Lesson 1 - Stock_beta.ipynb

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      "/Users/sachin/miniconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "import theano\n",
    "import pymc3 as pm\n",
    "from pymc3 import plot_posterior\n",
    "\n",
    "%matplotlib inline"
   ]
  },
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   "source": [
    "%%capture\n",
    "%%bash\n",
    "mkdir data/\n",
    "wget -P ./data/ https://github.com/sachinruk/bayes_school/raw/master/data/all_stocks_5yr.csv.zip \n",
    "wget -P ./data/ https://raw.githubusercontent.com/sachinruk/bayes_school/master/data/sandp500.csv"
   ]
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   "source": [
    "The data was downloaded from https://www.kaggle.com/camnugent/sandp500"
   ]
  },
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2012-08-13</td>\n",
       "      <td>92.29</td>\n",
       "      <td>92.59</td>\n",
       "      <td>91.74</td>\n",
       "      <td>92.40</td>\n",
       "      <td>2075391.0</td>\n",
       "      <td>MMM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2012-08-14</td>\n",
       "      <td>92.36</td>\n",
       "      <td>92.50</td>\n",
       "      <td>92.01</td>\n",
       "      <td>92.30</td>\n",
       "      <td>1843476.0</td>\n",
       "      <td>MMM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2012-08-15</td>\n",
       "      <td>92.00</td>\n",
       "      <td>92.74</td>\n",
       "      <td>91.94</td>\n",
       "      <td>92.54</td>\n",
       "      <td>1983395.0</td>\n",
       "      <td>MMM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2012-08-16</td>\n",
       "      <td>92.75</td>\n",
       "      <td>93.87</td>\n",
       "      <td>92.21</td>\n",
       "      <td>93.74</td>\n",
       "      <td>3395145.0</td>\n",
       "      <td>MMM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2012-08-17</td>\n",
       "      <td>93.93</td>\n",
       "      <td>94.30</td>\n",
       "      <td>93.59</td>\n",
       "      <td>94.24</td>\n",
       "      <td>3069513.0</td>\n",
       "      <td>MMM</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "         Date   Open   High    Low  Close     Volume Name\n",
       "0  2012-08-13  92.29  92.59  91.74  92.40  2075391.0  MMM\n",
       "1  2012-08-14  92.36  92.50  92.01  92.30  1843476.0  MMM\n",
       "2  2012-08-15  92.00  92.74  91.94  92.54  1983395.0  MMM\n",
       "3  2012-08-16  92.75  93.87  92.21  93.74  3395145.0  MMM\n",
       "4  2012-08-17  93.93  94.30  93.59  94.24  3069513.0  MMM"
      ]
     },
     "execution_count": 2,
     "metadata": {},
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   ],
   "source": [
    "df = pd.read_csv('./data/all_stocks_5yr.csv.zip', compression='zip')\n",
    "df.head()"
   ]
  },
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   "execution_count": 7,
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     "text": [
      "(1259, 2)\n"
     ]
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       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2014-07-09</td>\n",
       "      <td>1972.829956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014-07-10</td>\n",
       "      <td>1964.680054</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2014-07-11</td>\n",
       "      <td>1967.569946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2014-07-14</td>\n",
       "      <td>1977.099976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2014-07-15</td>\n",
       "      <td>1973.280029</td>\n",
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      "text/plain": [
       "        Date        Close\n",
       "0 2014-07-09  1972.829956\n",
       "1 2014-07-10  1964.680054\n",
       "2 2014-07-11  1967.569946\n",
       "3 2014-07-14  1977.099976\n",
       "4 2014-07-15  1973.280029"
      ]
     },
     "execution_count": 7,
     "metadata": {},
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   ],
   "source": [
    "sandp500 = pd.read_csv('./data/sandp500.csv')\n",
    "sandp500['Date'] = pd.to_datetime(sandp500['Date'])\n",
    "sandp500 = sandp500[['Date', 'Close']]\n",
    "print(sandp500.shape)\n",
    "sandp500.head()"
   ]
  },
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    {
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       "(1258, 2)"
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     "execution_count": 10,
     "metadata": {},
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   ],
   "source": [
    "stocks = ['MSFT']\n",
    "df_stocks = df.loc[df.Name.isin(stocks), ['Date', 'Close']]\n",
    "df_stocks['Date'] = pd.to_datetime(df_stocks['Date'])\n",
    "df_stocks.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Merge the two dataframes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_final = pd.merge(sandp500, df_stocks, on=['Date'], suffixes=('_sandp', '_MSFT'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
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     "output_type": "stream",
     "text": [
      "(781, 3)\n"
     ]
    },
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Close_sandp</th>\n",
       "      <th>Close_MSFT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2014-07-09</td>\n",
       "      <td>1972.829956</td>\n",
       "      <td>41.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014-07-10</td>\n",
       "      <td>1964.680054</td>\n",
       "      <td>41.68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2014-07-11</td>\n",
       "      <td>1967.569946</td>\n",
       "      <td>42.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2014-07-14</td>\n",
       "      <td>1977.099976</td>\n",
       "      <td>42.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2014-07-15</td>\n",
       "      <td>1973.280029</td>\n",
       "      <td>42.45</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date  Close_sandp  Close_MSFT\n",
       "0 2014-07-09  1972.829956       41.67\n",
       "1 2014-07-10  1964.680054       41.68\n",
       "2 2014-07-11  1967.569946       42.09\n",
       "3 2014-07-14  1977.099976       42.14\n",
       "4 2014-07-15  1973.280029       42.45"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(df_final.shape)\n",
    "df_final.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "cols = ['Close_sandp','Close_MSFT']\n",
    "df_final.sort_values('Date', inplace=True)\n",
    "df_final.reset_index(drop=True, inplace=True)\n",
    "df_final[cols] = np.log(df_final[cols])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_final[cols] = df_final[cols].diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
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KvEPbaUvE+oyEa0vEWL35RSaMaVVtpUGUElTy/wUvAG4AcPduMyt/fKNInRhK30jYrO0z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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_final.plot('Close_sandp', 'Close_MSFT', kind='scatter')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df_final['Close_sandp'].values[1:][:,None]\n",
    "y = df_final['Close_MSFT'].values[1:][:,None]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hEdLmTj5jpkG"
   },
   "source": [
    "## Scikit-Learn Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((780, 1), (780, 1))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 269
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1215,
     "status": "ok",
     "timestamp": 1561887818212,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "SKlIW45chWZM",
    "outputId": "0451b931-1fb4-4402-eaaf-bb8d3a2d54d6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model parameters are: [0.0003845] [[1.19160762]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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SzdrxBLesauWwA2/7tr8y9CgWzllER/OxJSlHz0FHU2MDhw8elHVFr0Xxqp+CQapbyhyq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\nEfFRMIiIiI+CQUREfBQMIiLi8/8BqkEBaz7XYOgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = LinearRegression()\n",
    "model.fit(x, y)\n",
    "print('Model parameters are:', model.intercept_, model.coef_)\n",
    "\n",
    "y_pred = model.predict(x)\n",
    "plt.scatter(x,y)\n",
    "plt.plot(x, y_pred, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 174
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 43246,
     "status": "ok",
     "timestamp": 1561887860639,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "BB6rDmNEhWZS",
    "outputId": "b78cabc8-516f-4e9b-aac6-441c6f1ec701"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [sd, β, α]\n",
      "Sampling 4 chains: 100%|██████████| 4000/4000 [00:02<00:00, 1448.77draws/s]\n",
      "The acceptance probability does not match the target. It is 0.9068457916439003, but should be close to 0.8. Try to increase the number of tuning steps.\n"
     ]
    }
   ],
   "source": [
    "x_t = theano.shared(x.squeeze())\n",
    "y_t = theano.shared(y.squeeze())\n",
    "\n",
    "n_samples=500\n",
    "\n",
    "with pm.Model() as model:\n",
    "    α = pm.Normal('α', mu=0, sd=1)\n",
    "    β = pm.Normal('β', mu=0, sd=1)\n",
    "    regression = α+β*x_t\n",
    "\n",
    "    sd = pm.Uniform('sd', 0, 1)\n",
    "    likelihood = pm.Normal('y', mu=regression, sd=sd, observed=y_t)\n",
    "    trace = pm.sample(n_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 42630,
     "status": "ok",
     "timestamp": 1561887860975,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "k01dntLGutGw",
    "outputId": "45c73ab3-b840-44f2-cfbb-dde4327eeb0e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000,)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trace['α'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ip67hW7EhWZX"
   },
   "outputs": [],
   "source": [
    "a_mean = trace['α'].mean(axis=0)\n",
    "b_mean = trace['β'].mean(axis=0)\n",
    "\n",
    "y_pred = a_mean + b_mean*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 336
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 41046,
     "status": "ok",
     "timestamp": 1561887861561,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "NlarwVmVhWZb",
    "outputId": "6226099d-9472-47ab-b4cf-2bafd57c81ee"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y6Zw7AGBmK4ELgV/k+d7l74MfDIWBiEgFyfeO4Vjn3MsA4e+JmoLqgJeifm8P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\nRfdgQgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_pred, 'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 40086,
     "status": "ok",
     "timestamp": 1561887861565,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "9G2ssKeqhWZe",
    "outputId": "a3784c37-844c-4c81-ab7a-f6b60cbb444d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(780, 2000)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_mean = trace['α']\n",
    "b_mean = trace['β']\n",
    "\n",
    "y_pred = a_mean + b_mean*x\n",
    "y_pred.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 336
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 40537,
     "status": "ok",
     "timestamp": 1561887862781,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "J2CcntA0hWZh",
    "outputId": "ef970365-0702-427d-89cd-92b4dea395c1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XDO58vk/1Ug2jwaBUA/hztHJddx5VPz/60fbTF+ygAJvb6/W5e6l6z+KyCuyuu4KoiBAK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\nSlloMCillLLQYFBKKWWhwaCUUsri/wGggBu3rA5HDgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = np.random.choice(len(y_pred), 200)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "for i in idx:\n",
    "    plt.plot(x, y_pred[:,i])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2dXdPT4udDP5qhOk+HgvbAVN4PJL8epIHgY8Bb+2Kp+6YLNEOGCKzjpUvHlluSoYXVtVj\nSV4EfDrJPVX15XWs2yisOOXEFDmvOx6nAHuTPNj1fiZWkl9hEJBHxlGn8ngs0g6YwuNRVTcDNyc5\nH3gv8Gqm8Jgs0Q4YIrOOlR79klMyVNWRx4eBzwIvX+/KjcCKU05MiwXH4xBwM4NhkImV5KXAtcD2\nqvpmVzx1x2OJdkzd8Vio+0D6mSSbmcJjcsRR7Rgqs46VoL8VeEt39c25wLer6mCSTUmeCdD9I57H\ndE6l3MSUE0lOTPLcI8+B1wCLXpUwCZK8EPgo8Oaq+s8Fq6bqeCzVjmk7HgBJfjZJuudnMzgZ/k0G\nd+m/pvs/v4lBW27buJoub6l2DJtZTQzdJLkBeCWwOckB4CrgGQBV9TcM7tC9GNgPfBe4vHvpLwB/\nm+SHDD70rq6qDQv6ldqR5KeAOeB5wA+TvJPB1RzfyQRNOTFsOxjM1Hdz9/t9PPAPVfXJ9W/BwCp+\nr/4YeD7w112dD1fVbE3YFCDDtgM4lQk6HrCqtvwGg07d94H/BX6zO6n5eJL3MvgQBviTqlruAo6x\nGrYdSYbKLO+MlaTGHStDN5J0zDLoJalxBr0kNc6gl6TGGfSS1DiDXpIaZ9BLUuMMeklq3P8BwG12\nSrkXz1EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(trace['β'], 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 269
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 39629,
     "status": "ok",
     "timestamp": 1561887862783,
     "user": {
      "displayName": "Sachinthaka Abeywardana",
      "photoUrl": "https://lh5.googleusercontent.com/--gSo4UaEc7c/AAAAAAAAAAI/AAAAAAAAM5s/0fU2XumVns0/s64/photo.jpg",
      "userId": "16787685245458597769"
     },
     "user_tz": -600
    },
    "id": "q5dX7AeVhWZl",
    "outputId": "5ea87072-6f8e-4c98-99ae-fa568b7c9bfd"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(trace['sd'], 50)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "Lesson 1 - Single stock.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}