8erI/kqa1PBjxY+q8mOl8fhf/3ih4P9O+73AkrLeJSPW+ntpvIbzyTGJ83uX5oXkSVMuObqS\nlLlkscafZy1X8bbxuBKl449d1F/36GC8RvPxketzB42s6F7cfA2WIIAAAggggAAC0yfQboL0\nQX20PYrzH4q7FQcr9lD8UnGr4hjFDxUXKSizQ6DyDpIOt93rYVbUcO0jA+9WK8mLH3SD4zof\nmMkVsPeoRt3YkYVC4e8e87XHftX6weU69lIrUrUSj3lfOKU+GVLL08vUpfn3Sqv5jfrup//2\nBX/yitHBBV1Lh86sbp4k+l4m/Yz7DdpH8VFEPY73ducyf19ax63Tsl/F6zca9+pBUMfxca1b\nk4yqb5CPnBZ1KtFo2zDP3oEaW9l7tFqe/q2ry13TlelarvH/yq/u/YC6Pn9BWG9zD63Di+FV\nPdYqTkEAAQQQQACBlAjoHqztYn+t/pTi7xQ90daPaPw0xTcU8U23JimTCNhf1r+jsFa5xydZ\nd0qLRy7sXtK1Q/dK27hwan6065fDxXM3knS/1SWZH9j8sWR4N73wcoeNU2a+wPD1Pft2d2X/\nV805uyihyav78qP0JbS/H1ude10mcT8t1+CRR0cH9vj9bcnGV++Ze1XBjf3NvqR3stqp17p/\n0LtOX6tZz/tL885/PJu4S/WZj+kzV6l1To/yJa9U69FRxXW9H3144+A22z0v2TB0Xd8e2Wyy\nszqTeIMSrXfZ8oL3xyo5eyzr3Ae0zTbqafAzXUuHf1vcVv9YhxB+de4KDZ4b5tUOrRXL6fUs\n/6VHNg6euvXc3oOHh4ZXzTkoeUDHUX6UsnaLdqfsUcCXP61vFzeibxbucau1/RzV83v3jw78\n447LkoGhVb2Lul3mNNX/r4nP2O+9JJ/xy3sWD17b7mexPgIIIIAAAh0iYPeVwwprPCm+mzyb\n66V7iikXexxrV8WTFGsU9ygoUxPYkgnSW5QgnWGHrQRpDyVIt0+tCmy1JQTWL0+27c/mXuQz\n/s7uxUNKLEpF7wSdrQTkaCUgx3UtGf5NmN/qcP21yTZz+3J3KRmpfKeZUhN9se7AKdZ1+Mjg\n0PqtDk6KyYElFOq17lJ93sFa50R9+a61MFeKdRjR0525WfvKKIV5UCnQvOp+/ePWkrVsWWId\nvCRqJTpZj+P9W2XjCUf8iPajX8jW4lXsGOLXypBu07yth0f8J6byBcDWcqUOKtQC7mre/yod\nhn9YQ/2I2Jfp1vUsqEcY1VX717OLB0+MD9mSxEd7hu5/0uLN84eP+LM217hM3ZpLkl7rjn5z\nfcZM2u9pauX86Ctzy+4fGLxhJn0dwEwy4lgQQACBBgIkSA1QmLVpAlssQRpOet6k1oYf2+Hn\nk+E9dTd866ZVha1nioDd2G5Kq4p1rGDvDqml5G/a1x8GRwb/39wDix21jKuifda65cn8hcuK\n3fyPW659/Uj7evO4BTbD+7vVQvNJDbdW1xD/pDnbjFvPq3fMUrfkC8ctazTDukv3/htjzl9X\nSDKP337z4INx9+4Dq3I7bVw3+Fh4J82OX0nlj3WMb2y0u5bn+eReJYBXqffER/RI4fY6A69U\nvUY0bd2qr7183cB/2vteLe9vC6xoSV13d+ZjEvmbWBboPTR7320nJYC/1PhWqsdCJaRdY37s\nXa20Rm6BKmzSR+ZX5z6vDk4+pPN23cbhwZfMf3ZiifEWKdZV/16Lckt+efPg9S/fKXlKz9zc\nP+gc7K3raYWus/m6Xg/VHyX+NDY29u8bx0bumd+be9bw6OCtnz83eUCJXvH9Ukv65yV9x2Uy\n7mVad61m/kx/jbj94YHBR0gAt8hp5UMR6FQBEqROPbNbsF6bP0G6uHtx1zbdxUer4kfslCC9\nQQnSmVZ3PRe5qC8ZvmULOvDRM0jgwSuTeQvm9B+57vGBi+yRuU05tOHlPc/q7u76U+0+dLtW\nzOE0V48IatRapUvFOpVwrkuP0n1Nw/V6vO3T9njbo1ckC+bN63u/3ov6RFh14qE6qEiKnVXc\n8PCGgedaPUZX9x1SfEzQJ3feNza4j+1XN8Vf103xe8fty/vbdZBn6Ub05Npl0bHXLphwSu+C\nfVmtTCfdeXWSW39Xko+Ttgk33MwLSy13yVsT74Z0472VzHZv4SMfHswn+87Zb2DWPj1g19Oc\nOX376vzupL8mPEvXwNtU/+2i6/Jveqz07zeMDl3fLPlvwantVUpd/ee+4ry66nf2nWT+CiWl\nB+lnobu1nVmrqrtVddlb2xW0nXW9X1uKP2PJZVr+mK5xtcYmV+UL7g8ZN/YU5zP7qlV6xTk3\nD5/3gj2SufPVSi2jhX4sf9e9I8MX27W7aFHvEfoDTPcV64bPn0rSP7wqeUZPknvULRm8u/bA\nmEIAgVkqQII0S0/cTD7sLZkgvVYJ0n8bjr6g9Om9yQhdtM/kK2UWH9vYqtyrMi6xa61b6cWH\nddP3NCU672pUJb2n9NPRscInyt8PNW6V0ZW552aL3+fk5uom8EVaQe/uaXzicu5YfvSjXdmu\nb2ndg4qrumS9PuuTujn+d80rdVKi96i07LfeuQsH8gNnz90veUhdmes4fb8SuZyO+TU6/u89\nnh/4WV+2+ymZJLtY71l9QduMb/mqPx7vB/Q5l2tfh+nG1252H1BrwIUbBwY+NDgnGd7O978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v6b4raraYzLTYbswNx+ey2Xs9VdZK+eVu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\nNOrRIbXb5QarmQGSiyZeH+O34sUb/end2Nijf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      "text/plain": [
       "Plot with title “Regular (Basic) MC Convergence”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A) Regular (Basic) Monte Carlo:\n",
    "\n",
    "# We implement this method as a function, this will help with the simulation study/comparison that comes next:\n",
    "\n",
    "option_A\t<-\tfunction(n){\t\t\t\t\t\t\t\t\t\t\t\t# The basic/simple MC to convert the integral into an expectation.\n",
    "\t\n",
    "\t\t\t\t\t\tz \t<-\t1\t\t\t\t\t\t\t\t\t\t\t\t\t# our integral's upper bound (or: max - min)\n",
    "\t\t\t\t\t\tu\t<-\trunif(n, min= 0, max= z)\t\t\t\t# uniform RVs: u ~ u [0, 1]\n",
    "\t\t\t\t\t\th\t<-\t z * (3*u^4+2*u*exp(u)+1)\t\t# this is the function h. NOTE: we need to multiply by upper bound z to convert the expression back to the original integral we are interested in. This is necessary because unifrom RVs are essentially dividing the expression by z and hence the need for multiplying by z to revert it.\n",
    "\t\t\t\t\t\treturn(mean(h))\t\t\t\t\t\t\t\t\t# evaluating the expectation to get a value for the integral\n",
    "\t\t\t\t\t\t\n",
    "}\n",
    "\n",
    "# Checking for different numbers of replications (iterations) n to get an overall picture of the behaviour of this method :\n",
    "option_A(10^2)\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# n = 100\n",
    "option_A(10^3)\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# n = 1,000\n",
    "option_A(10^6)\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# n = 1,000,000\t# Note: results get much closer to the true value of integral as n increases\n",
    "\n",
    "integrate(function(x){3*x^4+2*x*exp(x)+1}, 0, 1)\n",
    "\n",
    "# We can also check whether the estimates converge to the true value of the integral for a single sequence of simulations:\n",
    "\n",
    "set.seed(123456)\n",
    "estint <- rep(0, 10^4)\n",
    "esterr <- rep(0, 10^4)\n",
    "z \t\t\t\t<- 1\n",
    "u\t\t\t\t<-\trunif(10^4, min= 0, max= z)\n",
    "hA\t\t\t<-\t z * (3*u^4+2*u*exp(u)+1)\n",
    "for (i in 1:10^4){\n",
    "\testint[i] \t<- sum(hA[1:i]) / (i) \n",
    "\testerr[i] \t<- sqrt(sum((hA[1:i]-estint[1:i])^2))  / i \n",
    "}\n",
    "\n",
    "plot(estint, xlab=\"Mean and Error Range\", type=\"l\", lwd=2, col= \"red\", ylim= c(3,4.5), main=\"Regular (Basic) MC Convergence\")\n",
    "lines(estint + 2*esterr, col= \"gold\", lwd=2)\n",
    "lines(estint - 2*esterr, col=\"gold\", lwd=2)\n",
    "abline(h=3.6)\n",
    "\n",
    "# By the 10^4 th simulation this given sequence gets very close to the true value of the integral"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.33226986068167"
      ],
      "text/latex": [
       "3.33226986068167"
      ],
      "text/markdown": [
       "3.33226986068167"
      ],
      "text/plain": [
       "[1] 3.33227"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.43961246056629"
      ],
      "text/latex": [
       "3.43961246056629"
      ],
      "text/markdown": [
       "3.43961246056629"
      ],
      "text/plain": [
       "[1] 3.439612"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.60553461734854"
      ],
      "text/latex": [
       "3.60553461734854"
      ],
      "text/markdown": [
       "3.60553461734854"
      ],
      "text/plain": [
       "[1] 3.605535"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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MJf1v/PNOzOVPq3pPIT8xW3n9W1uaE8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\nAAIIIIAAAggggAACCCCAAAIIIFAMgf8HChmgc0PyTiUAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Example 1 : Importance Density g(x) & Function f(x)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KzyDNvoLkk+qLGjwNpB6vR7KHAAIIIIAAAggg0F0BGkjd9eyntVWv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2JeBBBAAAEEEEAAgf4RoIHUP3W1ZDnVTnFfZWN+8Hbn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Rk24fxJPd2aWG6vbZZkhZIsGsYJFwUK+R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\nOuZT9hXadkbdNHMZwvgv6sV16Ut5frfg0GF6K4XMLt3ZTmr8/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Q6ss/cH/j9yrJm1bvXduzbjaKrnhTMfQk9BvCxmGHQTJPEimKCwMDdA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\nTHk9+n0iXhLx7Ih6+075pMppfVu1rspzk77eQ3XJyS0fHIf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      "text/plain": [
       "Plot with title “Example 1 : Importance Sampling MC Convergence”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# B) Importance Sampling: hypothetically, we have an infinite number of combinations for the function f and the candidate density g. However, we would like the density to have certain properties that match the function's properties. We take two different importance densities and compare their performance:\n",
    "\n",
    "\n",
    "# IMPORTANCE DENSITY No 1:\n",
    "\n",
    "# We propose that g(x) = c * x^2 and evaluate the integral x^2 over [0, 1] to find that c = 3 : \n",
    " # Proceeding with g(x) = 3*x^2 as our importance density and plotting both g and f :\n",
    " \n",
    "curve(3*x^2, xlim=c(-3,3), ylim=c(0,20), col=\"red\", main=\"Example 1 : Importance Density g(x) & Function f(x)\")\t\t# g, the importance (or:instrumental) density\n",
    "curve(3*x^4 + 2*x*exp(x) + 1 , xlim=c(-3,3), ylim=c(0,20), col=\"blue\", add=T)\t\t\t# f, the function\n",
    "abline(v=1, col=\"green\")\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# upper bound of the integral\n",
    "\n",
    "# 1) According to a rule of thumb, when the function f is large importance density g has to be large too. In other words the candidate density g(x) has to be approximately proportional to the function f(x). This rule holds in the case of g(x) = 3*x^2 and this is desirable.\n",
    "\n",
    "# 2) In addition, we can see that it has a compatible support with our function h (i.e. g > 0 when h > 0).\n",
    "\n",
    "# \t>> hence we continue with g(x) = 3*x^2\n",
    "\n",
    "g_1 \t\t<- function(x) {3*x^2}\n",
    "f \t\t\t<-function(x) {(3*x^4 + 2*x*exp(x) + 1)}\t\n",
    "G_1\t\t<-\tfunction(x) {x^3}\t\t\t\t\t\t\t\t\t\t\t\t\t\n",
    "# Note also that inverse of G(x) is: (x)^(1/3)\n",
    "\n",
    "gene_1 <- function(n, min, max){\t\t# this function samples from the importance density g(x) by using the Inverse Transform method\n",
    "  \tu \t<- runif(n, 0, 1)\n",
    "  \ty \t<- (G_1(min) + u*(G_1(max)-G_1(min))) ^ (1/3)   \t# inverse of G(x) \n",
    "  \treturn(y)\n",
    "}\n",
    "\n",
    "\n",
    "option_B1 <- function(n){\t\t\t# implementing \n",
    "\tu \t<- runif(n, 0, 1)\t\t\t\t\t# n uniform RVs generated\t\n",
    "\tx <- gene_1(n, 0, 1)\n",
    "\th <- f(x) / g_1(x)\n",
    "\treturn(mean(h))\t\t\t\t\t\t# evaluating the mean of h (a vector) once is equal to one estimate for our integral\n",
    "}\n",
    "\n",
    "option_B1(10^2)\t\t\t\t\t\t\t# n = 100\n",
    "option_B1(10^3)\t\t\t\t\t\t\t# n = 1,000\n",
    "option_B1(10^6)\t\t\t\t\t\t\t# n = 1,000,000\t Note: results get much closer to the true value of integral as n increases\n",
    "\n",
    "\n",
    "# Similar to part A, we can check the convergence of a single sequence to the true value of the integral when using this method :\n",
    "\n",
    "set.seed(12345)\n",
    "estint_B1 \t<- rep(0, 10^4)\n",
    "esterr_B1\t\t<- rep(0, 10^4)\n",
    "h1\t\t\t\t<-\t gene_1(10^4, 0, 1)\t\t\t\t# sampling from g(x) using the previously defined function gene()\n",
    "h2 \t\t\t\t<- f(h1) / g_1(h1)\n",
    "for (i in 1:10^4){\n",
    "\testint_B1[i] \t<- sum(h2[1:i]) / (i) \n",
    "\testerr_B1[i] \t<- sqrt(sum((h2[1:i]-estint_B1[1:i])^2))  / i \n",
    "}\n",
    "\n",
    "plot(estint_B1, xlab=\"Mean and Error Range\", type=\"l\", lwd=2, col= \"red\", main=\"Example 1 : Importance Sampling MC Convergence\", ylim=c(2.5,4.5))\n",
    "lines(estint_B1 + 2*esterr_B1, col= \"gold\", lwd=2)\n",
    "lines(estint_B1 - 2*esterr_B1, col=\"gold\", lwd=2)\n",
    "abline(h=3.6)\n",
    "\n",
    "# Again, the sequence converges close to the true value as the number of simulations increases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# C) Stratified Sampling:\n",
    "\n",
    "f \t\t\t<-function(x) {(3*x^4 + 2*x*exp(x) + 1)}\n",
    "h_1  \t<-\tfunction(x) {(3*x^4 + 2*x*exp(x) + 1) / (3*x^2)}\t\t\t\t# s.t : h = f / g\n",
    "G_1\t\t<-\tfunction(x) {x^3}\n",
    "\n",
    "gene_1 <- function(n, min, max){\t\t\t\t\t# this function samples from the importance density g(x) by using the Inverse Transform method\n",
    "  \tu \t<- runif(n, 0, 1)\n",
    "  \ty \t<- (G_1(min) + u*(G_1(max)-G_1(min))) ^ (1/3)   \t\n",
    "  \treturn(y)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.59725449564116"
      ],
      "text/latex": [
       "3.59725449564116"
      ],
      "text/markdown": [
       "3.59725449564116"
      ],
      "text/plain": [
       "[1] 3.597254"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# m strata, number of RVs taken on each stratum = ni = n/m --> equal number per stratum\n",
    "\n",
    "strat_B1  \t<-\tfunction(n, m){\n",
    "  \n",
    "  res\t\t\t<-\trep(0, m)\n",
    "  s\t\t\t\t<-\tseq(0, 1, length.out=m+1)\n",
    "  a\t\t\t\t<-\tdiff(G_1(s))\t\n",
    "  for(i in 1:m){\n",
    "    u\t\t\t<-\tgene_1(n/m, min=s[i], max=s[i+1])\n",
    "    res[i]\t<-\tmean(h_1(u))\n",
    "  }\n",
    "  return(sum(a*res))\n",
    "  \n",
    "}\n",
    "strat_B1(1000, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.60949817968539"
      ],
      "text/latex": [
       "3.60949817968539"
      ],
      "text/markdown": [
       "3.60949817968539"
      ],
      "text/plain": [
       "[1] 3.609498"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# m strata, number of RVs taken on each stratum = ni = n*(a*devs)/sum(a*devs)  --> \"proportional allocation\"\n",
    "\n",
    "strat_C1  \t<-\tfunction(n, m, B){\n",
    "  \n",
    "  devs\t\t<-\trep(0, m)\n",
    "  s\t\t\t\t<-\tseq(0, 1, length.out=m+1)\t\n",
    "  \n",
    "  for(i in 1:m){\n",
    "    u\t\t\t<-\tgene_1(B, min=s[i], max=s[i+1])\n",
    "    devs[i]\t<-\tsd(h_1(u))\n",
    "  }\n",
    "  \n",
    "  a\t\t\t\t<-\tdiff(G_1(s))\t\n",
    "  ens\t\t\t<-\tn*(a*devs)/sum(a*devs)\t\t\t\t\t\t\t# \"proportional allocation\" to each stratum\n",
    "  ens\t\t\t<-\tround(ens)\n",
    "  \n",
    "  res\t\t\t<-\trep(0, m)\n",
    "  s\t\t\t\t<-\tseq(0, 1, length.out=m+1)\t\n",
    "  for(i in 1:m){\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# for each stratum do the following...\n",
    "    u\t\t\t<-\tgene_1(ens[i], min=s[i], max=s[i+1])\t\t# sample according to importance density g (through function gene() defined earlier)\n",
    "    res[i]\t<-\tmean(h_1(u))\t\t\t\t\t\t\t\t\t\t\t# evaluate h (x=u) and take their average\n",
    "  }\n",
    "  return(sum(a*res))\t\t\t\t\t\t\t\t\t\t\t\t\t\t# evaluating over all strata: our estimate for the integral\n",
    "  \n",
    "}\n",
    "strat_C1(1000, 10, 1000)\t\t\t\t\t\t\t\t\t\t\t# evaluating once to check that it works"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RM4Jf1pfgDUTfcTNogfyfam1I3guxLN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nTT+X1F+px1B21ITbTggV0eOZyXNbJXXuy+7X7qvDFJ8Tyyv7Kq8rryjhWFZbrpot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\nBBBAAAEEer3A/wPM4Nzg5e9r5gAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Example 1 : Stratified Sampling Methods”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparing the three different stratified sampling methods via a simple simulation study:\n",
    "\n",
    "set.seed(1234567)\t\t\t\t\t\t\t\t\t# making results reproducible by using the built-in set.seed() function\n",
    "B\t\t\t<-\t10^3\t\t\t\t\t\t\t\t\t\t\t# Number of simulations for this study\n",
    "resA1\t<-\trep(0, B)\t\t\t\t\t\t\t\t\t# containers for three methods\n",
    "resB1\t<-\trep(0, B)\n",
    "resC1\t<- rep(0, B)\n",
    "resD1\t<- rep(0, B)\n",
    "\n",
    "n\t\t<-\t10^5\n",
    "\n",
    "for(i in 1:B){\n",
    "\tresA1[i]\t\t<- strat_B1(n, 1)\t\t\t\t\t\t\t\t\t# No stratification (m=1)\n",
    "\tresB1[i]\t\t<- strat_B1(n, m=10)\t\t\t\t\t\t\t# 10 strata, equal allocation\n",
    "\tresC1[i] \t\t<- strat_C1(n, m=10, B=1000)\t\t\t# 10 strata, proportional allocation\n",
    "\tresD1[i]\t\t<- strat_C1(n, m= 30, B=1000)\t\t\t# 30 strata, proportional allocation\n",
    "}\n",
    "\n",
    "boxplot(resA1, resB1, resC1, resD1, names=c(\"No Stratification\", \"Equal Number\", \"Proportional, 10\", \"Proportional, 30\"), ylim=c(3.5,3.75), col=grey(0.8), range=0, main= \"Example 1 : Stratified Sampling Methods\")\n",
    "abline(h=3.6, col=\"red\", lwd=1)\t\t # the 'true' value of the integral from before\n",
    "\n",
    "# Conclusion: As expected, the fourth method (30 strata with proportional allocation) is the most accurate of all stratified methods above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CBAgACBJRVY7QnOkg5HtwkQmKOA3x9zxHYpAossUH+10ggQIECAAAECBAgQIEAg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\nfd8ZX78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      "text/plain": [
       "Plot with title “Example 1 : All Methods Compared”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulation Study: we now compare all different methods for this given importance density example:\n",
    "\n",
    "set.seed(1234567)\t\t\t\t\t\t\t\t# making results reproducible by using set.seed() function\n",
    "B\t\t<-\t10^4\t\t\t\t\t\t\t\t\t\t\t# number of simulations\n",
    "res1_1\t<-\trep(0, B)\t\t\t\t\t\t\t\t# containers\n",
    "res2_1\t<-\trep(0, B)\n",
    "res3_1\t<- rep(0, B)\n",
    "res4_1\t<- rep(0, B)\n",
    "res5_1\t<- rep(0, B)\n",
    "\n",
    "n\t\t<-\t10^4\n",
    "\n",
    "for(i in 1:B){\n",
    "\tres1_1[i]\t<- option_A(n)\n",
    "\tres2_1[i]\t<- option_B1(n)\n",
    "\tres3_1[i] \t<- strat_B1(n, m=10)\t\n",
    "\tres4_1[i]\t<-\tstrat_C1(n, m=10, B=1000)\n",
    "\tres5_1[i] <- strat_C1(n, m=30, B=1000)\n",
    "}\n",
    "\n",
    "boxplot(res1_1, res2_1, res3_1, res4_1, res5_1, names=c(\"Basic MC\", \"Importance MC\", \"Strat A\", \"Strat B\", \"Strat C\"), ylim=c(3.45,3.7), col=grey(0.8), range=0, main = \"Example 1 : All Methods Compared\")\n",
    "abline(h=3.6, col=\"red\", lwd=1)\n",
    "\n",
    "# Conclusion: The stratified with proportional allocation (optimal) from each stratum and 30 strata is the best method. It has the closest estimate to the true value of the integral as well as having the smallest error margin. Next are the other stratified sampling methods followed by simple monte carlo and importance sampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.08700522831943"
      ],
      "text/latex": [
       "3.08700522831943"
      ],
      "text/markdown": [
       "3.08700522831943"
      ],
      "text/plain": [
       "[1] 3.087005"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.43711730700536"
      ],
      "text/latex": [
       "3.43711730700536"
      ],
      "text/markdown": [
       "3.43711730700536"
      ],
      "text/plain": [
       "[1] 3.437117"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "3.63166308907774"
      ],
      "text/latex": [
       "3.63166308907774"
      ],
      "text/markdown": [
       "3.63166308907774"
      ],
      "text/plain": [
       "[1] 3.631663"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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I3h+rduswf0RdqsYz+Q9of1sR/c/NA9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lYAIEIFAIATtIh+tBZ99CUiMRCECgTAIZ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\n9VEcNWDKpggggAACcQswghR3/5AdAgggkJqAbvA6V6fSnaPrjNYftHB8j5U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ZEEAAAQQQQAABBBBAAIHCCfio0Z2KXoWPJl2p6FCwIIAA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\neQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Example 2 : Importance Density g(x) & Function f(x)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5KGawX3boXZwNfKbrPGIdxc4xGkk+4NJ6lQcTnN/0up3RfsfvKgNMSvlT8nDdLo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\nXKkcuBElNgvsboJc7hOaknt35UMbHx0a+n4+1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yXpjyR1rUlJ3hdJ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\nb9Rrr1RYAvhhxZ8VL1OYgyVQs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      "text/plain": [
       "Plot with title “Example 2 : Importance Sampling MC Convergence”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# IMPORTANCE DENSITY No 2:  another importance density:\n",
    "\n",
    "# We should redo parts B & C as A remains the same (because it does not depend on the candidate importance density).\n",
    "# We propose that g(x) = c * x^3 and evaluate the integral x^3 over [0, 1] to find that c = 4 : \n",
    " # Proceeding with g(x) =  4*x^3 as our importance density and plotting both g and f :\n",
    " \n",
    "curve(4*x^3, xlim=c(-3,3), ylim=c(0,20), col=\"red\", main=\"Example 2 : Importance Density g(x) & Function f(x)\")\t# g, the importance density\n",
    "curve(3*x^4 + 2*x*exp(x) + 1 , xlim=c(-3,3), ylim=c(0,20), col=\"blue\", add=T)\t\t\t# f, the function\n",
    "abline(v=1, col=\"green\")\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# upper bound of the integral\n",
    "\n",
    "# According to a rule of thumb, when the function f is large importance density g has to be large too. In other words the candidate density g(x) has to be approximately proportional to the function f(x). This rule holds in the case of g(x) =  4*x^3 and this is desirable.\n",
    "\n",
    "# \t>> hence we continue with g(x) =  4*x^3\n",
    "\n",
    "g_2 \t\t<- function(x) {4*x^3}\n",
    "f \t\t\t<- function(x) {(3*x^4 + 2*x*exp(x) + 1)}\t\t\n",
    "G_2 \t\t<- function(x) {x^4}\t\t\t\t\t\t\t\t\t\t\n",
    "# Note also that inverse of G(x) is: (x)^(1/4)\n",
    "\n",
    "gene_2 <- function(n, min, max){\t\t# this function samples from the importance density g(x) by using the Inverse Transform method\n",
    "  \tu \t<- runif(n, 0, 1)\n",
    "  \ty \t<- (G_2(min) + u*(G_2(max)-G_2(min))) ^ (1/4)   \t# inverse of G(x) \n",
    "  \treturn(y)\n",
    "}\n",
    "\n",
    "\n",
    "option_B2 <- function(n){\t\t\t# implementing \n",
    "\tu \t<- runif(n, 0, 1)\t\t\t\t\t# n uniform RVs generated\t\n",
    "\tx <- gene_2(n, 0, 1)\n",
    "\th <- f(x) / g_2(x)\n",
    "\treturn(mean(h))\t\t\t\t\t\t# evaluating the mean of h (a vector) once is equal to one estimate for our integral\n",
    "}\n",
    "\n",
    "option_B2(10^2)\t\t\t\t\t\t\t# n = 100\n",
    "option_B2(10^3)\t\t\t\t\t\t\t# n = 1,000\n",
    "option_B2(10^6)\t\t\t\t\t\t\t# n = 1,000,000\t Note: results get much closer to the true value of integral as n increases\n",
    "\n",
    "\n",
    "# Similar to part A and part B for Example no 1, we can check the convergence of a single sequence to the true value of the integral when using this method :\n",
    "\n",
    "set.seed(12345)\n",
    "estint_B2 \t<- rep(0, 10^4)\n",
    "esterr_B2 \t<- rep(0, 10^4)\n",
    "h1\t\t\t\t<-\t gene_2(10^4, 0, 1)\t\t\t# sampling from g(x) using the previously defined function gene()\n",
    "h2 \t\t\t\t<- f(h1) / g_2(h1)\n",
    "for (i in 1:10^4){\n",
    "\testint_B2[i] \t<- sum(h2[1:i]) / (i) \n",
    "\testerr_B2[i] \t<- sqrt(sum((h2[1:i]-estint_B2[1:i])^2))  / i \n",
    "}\n",
    "\n",
    "plot(estint_B2, xlab=\"Mean and Error Range\", type=\"l\", lwd=2, col= \"red\", main=\"Example 2 : Importance Sampling MC Convergence\", ylim=c(2.5,4.5))\n",
    "lines(estint_B2 + 2*esterr_B2, col= \"gold\", lwd=2)\n",
    "lines(estint_B2 - 2*esterr_B2, col=\"gold\", lwd=2)\n",
    "abline(h=3.6)\n",
    "\n",
    "# Again, the sequence converges close to the true value as the number of simulations increases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# C) Stratified Sampling:\n",
    "\n",
    "f \t\t\t<-function(x) {(3*x^4 + 2*x*exp(x) + 1)}\n",
    "h_2 \t\t<-\tfunction(x) {(3*x^4 + 2*x*exp(x) + 1) / (4*x^3)}\t\t\t\t# s.t : h = f / g\n",
    "G_2\t\t<-\tfunction(x) {x^4}\n",
    "\n",
    "gene_2 <- function(n, min, max){\t\t\t\t\t\t\t# this function samples from the importance density g(x) by using the Inverse Transform method\n",
    "  \tu \t<- runif(n, 0, 1)\n",
    "  \ty \t<- (G_2(min) + u*(G_2(max)- G_2(min))) ^ (1/4)   \t\n",
    "  \treturn(y)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.59495696292314"
      ],
      "text/latex": [
       "3.59495696292314"
      ],
      "text/markdown": [
       "3.59495696292314"
      ],
      "text/plain": [
       "[1] 3.594957"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# m strata, number of RVs taken on each stratum = ni = n/m --> equal number per stratum\n",
    "\n",
    "strat_B2  \t<-\tfunction(n, m){\n",
    "  \n",
    "  res\t\t\t<-\trep(0, m)\n",
    "  s\t\t\t\t<-\tseq(0, 1, length.out=m+1)\n",
    "  a\t\t\t\t<-\tdiff(G_2(s))\t\n",
    "  for(i in 1:m){\n",
    "    u\t\t\t<-\tgene_2(n/m, min=s[i], max=s[i+1])\n",
    "    res[i]\t<-\tmean(h_2(u))\n",
    "  }\n",
    "  return(sum(a*res))\n",
    "  \n",
    "}\n",
    "strat_B2(1000, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.6207344118628"
      ],
      "text/latex": [
       "3.6207344118628"
      ],
      "text/markdown": [
       "3.6207344118628"
      ],
      "text/plain": [
       "[1] 3.620734"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# m strata, number of RVs taken on each stratum = ni = n*(a*devs)/sum(a*devs)  --> \"proportional allocation\"\n",
    "\n",
    "strat_C2  \t<-\tfunction(n, m, B){\n",
    "  \n",
    "  devs\t\t<-\trep(0, m)\n",
    "  s\t\t\t\t<-\tseq(0, 1, length.out=m+1)\t\n",
    "  \n",
    "  for(i in 1:m){\n",
    "    u\t\t\t<-\tgene_2(B, min=s[i], max=s[i+1])\n",
    "    devs[i]\t<-\tsd(h_2(u))\n",
    "  }\n",
    "  \n",
    "  a\t\t\t\t<-\tdiff(G_2(s))\t\n",
    "  ens\t\t\t<-\tn*(a*devs)/sum(a*devs)\t\t\t\t\t\t\t# \"proportional allocation\" to each stratum\n",
    "  ens\t\t\t<-\tround(ens)\n",
    "  \n",
    "  res\t\t\t<-\trep(0, m)\n",
    "  s\t\t\t\t<-\tseq(0, 1, length.out=m+1)\t\n",
    "  for(i in 1:m){\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t# for each stratum do the following...\n",
    "    u\t\t\t<-\tgene_2(ens[i], min=s[i], max=s[i+1])\t\t# sample according to importance density g (through function gene() defined earlier)\n",
    "    res[i]\t<-\tmean(h_2(u))\t\t\t\t\t\t\t\t\t\t\t# evaluate h (x=u) and take their average\n",
    "  }\n",
    "  return(sum(a*res))\t\t\t\t\t\t\t\t\t\t\t\t\t\t# evaluating over all strata: our estimate for the integral\n",
    "  \n",
    "}\n",
    "strat_C2(1000, 10, 1000)\t\t\t\t\t\t\t\t\t\t\t# evaluating once to check that it works\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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mw39Xx+61i9e3p261j9DHlZ4n8l6mdMc00t/zjRTuO+dmqi2s73Bdm+f+I+iSq3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\nRK5CYII=",
      "text/plain": [
       "Plot with title “Example 2 : Stratified Sampling Methods”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Comparing the three different stratified sampling methods via a simple simulation study:\n",
    "\n",
    "set.seed(1234567)\t\t\t\t\t\t\t\t\t\t# making results reproducible by using the built-in set.seed() function\n",
    "B\t\t\t\t<-\t10^3\t\t\t\t\t\t\t\t\t\t\t# Number of simulations for this study\n",
    "resA2\t\t<-\trep(0, B)\t\t\t\t\t\t\t\t\t# containers for three methods\n",
    "resB2\t\t<-\trep(0, B)\n",
    "resC2\t\t<- rep(0, B)\n",
    "resD2\t\t<- rep(0, B)\n",
    "\n",
    "n\t\t<-\t10^5\n",
    "\n",
    "for(i in 1:B){\n",
    "\tresA2[i]\t\t<- strat_B2(n, 1)\t\t\t\t\t\t\t\t\t# No stratification (m=1)\n",
    "\tresB2[i]\t\t<- strat_B2(n, m=10)\t\t\t\t\t\t\t# 10 strata, equal allocation\n",
    "\tresC2[i] \t\t<- strat_C2(n, m=10, B=1000)\t\t\t# 10 strata, proportional allocation\n",
    "\tresD2[i]\t\t<- strat_C2(n, m= 30, B=1000)\t\t\t# 30 strata, proportional allocation\n",
    "}\n",
    "\n",
    "boxplot(resA2, resB2, resC2, resD2, names=c(\"No Stratification\", \"Equal Number\", \"Proportional, 10\", \"Proportional, 30\"), ylim=c(3.5,3.75), col=grey(0.8), range=0, main= \"Example 2 : Stratified Sampling Methods\")\n",
    "abline(h=3.6, col=\"red\", lwd=1)\t\t # the 'true' value of the integral from before\n",
    "\n",
    "# Conclusion: As expected, the fourth method (30 strata with proportional allocation) is the most accurate of all stratified methods above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NOuzMzLEndOlFO1vRKPuW5u/H8mffxO+lgZv2f2JECAAAECBNYUqCeOt0scmbjF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\nAjtP4P8BPhs+NuzxJS8AAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “Example 2 : All Methods Compared”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulation Study: we now compare all different methods for this given importance density example:\n",
    "\n",
    "set.seed(1234567)\t\t\t\t\t\t\t\t# making results reproducible by using set.seed() function\n",
    "B\t\t\t<-\t10^4\t\t\t\t\t\t\t\t\t\t# Number of simulations\n",
    "res1_2\t<-\trep(0, B)\t\t\t\t\t\t\t\t# containers\n",
    "res2_2\t<-\trep(0, B)\n",
    "res3_2\t<- rep(0, B)\n",
    "res4_2 \t<- rep(0, B)\n",
    "res5_2\t<- rep(0, B)\n",
    "\n",
    "n\t\t<-\t10^4\n",
    "\n",
    "for(i in 1:B){\n",
    "\tres1_2[i]\t<- option_A(n)\n",
    "\tres2_2[i]\t<- option_B2(n)\n",
    "\tres3_2[i] \t<- strat_B2(n, m=10)\t\n",
    "\tres4_2[i]\t<-\tstrat_C2(n, m=10, B=1000)\n",
    "\tres5_2[i] <- strat_C2(n, m=30, B=1000)\n",
    "}\n",
    "\n",
    "boxplot(res1_2, res2_2, res3_2, res4_2, res5_2, names=c(\"Basic MC\", \"Importance MC\", \"Strat A\", \"Strat B\", \"Strat C\"), ylim=c(3.45,3.7), col=grey(0.8), range=0, main = \"Example 2 : All Methods Compared\")\n",
    "abline(h=3.6, col=\"red\", lwd=1)\n",
    "\n",
    "# Conclusion: In this case too, the stratified with proportional allocation (optimal) from each stratum and 30 strata is the best method. It has the closest estimate to the true value of the integral as well as having the smallest error margin. Next are the other stratified sampling methods followed by simple monte carlo and importance sampling. Also note that this importance density does not do as well as the first density.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AACCCCAAAII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\n5ffoof08ajCv7j+as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      "text/plain": [
       "Plot with title “Example 1 & 2 : All Methods Compared”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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uqX+N6I74tBaR21PCad/mnUZ4M4DLoW16OuB+I2yQ+R4jYlricGhTns2vflwGUT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\nvQmQOgiXrCEAgSQIBHvrxl6LLgQvSj8rnZ5Eq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      "text/plain": [
       "Plot with title “Examples 1 & 2 : Importance Densities & Function f(x)”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# After running all the above code, the following lines generate the comparative boxplot of all methods considered for both examples:\n",
    "\n",
    "boxplot(res1_1, res2_1, res2_2, res3_1, res3_2, res4_1, res4_2, res5_1, res5_2, names=c(\"Basic\", \"Importance 1\", \"Importance 2\", \"Strat A 1\", \"Strat A 2\", \"Strat B 1\", \"Strat B 2\", \"Strat C 1\", \"Strat C 2\"), ylim=c(3.45,3.7), col=grey(0.8), range=0, main = \"Example 1 & 2 : All Methods Compared\")\n",
    "abline(h=3.6, col=\"red\", lwd=1)\n",
    "\n",
    "# And this generates all the functions in one graph:\n",
    "\n",
    "curve(3*x^4 + 2*x*exp(x) + 1 , xlim=c(-3,3), ylim=c(-1,20), col=\"black\", lwd=2, main=\"Examples 1 & 2 : Importance Densities & Function f(x)\")\t# f,  the function\n",
    "curve(3*x^2, xlim=c(-3,3), ylim=c(-1,20), col=\"blue\", add=T)\t# first density\n",
    "curve(4*x^3, xlim=c(-3,3), ylim=c(-1,20), col=\"red\", add=T)\t\t\t\t\t\t # second density\n",
    "abline(v=1, col=\"green\")\t\t\t\t\t\t\t\t\t\t\t\t"
   ]
  }
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