3 Bootstrap and Monte Carlo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bootstrap and Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "\n",
    "import time\n",
    "\n",
    "import scipy.stats "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem:\n",
    "Using the following sample data: 4.94, 5.06, 4.53, 5.07, 4.99, 5.16, 4.38, 4.43, 4.93, 4.72, 4.92, 4.96 <br>\n",
    "a) Compute the mean and its standard error (from the standard deviation) and the median. <br>\n",
    "b) Compute bootstrap estimates of the mean and median with estimates of their standard errors, using B = 1000 resamples. Also compute the median of the median estimates. <br>\n",
    "c) Compare the results of parts a) and b). <br>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) Use numpy library to compute statistical parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean  : 4.84083333333\n",
      "std   : 0.250880394256\n",
      "median: 4.935\n"
     ]
    }
   ],
   "source": [
    "data=[4.94, 5.06, 4.53, 5.07, 4.99, 5.16, 4.38, 4.43, 4.93, 4.72, 4.92, 4.96]\n",
    "print (\"mean  :\",np.mean(data))\n",
    "print (\"std   :\",np.std(data))\n",
    "print (\"median:\",np.median(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Using bootstrap estimations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimated mean  :  4.840055\n",
      "Bootstrap estimated std   :  0.236772492946\n",
      "Bootstrap estimated median:  4.91015\n"
     ]
    }
   ],
   "source": [
    "# Sample size\n",
    "n = len(data)\n",
    "# Bootstrap resamples\n",
    "B = 1000\n",
    "# Sample mean list\n",
    "mean = np.empty(B)\n",
    "std =np.empty(B)\n",
    "med =np.empty(B)\n",
    "# 1000 bootstrap samples of size n\n",
    "for i in range(B):\n",
    "    random_sample=np.random.choice(data,n)\n",
    "    sample_mean=np.mean(random_sample)\n",
    "    sample_std=np.std(random_sample)\n",
    "    sample_med=np.median(random_sample)\n",
    "    \n",
    "    mean[i]=sample_mean\n",
    "    std[i]=sample_std\n",
    "    med[i]=sample_med\n",
    "\n",
    "print(\"Bootstrap estimated mean  : \", np.mean(mean))\n",
    "print(\"Bootstrap estimated std   : \", np.mean(std))\n",
    "print(\"Bootstrap estimated median: \", np.mean(med))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) By comparing the result from raw data and their bootstrap resampling estimation:<br>\n",
    "For original data: <br>\n",
    "&emsp;&emsp; mean=4.84033; standard derviation=0.25088; median=4.93500<br>\n",
    "For Bootstrap sampled data:<br>\n",
    "&emsp;&emsp; mean=4.84293; standard derviation=0.23551; median=4.91074<br>\n",
    "which highly matched with each other, so it can be considered a good estimation.<br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem:\n",
    "Outliers can strongly influence statistics such as the mean and the least-squares line. The following data contains a low outlier in the value 29.12: \n",
    "41.28, 45.16, 34.75, 40.76, 43.61, 39.05, 41.20, 41.02, 41.33, 40.61, 40.49, 41.77, 42.07, 44.83, 29.12, 45.59, 41.95, 45.78, 42.89, 40.42, 49.31, 44.01, 34.87, 38.60, 39.63, 38.52, 38.52, 43.95, 49.08, 50.52, 43.85, 40.64, 45.86, 41.25, 50.35, 45.18, 39.67, 43.89, 43.89, 42.16. <br>\n",
    "a) Generate a boxplot of the data to identify 29.12 as an outlier. <br>\n",
    "b) Bootstrap the data and obtain bootstrap mean with and without the outlier. Plot histograms of the resampling distributions of the bootstrap means. How does the outlier influence the shape and bias of the bootstrap distribution? <br>\n",
    "c) Find 95% confidence intervals for the population mean from both bootstrap distributions. Discuss the differences. <br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) By simply using boxplot method in matplotlib:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'boxes': [<matplotlib.lines.Line2D at 0x6b417550>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x6b3a8510>,\n",
       "  <matplotlib.lines.Line2D at 0x6b3a8bf0>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x6b3ac9d0>],\n",
       " 'means': [],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x6b3ac910>],\n",
       " 'whiskers': [<matplotlib.lines.Line2D at 0x6b417510>,\n",
       "  <matplotlib.lines.Line2D at 0x6b417e10>]}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b49a7b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data=[41.28, 45.16, 34.75, 40.76, 43.61, 39.05, 41.20, 41.02, 41.33, 40.61, 40.49, 41.77, 42.07, 44.83, 29.12, 45.59, 41.95, 45.78, 42.89, 40.42, 49.31, 44.01, 34.87, 38.60, 39.63, 38.52, 38.52, 43.95, 49.08, 50.52, 43.85, 40.64, 45.86, 41.25, 50.35, 45.18, 39.67, 43.89, 43.89, 42.16]\n",
    "plt.boxplot(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As shown, the data point 29.12 located far away from the major range of the distribution of this data set, which can be regarded as a outlier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Now bootstrap the data set, I randomly resample the data set, with the same length of the original data, return the mean of the each sample set, and plot the histogram of bootstrap mean.\n",
    "$$ $$\n",
    "with the outlier 29.12:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimated mean: 42.17062475\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b49ab70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = len(data)\n",
    "B = 1000\n",
    "\n",
    "mean1 = np.empty(B)\n",
    "for i in range(B):\n",
    "    random_sample1=np.random.choice(data,n)\n",
    "    sample_mean1=np.mean(random_sample1)    \n",
    "    mean1[i]=sample_mean1    \n",
    "\n",
    "plt.hist(mean1,rwidth=0.7,alpha=0.7)\n",
    "print(\"Bootstrap estimated mean:\",np.mean(mean1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "without the outlier: 29.12:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimated mean: 42.53463425\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b378ab0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data1=[41.28, 45.16, 34.75, 40.76, 43.61, 39.05, 41.20, 41.02, 41.33, 40.61, 40.49, 41.77, 42.07, 44.83, 45.59, 41.95, 45.78, 42.89, 40.42, 49.31, 44.01, 34.87, 38.60, 39.63, 38.52, 38.52, 43.95, 49.08, 50.52, 43.85, 40.64, 45.86, 41.25, 50.35, 45.18, 39.67, 43.89, 43.89, 42.16]\n",
    "n2 = len(data1)\n",
    "\n",
    "mean2 = np.empty(B)\n",
    "for i in range(B):\n",
    "    random_sample2=np.random.choice(data1,n)\n",
    "    sample_mean2=np.mean(random_sample2)    \n",
    "    mean2[i]=sample_mean2 \n",
    "\n",
    "plt.hist(mean2,rwidth=0.7,alpha=0.7)\n",
    "print(\"Bootstrap estimated mean:\",np.mean(mean2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, by camparing the distribution of the bootstrap mean in which cases with and without outlier:<br>\n",
    "&emsp;&emsp;(i) the outlier 29.12 influenced the bootstrap mean by a certain degree, which decreased the mean by almost 0.3 (from 42.5135 to 42.1936); <br>\n",
    "&emsp;&emsp;(ii) the outlier influenced the distribution of the bootstrap mean, in a situation which sharpen the distribution near the histogram peak area in terms of the distrubution graph shape.<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(c) 95% confidence intervals for the population mean from both bootstrap distributions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% CI(with Outlier): [ 40.926525  43.335075] ; Interval= 2.40855\n",
      "95% CI(no Outliter) : [ 41.4290875   43.59285625] ; Interval= 2.40855\n"
     ]
    }
   ],
   "source": [
    "Confidence=95\n",
    "C_low=(100-Confidence)/2\n",
    "C_high=100-C_low\n",
    "C_interval1=np.percentile(mean1,[C_low,C_high])\n",
    "C_interval2=np.percentile(mean2,[C_low,C_high])\n",
    "\n",
    "print('95% CI(with Outlier):',C_interval1,'; Interval=',C_interval1[1]-C_interval1[0])\n",
    "print('95% CI(no Outliter) :',C_interval2,'; Interval=',C_interval1[1]-C_interval1[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Confidence Interval can be expressed as 'shifted' a little to the direction which is pointing to the outlier. However, the length of the CI remains the same; <br> \n",
    "The differences between the cases which involves outlier or not indicates: Only one single outlier could influenced the distribution of the Bootstrap mean, which includes the the mean value, the confidence intervals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem:\n",
    "\n",
    "Implement code in Python using the sample code on Bright Space (Monte Carlo Code Example.ipynb) so that you reproduce figures  3.6-3.8 and results that correspond to these figures from the book Understanding Computational Bayesian Statistics. Please make sure that you read whole chapter 3 from the book. <br>\n",
    "a)Use acceptance-rejection sampling as explained in the book Understanding Computational Bayesian Statistics on page 54. <br>\n",
    "b)Use importance sampling from Monte Carlo Code Example.ipynb.<br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(a) Acceptance-Rejection Sampling: find a constant $M$ such that $f_X \\leq M g$ where $g$ is the proposal distribution. We want $M$ to be as small as possible. but in this case I will simply pick the $M$ based on visualizations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b285510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "functools.partial(<function normal_dist at 0x6b2686a8>, mu=0, sigma=2.7)\n",
      "functools.partial(<function uniform_dist at 0x6b2f1270>, a=-4, b=8)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b240c90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rejection Sampling estimate of E[h(x)] (using normal): 0.07230929896881355\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b397490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b192dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rejection Sampling estimate of E[h(x)] (using uniform): 0.07141761984973469\n"
     ]
    }
   ],
   "source": [
    "from functools import partial\n",
    "from scipy.stats import norm\n",
    "\n",
    "def f_X(x):\n",
    "    A = 0.8*np.exp(-(x)**2/2)\n",
    "    B = 0.1*np.exp(-(x-3)**2/8)\n",
    "    return A+B\n",
    "\n",
    "#visualize pdf\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "x = np.linspace(-4, 8, 200)\n",
    "ax.plot(x, list(map(f_X, x)), color='gray', linewidth=3)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_title('pdf f_X')\n",
    "plt.show()\n",
    "\n",
    "#setting up proposal distributions, normal pdf: for sampling and evaluation\n",
    "def normal_dist(mu, sigma, x=None, n=None):\n",
    "    if x is not None:\n",
    "        return norm.pdf(x, mu, sigma)\n",
    "    elif n is not None:\n",
    "        return np.random.normal(mu, sigma, n)\n",
    "    else:\n",
    "        return None\n",
    "    \n",
    "def uniform_dist(a, b, x=None, n=None):\n",
    "    if x is not None:\n",
    "        return np.array([1 / (b - a)] * len(x))\n",
    "    elif n is not None:\n",
    "        return np.random.uniform(a, b, n)\n",
    "    else:\n",
    "        return None\n",
    "    \n",
    "prop = partial(normal_dist, mu=0, sigma=2.7)\n",
    "M = 6\n",
    "\n",
    "prop1 = partial(uniform_dist, a=-4, b=8)\n",
    "M1 = 12\n",
    "\n",
    "\n",
    "n_samples = 1000\n",
    "\n",
    "print(prop)\n",
    "print(prop1)\n",
    "\n",
    "def h(x):\n",
    "    return 1/(2.7 * 2**.5 * np.pi) * np.exp(-1*(x)**2/(2*2.7**2))\n",
    "\n",
    "fig, (ax1,ax2) = plt.subplots(1,2, figsize=(10, 5))\n",
    "ax1.plot(x, list(map(f_X, x)), color='gray', linewidth=3, label='f_X')\n",
    "ax1.plot(x, M * prop(x=x), '--', color='salmon', linewidth=2, label='proposal distr, M={}'.format(M))\n",
    "ax1.set_xlabel('X')\n",
    "ax1.set_title('normal pdf as proposal')\n",
    "ax1.legend(loc='best')\n",
    "ax2.plot(x, list(map(f_X, x)), color='gray', linewidth=3, label='f_X')\n",
    "ax2.plot(x, M1 * prop1(x=x), '--', color='blue', linewidth=2, label='proposal distr, M={}'.format(M1))\n",
    "ax2.set_xlabel('X')\n",
    "ax2.set_title('uniform pdf as proposal')\n",
    "ax2.legend(loc='best')\n",
    "plt.show()\n",
    "\n",
    "# Reject sampling\n",
    "def rejection(n, prop_dist, M, true_dist, h):\n",
    "    samples = []\n",
    "    while len(samples) < n:\n",
    "        sample = prop_dist(n=1)\n",
    "        if np.random.uniform(0, M * prop_dist(x=sample)) <= true_dist(sample):\n",
    "            samples.append(sample[0])    \n",
    "    mean_rej = np.mean(list(map(h, samples)))\n",
    "    return samples, mean_rej\n",
    "\n",
    "x_samples, mean_rej = rejection(n_samples, prop, M, f_X, h)\n",
    "fig, ax= plt.subplots(1, 1, figsize=(10, 5))\n",
    "ax.plot(x, list(map(f_X, x)), color='gray', linewidth=3)\n",
    "ax.hist(x_samples, bins=50, normed=1, color='blue', linewidth=0)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_title('Rejection Sampling Sampling Sanity Check (using normal)')\n",
    "print ('Rejection Sampling estimate of E[h(x)] (using normal): {}'.format(mean_rej)) \n",
    "\n",
    "x_samples, mean_rej = rejection(n_samples, prop1, M1, f_X, h)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "x=x = np.linspace(-4, 8, 200)\n",
    "ax.plot(x, list(map(f_X, x)), color='gray', linewidth=3)\n",
    "ax.hist(x_samples, bins=50, normed=1, color='blue', linewidth=0, alpha=0.4)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_title('Rejection Sampling Sampling Sanity Check (using uniform)')\n",
    "plt.show()\n",
    "print ('Rejection Sampling estimate of E[h(x)] (using uniform): {}'.format(mean_rej))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(b) Use importance sampling from Monte Carlo Code Example.ipynb.<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Importance Sampling estimate of E[h(x)] (using uniform): 0.17974661630291572\n"
     ]
    }
   ],
   "source": [
    "def importance(n, prop_dist, f_X, h):\n",
    "    samples = prop_dist(n=n)\n",
    "    weights = np.multiply(list(map(f_X, samples)), prop_dist(x=samples)**-1.)\n",
    "    mean_imp = np.mean(np.multiply(list(map(h, samples)), weights))\n",
    "    return mean_imp\n",
    "\n",
    "mean_imp = importance(n_samples, prop, f_X, h)\n",
    "print ('Importance Sampling estimate of E[h(x)] (using uniform): {}'.format(mean_imp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Problem:\n",
    "In order to determine that there is significant evidence at 98% level of confidence that the mean calcium level of two types of products differ by more than 5 units, independent analysis of these two products was done. 20 samples of the first products were tested and the following results were obtained: mean = 21.3 and standard deviation = 1.8. 15 samples of the second product were tested with the mean of 14.2 and standard deviation of 2.4. Measurements of both products follow normal distribution. <br>\n",
    "To determine that one product has higher calcium level than the other at 98% confidence level is the same as determining if confidence intervals of difference of the means of the concentration levels of two products does not include value 5 at 98% level. Compute confidence level of the difference using the hint below and comment on if the difference is significant or not.\n",
    "<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "For A product: $\\mu_A=21.3$, $\\sigma_A=1.8/\\sqrt20=0.40$ <br>\n",
    "For B product: $\\mu_B=14.2$, $\\sigma_B=2.4/\\sqrt15=0.62$ <br>\n",
    "Therefore, I can say: $A$~$N(21.3,0.40)$, and $B$~$N(14.2,0.62)$, what I do next is computing the probabilistic expression of the difference between these two product: $P(|A-B|)$. Further, the confidence level of $P(|A-B|\\leq5)$<br>\n",
    "Using Bootstrap Resampling to compute the Confidence Interval:<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean(Mul) = 7.10\n",
      "STD(Mul)  = 0.75\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b265f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "u_x=21.3\n",
    "s_x=0.4\n",
    "\n",
    "u_y=14.2\n",
    "s_y=0.62\n",
    "\n",
    "data_x= np.random.normal(loc=u_x, scale=s_x, size=10000)\n",
    "data_y= np.random.normal(loc=u_y, scale=s_y, size=10000)\n",
    "\n",
    "data=data_x-data_y\n",
    "\n",
    "print('Mean(Mul) = {:.2f}'.format(data.mean()))\n",
    "print('STD(Mul)  = {:.2f}'.format(data.std()))\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "plt.hist(data, bins=200, normed=True, histtype='step', lw=2)\n",
    "ax.set_xlabel('Difference between A and B')\n",
    "ax.set_title('Distribution of Differences between A and B')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bootstrap estimated mean: 7.09982343618\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6b0581d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length = len(data)\n",
    "B=10000\n",
    "mean = np.empty(B)\n",
    "\n",
    "for i in range(B):\n",
    "    randn_sp=np.random.choice(data,length)\n",
    "    sp_mean=np.mean(randn_sp)    \n",
    "    mean[i]=sp_mean \n",
    "\n",
    "print(\"Bootstrap estimated mean:\",np.mean(mean))\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(10, 5))\n",
    "plt.hist(mean,rwidth=0.7,alpha=0.7)\n",
    "#plt.hist(mean, bins=200, normed=True, histtype='step', lw=2)\n",
    "ax.set_xlabel('Difference between A and B')\n",
    "ax.set_title('Bootstrap Distribution of Differences between A and B')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Bootstrap resampling to compute the Confidence Interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "98% CI: [ 7.08270646  7.12801815] ; Interval= 0.0453116868033\n"
     ]
    }
   ],
   "source": [
    "Conf=98\n",
    "C_low=(100-Conf)/2\n",
    "C_high=100\n",
    "C_itv=np.percentile(mean,[C_low,C_high])\n",
    "\n",
    "print('98% CI:',C_itv,'; Interval=',C_itv[1]-C_itv[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, I can make the decision that: the Confidence Intervals of difference of the means of the concentration levels of two products is 7.08899 units when comes with 98% CI level. "
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}