probs_n_stats_-_bootstrapping.ipynb

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  {
   "source": [
    "# Bootstrapping and resampling"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd \n",
    "from scipy.stats import ttest_ind\n",
    "from scipy.stats import norm\n",
    "sns.set()"
   ]
  },
  {
   "source": [
    "## Permutation test\n",
    "\n",
    "1. combine results from different groups in single data set.\n",
    "2. shuffle combined data, randomly draw (without replacing) a resample of same size as group A \n",
    "3. From remaining data, randomly draw (without replacing) a resample of same size as groub B \n",
    "4. calculate statistic for resamples\n",
    "5. repeat previous steps\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "mean difference: -0.42155447194141077\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-1.3848768419600213, pvalue=0.1724935970038468)"
      ]
     },
     "metadata": {},
     "execution_count": 105
    }
   ],
   "source": [
    "sample_a = np.random.normal(0, 1, 20)\n",
    "sample_b = np.random.normal(0.2, 1, 30)\n",
    "sample_mean_diff= np.mean(sample_a) - np.mean(sample_b)\n",
    "print(\"mean difference: {}\".format(sample_mean_diff))\n",
    "ttest_ind(sample_a, sample_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
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       "<matplotlib.axes._subplots.AxesSubplot at 0x1d987c9dc08>"
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "sns.distplot(sample_a)\n",
    "sns.distplot(sample_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "p-value: 0.1705\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {}
    }
   ],
   "source": [
    "diffs = np.array([])\n",
    "iterations = 10000\n",
    "sample = np.concatenate((sample_a, sample_b), axis=None)\n",
    "for i in range(iterations):\n",
    "    permutation = np.random.permutation(sample)\n",
    "    mean_a = np.mean(permutation[:len(sample_a)])\n",
    "    mean_b = np.mean(permutation[len(sample_a):])\n",
    "    diffs = np.append(diffs, mean_a - mean_b)\n",
    "sns.distplot(diffs)\n",
    "p_value = np.sum((np.abs(diffs)>np.abs(sample_mean_diff)))/diffs.shape[0]\n",
    "plt.axvline(sample_mean_diff, color='r')\n",
    "print(\"p-value: {}\".format(p_value))"
   ]
  },
  {
   "source": [
    "### Bootstrapping\n",
    "resample *with* replacement"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 30\n",
    "sample= np.random.normal(0, 1, size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d987bb91c8>]"
      ]
     },
     "metadata": {},
     "execution_count": 119
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "iterations = 1000\n",
    "means = np.array([])\n",
    "for i in range(iterations):\n",
    "    mean = np.mean(np.random.choice(sample, replace=True, size=size))\n",
    "    means = np.append(means, mean)\n",
    "sns.distplot(means)\n",
    "x = np.linspace(-1, 1, 100)\n",
    "plt.plot(x, norm.pdf(x, 0, 1/np.sqrt(size)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}