review_bayesian_stats.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RendererRegistry.enable('notebook')"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import altair as alt\n",
    "%matplotlib inline\n",
    "alt.renderers.enable('notebook')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binomial distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10  # number of tosses\n",
    "k = 9   # number of heads\n",
    "p = 0.5 # probability of heads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
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   ],
   "source": [
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "arrays must all be same length",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-141-03ccd5118a1e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m     \u001b[0mprobs_1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbinom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpmf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mitem\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m bin_data_1 = pd.DataFrame(data={'k': k,\n\u001b[0;32m----> 6\u001b[0;31m                               'probabilities':probs})\n\u001b[0m",
      "\u001b[0;32m~/Envs/bayesian/lib/python3.6/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, index, columns, dtype, copy)\u001b[0m\n\u001b[1;32m    328\u001b[0m                                  dtype=dtype, copy=copy)\n\u001b[1;32m    329\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 330\u001b[0;31m             \u001b[0mmgr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_init_dict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolumns\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    331\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mMaskedArray\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    332\u001b[0m             \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmrecords\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmrecords\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Envs/bayesian/lib/python3.6/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m_init_dict\u001b[0;34m(self, data, index, columns, dtype)\u001b[0m\n\u001b[1;32m    459\u001b[0m             \u001b[0marrays\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mkeys\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    460\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 461\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0m_arrays_to_mgr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marrays\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata_names\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolumns\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    462\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    463\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_init_ndarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalues\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolumns\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Envs/bayesian/lib/python3.6/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m_arrays_to_mgr\u001b[0;34m(arrays, arr_names, index, columns, dtype)\u001b[0m\n\u001b[1;32m   6161\u001b[0m     \u001b[0;31m# figure out the index, if necessary\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   6162\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 6163\u001b[0;31m         \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mextract_index\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marrays\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   6164\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   6165\u001b[0m         \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_ensure_index\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Envs/bayesian/lib/python3.6/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36mextract_index\u001b[0;34m(data)\u001b[0m\n\u001b[1;32m   6209\u001b[0m             \u001b[0mlengths\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mraw_lengths\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   6210\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlengths\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 6211\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'arrays must all be same length'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   6212\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   6213\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mhave_dicts\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mValueError\u001b[0m: arrays must all be same length"
     ]
    }
   ],
   "source": [
    "k=np.linspace(0,n,n+1,dtype=int)\n",
    "probs_1 = np.zeros(n+1)\n",
    "for item in k:\n",
    "    probs_1[item] = binom.pmf(item, n, p, loc=0)\n",
    "bin_data_1 = pd.DataFrame(data={'k': k,\n",
    "                              'probabilities':probs})"
   ]
  },
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"
     },
     "metadata": {
      "jupyter-vega3": "#9518bea3-9ab0-4f2c-9366-6a84ec9b53cc"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bar1 = alt.Chart(bin_data).mark_bar().encode(\n",
    "    x='k:Q',\n",
    "    y='probabilities:Q'\n",
    ")\n",
    "bar1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Bayesian",
   "language": "python",
   "name": "bayesian"
  },
  "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": 2
}