bayesian/switchpoint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is based on the example in Chapter 1 of Hacker, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NASA Goddard Institute for Space Studies\n",
      "https://data.giss.nasa.gov/gistemp/\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Jan</th>\n",
       "      <th>Feb</th>\n",
       "      <th>Mar</th>\n",
       "      <th>Apr</th>\n",
       "      <th>May</th>\n",
       "      <th>Jun</th>\n",
       "      <th>Jul</th>\n",
       "      <th>Aug</th>\n",
       "      <th>Sep</th>\n",
       "      <th>Oct</th>\n",
       "      <th>Nov</th>\n",
       "      <th>Dec</th>\n",
       "      <th>J-D</th>\n",
       "      <th>D-N</th>\n",
       "      <th>DJF</th>\n",
       "      <th>MAM</th>\n",
       "      <th>JJA</th>\n",
       "      <th>SON</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Year</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016</th>\n",
       "      <td>0.79</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.92</td>\n",
       "      <td>0.62</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.74</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.79</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017</th>\n",
       "      <td>0.67</td>\n",
       "      <td>0.76</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.88</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.54</td>\n",
       "      <td>0.49</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.78</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.81</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.70</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.78</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.74</td>\n",
       "      <td>0.67</td>\n",
       "      <td>0.64</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec  \\\n",
       "Year                                                                           \n",
       "2016  0.79  0.80  0.81  0.76  0.80  0.53  0.67  0.92  0.62  0.73  0.71  0.69   \n",
       "2017  0.67  0.76  0.80  0.67  0.88  0.53  0.69  0.73  0.60  0.75  0.54  0.49   \n",
       "2018  0.50  0.46  0.61  0.81  0.64  0.70  0.75  0.68  0.65  0.78  0.68  0.74   \n",
       "\n",
       "       J-D   D-N   DJF   MAM   JJA   SON  \n",
       "Year                                      \n",
       "2016  0.73  0.74  0.79  0.79  0.71  0.69  \n",
       "2017  0.68  0.69  0.71  0.78  0.65  0.63  \n",
       "2018  0.67  0.64  0.48  0.69  0.71  0.70  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pymc as pm\n",
    "import requests\n",
    "\n",
    "print('NASA Goddard Institute for Space Studies')\n",
    "print('https://data.giss.nasa.gov/gistemp/')\n",
    "\n",
    "# glbl = 'https://data.giss.nasa.gov/gistemp/tabledata_v4/GLB.Ts+dSST.csv'\n",
    "# north = 'https://data.giss.nasa.gov/gistemp/tabledata_v4/NH.Ts+dSST.csv'\n",
    "# south = 'https://data.giss.nasa.gov/gistemp/tabledata_v4/SH.Ts+dSST.csv'\n",
    "\n",
    "# res = requests.get(south)\n",
    "# os.makedirs('./data', exist_ok=True)\n",
    "# with open('./data/south-temps.csv', 'wb') as fi:\n",
    "#     fi.write(res.content)\n",
    "    \n",
    "data = pd.read_csv('./data/south-temps.csv', header=1, index_col=0)\n",
    "data = data.replace(\"***\", 0)\n",
    "data = data.iloc[:-1, :]\n",
    "data = data.astype(float)\n",
    "\n",
    "data.tail(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Year\n",
       "1880   -0.05\n",
       "1881   -0.01\n",
       "1882   -0.02\n",
       "Name: J-D, dtype: float64"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual = data.loc[:, 'J-D']\n",
    "annual.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11e8b1278>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "annual.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the annual temperature is a continuous, an exponential probability density is a good choice\n",
    "\n",
    "$$Z(z|\\lambda) = \\lambda e^{- \\lambda z}$$\n",
    "\n",
    "The expected value of the exponential random variable is equal to the inverse of the parameter $\\lambda$ \n",
    "\n",
    "$$ \\mathbf{E}[Z|\\lambda] = \\frac{1}{\\lambda}$$\n",
    "\n",
    "Let's create variables for the parameter before and after the switch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# before_mu = pm.Uniform('before_mu', -2, 2)\n",
    "# before_sigma = pm.Exponential('before_sigma', 1 / annual.std())\n",
    "\n",
    "# after_mu = pm.Uniform('after_mu', -2, 2)\n",
    "# after_sigma = pm.Exponential('after_sigma', 1 / annual.std())\n",
    "\n",
    "# x\n",
    "size = 2\n",
    "mu = pm.Uniform('mu', -2, 2, size=size)\n",
    "sigma = pm.Exponential('sigma', 1 / annual.std(), size=size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need a parameter to control the switch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau = pm.DiscreteUniform('tau', lower=0, upper=annual.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of these `pymc` variables are stochastic - they can be sampled from:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.9632591 , -0.56202541])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu.random()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02245813, 0.2583534 ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigma.random()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(135)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tau.random()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to combine these into a single parameter.  \n",
    "\n",
    "We use the `pm.deterministic` decorator to tell `pymc` that this is a deterministic function\n",
    "- all variables need to be kwargs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "@pm.deterministic\n",
    "def mu_p(tau=tau, mu=mu, count=annual.shape[0]):\n",
    "    out = np.zeros(count)\n",
    "    out[:tau] = mu[0]\n",
    "    out[tau:] = mu[1]\n",
    "    return out\n",
    "\n",
    "@pm.deterministic\n",
    "def sigma_p(tau=tau, sigma=sigma, count=annual.shape[0]):\n",
    "    out = np.zeros(count)\n",
    "    out[:tau] = sigma[0]\n",
    "    out[tau:] = sigma[1]\n",
    "    return out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can finally create our object combines our data with our priors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "observation = pm.Normal('temperature', mu=mu_p, tau=1/sigma_p, value=annual, observed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And make a `Model` instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 40000 of 40000 complete in 7.2 sec"
     ]
    }
   ],
   "source": [
    "model = pm.Model([observation, mu_p, sigma_p, tau])\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(40000, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.18877774, -0.18877774, -0.18877774, ...,  0.37593162,\n",
       "         0.37593162,  0.37593162],\n",
       "       [-0.19431185, -0.19431185, -0.19431185, ...,  0.34195811,\n",
       "         0.34195811,  0.34195811],\n",
       "       [-0.19431185, -0.19431185, -0.19431185, ...,  0.34195811,\n",
       "         0.34195811,  0.34195811],\n",
       "       ...,\n",
       "       [-0.17681311, -0.17681311, -0.17681311, ...,  0.38953892,\n",
       "         0.38953892,  0.38953892],\n",
       "       [-0.17681311, -0.17681311, -0.17681311, ...,  0.38953892,\n",
       "         0.38953892,  0.38953892],\n",
       "       [-0.17681311, -0.17681311, -0.17681311, ...,  0.38953892,\n",
       "         0.38953892,  0.38953892]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mcmc.trace('mu_p')[:, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x132093470>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5aj82b4+IWcA64NOl7l3AR4E24OVSl8zcEhFfBx4u9a7aeQO9JNXDwCWpoWXmY0BrF4umdVE3gUu62c6NwI192zpJQ4WXFCVJkipWV+DySc2SJEl7r94zXD6pWZIkaS/1GLg6Pal5PtSe1JyZ26g9kXlBqbYAOLdM73pSc2Y+AOx8UvOZlCc1Z+ZWYOeTmiVJkhpaPWe4fFKzJEnSPqgncPXrk5p9SrMkSWo09QSufn1Ss09pliRJjabHwOWTmiVJkvZNvQ8+9UnNkiRJe6muwOWTmiVJkvaer/aRpCGgZc6dA90EaUjz1T6SJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcElqaBHRHhG/jYjHImJ5KTsyIpZGxJryPaKUR0RcHxFtEbEyIiZ22s7MUn9NRMwcqP5IGpwMXJKGgg9n5oTM3PlO2DnAsswcCywr8wBnA2PLZzZwA9QCGnAlMBmYBFy5M6RJUj0MXJKGohnAgjK9ADi3U/nNWfMAMDwijgHOBJZm5pbM3AosBc7q70ZLGrwMXJIaXQL/EhErImJ2KTs6M58v038Aji7To4D1ndbtKGXdlUtSXQ4c6AZIUsU+kJkbIuIvgKUR8VTnhZmZEZF9tbMS6mYDHHvssX21WUmDnGe4JDW0zNxQvjcCd1C7B+uFcqmQ8r2xVN8AjO60enMp6668q/3Ny8zWzGxtamrqy65IGsQMXJIaVkQcGhGH75wGpgNPAEuAnSMNZwKLy/QS4KIyWnEKsL1cerwHmB4RI8rN8tNLmSTVxUuKkhrZ0cAdEQG1492tmXl3RDwM3B4Rs4B1wKdL/buAjwJtwMvA5wAyc0tEfB14uNS7KjO39F83JA12Bi5JDSsz1wKndFG+GZjWRXkCl3SzrRuBG/u6jZKGBi8pSpIkVczAJUmSVDEvKUqSKtMy58666rVfe07FLZEGlme4JEmSKmbgkiRJqpiBS5IkqWIGLkmSpIoZuCRJkipm4JIkSaqYgUuSJKliBi5JkqSKGbgkSZIqZuCSJEmqmIFLkiSpYgYuSZKkihm4JEmSKmbgkiRJqpiBS5IkqWIGLkmSpIoZuCRJkipm4JLU8CLigIh4NCJ+WubHRMSDEdEWEbdFxMGl/K1lvq0sb+m0jctL+dMRcebA9ETSYGXgkjQUfAVY3Wn+m8B1mfluYCswq5TPAraW8utKPSJiHHA+cBJwFjA3Ig7op7ZLagAGLkkNLSKagXOA75f5AD4CLCpVFgDnlukZZZ6yfFqpPwNYmJmvZuazQBswqX96IKkRGLgkNbpvA18FXi/zI4FtmbmjzHcAo8r0KGA9QFm+vdTfVd7FOpLUIwOXpIYVER8DNmbmin7c5+yIWB4Ryzdt2tRfu5W0nzNwSWpkU4GPR0Q7sJDapcTvAMMj4sBSpxnYUKY3AKMByvIjgM2dy7tY5w0yc15mtmZma1NTU9/2RtKgZeCS1LAy8/LMbM7MFmo3vf88My8A7gXOK9VmAovL9JIyT1n+88zMUn5+GcU4BhgLPNRP3ZDUAOoOXA6rltRALgP+W0S0UbtHa34pnw+MLOX/DZgDkJlPArcDq4C7gUsy87V+b7WkQevAnqvssnNY9dvL/M5h1Qsj4nvUhlPfQKdh1RFxfqn3md2GVb8T+FlEHOdBS1J/yMxfAL8o02vpYpRhZr4CfKqb9a8BrqmuhZIaWV1nuBxWLUmStPfqvaTosGpJkqS91GPg6u9h1Q6pliRJjaaeM1z9OqzaIdWSJKnR9Bi4HFYtSZK0b3ozSnF3lwELI+Jq4FHeOKz6B2VY9RZqIY3MfDIidg6r3oHDqiVJ0hDRq8DlsGpJkqTe80nzkiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkV25dX+wxZLXPufMN8+7XnDFBLJEnSYOAZLkmSpIoZuCRJkipm4JLUsCJiWEQ8FBGPR8STEfG1Uj4mIh6MiLaIuC0iDi7lby3zbWV5S6dtXV7Kn46IMwemR5IGKwOXpEb2KvCRzDwFmACcFRFTgG8C12Xmu4GtwKxSfxawtZRfV+oREeOA84GTgLOAuRFxQL/2RNKgZuCS1LCy5t/K7EHlk8BHgEWlfAFwbpmeUeYpy6dFRJTyhZn5amY+C7QBk/qhC5IahIFLUkOLiAMi4jFgI7AUeAbYlpk7SpUOYFSZHgWsByjLtwMjO5d3sY4k9cjAJamhZeZrmTkBaKZ2VuqEKvcXEbMjYnlELN+0aVOVu5I0iBi4JA0JmbkNuBd4HzA8InY+h7AZ2FCmNwCjAcryI4DNncu7WGf3/czLzNbMbG1qaurzfkganAxckhpWRDRFxPAy/TbgDGA1teB1Xqk2E1hcppeUecryn2dmlvLzyyjGMcBY4KH+6YWkRuCT5iU1smOABWVE4VuA2zPzpxGxClgYEVcDjwLzS/35wA8iog3YQm1kIpn5ZETcDqwCdgCXZOZr/dwXSYOYgUtSw8rMlcCpXZSvpYtRhpn5CvCpbrZ1DXBNX7dR0tDgJUVJkqSKGbgkSZIqZuCSJEmqmIFLkiSpYgYuSZKkihm4JEmSKmbgkiRJqpiBS5IkqWIGLkmSpIoNuSfNt8y5c6CbIEmShhjPcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDl6SGFRGjI+LeiFgVEU9GxFdK+ZERsTQi1pTvEaU8IuL6iGiLiJURMbHTtmaW+msiYuZA9UnS4GTgktTIdgD/PTPHAVOASyJiHDAHWJaZY4FlZR7gbGBs+cwGboBaQAOuBCYDk4Ard4Y0SarHkHt5taShIzOfB54v0y9GxGpgFDADOL1UWwD8ArislN+cmQk8EBHDI+KYUndpZm4BiIilwFnAj/qtMw2uZc6dddVrv/acilsiVcMzXJKGhIhoAU4FHgSOLmEM4A/A0WV6FLC+02odpay7ckmqS4+By3sgJA12EXEY8P8A/5CZf+y8rJzNyj7c1+yIWB4Ryzdt2tRXm5U0yNVzhst7ICQNWhFxELWwdUtm/rgUv1AuFVK+N5byDcDoTqs3l7Luyt8kM+dlZmtmtjY1NfVdRyQNaj0Grsx8PjMfKdMvAp3vgVhQqi0Azi3Tu+6ByMwHgJ33QJxJuQciM7cCO++BkKRKREQA84HVmfmtTouWADvPss8EFncqv6icqZ8CbC+XHu8BpkfEiPJDcXopk6S69Oqmee+BkDTITAX+C/DbiHislP1vwLXA7RExC1gHfLosuwv4KNAGvAx8DiAzt0TE14GHS72rdt5AL0n1qDtw7X4PRO2HY01mZkT0yT0QETGb2qVIjj322L7YpKQhKjPvB6KbxdO6qJ/AJd1s60bgxr5rnaShpK5Riv15D4T3P0iSpEZTzyhF74GQJEnaB/VcUvQeCEmSpH3QY+DyHghJkqR945PmJUmSKua7FCVpEKv3HYSSBpZnuCRJkipm4JIkSaqYgUuSJKliBi5JkqSKGbgkSZIqZuCSJEmqmIFLkiSpYgYuSZKkihm4JEmSKmbgkiRJqpiBS5IkqWIGLkmSpIoZuCRJkipm4JIkSaqYgUtSQ4uIGyNiY0Q80ansyIhYGhFryveIUh4RcX1EtEXEyoiY2GmdmaX+moiYORB9kTR4GbgkNbr/Gzhrt7I5wLLMHAssK/MAZwNjy2c2cAPUAhpwJTAZmARcuTOkSVI9DFySGlpm/n/Alt2KZwALyvQC4NxO5TdnzQPA8Ig4BjgTWJqZWzJzK7CUN4c4SeqWgUvSUHR0Zj5fpv8AHF2mRwHrO9XrKGXdlUtSXQ4c6AY0gpY5d76prP3acwagJZJ6KzMzIrKvthcRs6ldjuTYY4/tq81KGuQ8wyVpKHqhXCqkfG8s5RuA0Z3qNZey7srfJDPnZWZrZrY2NTX1ecMlDU4GLklD0RJg50jDmcDiTuUXldGKU4Dt5dLjPcD0iBhRbpafXsokqS5eUpTU0CLiR8DpwFER0UFttOG1wO0RMQtYB3y6VL8L+CjQBrwMfA4gM7dExNeBh0u9qzJz9xvxJalbBi5JDS0z/6abRdO6qJvAJd1s50bgxj5smqQhxEuKkiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklSxhn4OV1fvOJQkDV71Htd9n632N57hkiRJqpiBS5IkqWIGLkmSpIoZuCRJkipm4JIkSaqYgUuSJKliBi5JkqSKGbgkSZIqZuCSJEmqmIFLkiSpYg39ah9J0tDUm1e7+Rog9QcDlyTth3wXrNRY+j1wRcRZwHeAA4DvZ+a1/d2G/rD7wdJfUNLgN1SOX5L6Xr/ewxURBwDfBc4GxgF/ExHj+rMNkrQ3PH5J2hf9fYZrEtCWmWsBImIhMANY1Rcb9xS8pApVevzSwKn3/zu8UqF90d+jFEcB6zvNd5QySdrfefyStNf2u5vmI2I2MLvM/ltEPF3h7o4C/rXC7e8S3+yPvfRKv/V9PzSU+w77f//fNdAN2Bf7cAzbn/5d9qe2wH7Snk7H8f2iPcX+1BawPd0ev/o7cG0ARneaby5lu2TmPGBefzQmIpZnZmt/7Gt/Y9+HZt/B/u+DHo9fsPfHsP3p32V/agvYnj3Zn9oCtmdP+vuS4sPA2IgYExEHA+cDS/q5DZK0Nzx+Sdpr/XqGKzN3RMTfAvdQG1Z9Y2Y+2Z9tkKS94fFL0r7o93u4MvMu4K7+3m83+uXS5X7Kvg9dQ73/e63i49f+9O+yP7UFbM+e7E9tAdvTrcjMgW6DJElSQ/Pl1ZIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQ4c6AbsyVFHHZUtLS0D3QxJ/WjFihX/mplNA92OvuAxTBpa9nT82q8DV0tLC8uXLx/oZkjqRxGxbqDb0Fc8hklDy56OX15SlCRJqpiBS5IkqWIGLkmSpIrt1/dwafD405/+REdHB6+88spAN0WDxLBhw2hubuaggw4a6KZIUuUMXOoTHR0dHH744bS0tBARA90c7ecyk82bN9PR0cGYMWMGujmSVDkvKapPvPLKK4wcOdKwpbpEBCNHjvSMqKQhw8ClPmPYUm/434ukocTAJUmSVDEDlyRJUsW8aV7qZNu2bdx6661cfPHFvV73/e9/P7/+9a8raBVcf/313HDDDUycOJFbbrml23orO7btcTsnNw/vdrvf/e5397rvGrpa5txZ2bbbrz2nsm1L/c3ApUr09UG4vw6827ZtY+7cub0KHZlJZvYqbO1c5y1vqe8k89y5c/nZz35Gc3Nz3fvo7Xbb29v3uu/19kOShiqPkmoY7e3tnHDCCVxwwQWceOKJnHfeebz88ssAfOtb32L8+PGMHz+eb3/72wC89NJLnHPOOZxyyimMHz+e2267jTlz5vDMM88wYcIELr30UgB++MMfMmnSJCZMmMAXv/hFXnvtNdrb2zn++OO56KKLGD9+POvXr+ewww7b1Zau9tfVOrvrar0vfelLrF27lrPPPpvrrrvuDfVPP/10nnrqKQA2b97MJ6e9r8u/zT/MuoDzP3o6J510EvPmzetyu7v3vat+99SPP/7xj5x66qmcdNJJHHLIIUyYMIEpU6bw+uuv9/JfU5Iai2e41FCefvpp5s+fz9SpU/n85z/P3Llz+fCHP8xNN93Egw8+SGYyefJkPvShD7F27Vre+c53cuedtbNx2xGesMEAACAASURBVLdvZ/LkyTzxxBM89thjAKxevZrbbruNX/3qVxx00EFcfPHF3HLLLXzwgx9kzZo1LFiwgClTpryhDStWrOhyfyNGjOh2nT2t973vfY+7776be++9l6OOOuoN67S1tXHccccBsHLlSsaeMK7Lv8vX/vGfOGLECMaOfCvvfe97+eu//us3bbe9vX1X31evXs1Xv/rVN/X7oosuAui2H29/+9t59NFHeeihh7jmmmtYvHjxXvwrSlLj8QyXGsro0aOZOnUqABdeeCH3338/999/P5/4xCc49NBDOeyww/jkJz/Jfffdx3ve8x6WLl3KZZddxn333ccRRxzxpu0tW7aMFStW8N73vpcJEyawbNky1q5dC8C73vWuLoNTd/vb0zo9rdeVdevWMWrUqF2X81auXMlxJ57UZd1bb/q/+NT0DzBlyhTWr1/PmjVr9vBX3HO/e+oHwBNPPMFJJ3XdFkkaino8wxURxwO3dSr6T8D/CdxcyluAduDTmbk1ag/X+Q7wUeBl4LOZ+UjZ1kzgirKdqzNzQd90Q6rZ/dlOe3rW03HHHccjjzzCXXfdxRVXXMG0adN2ncHZKTOZOXMm3/jGN95Q3t7ezqGHHtrr9u3NOt15/PHHOfnkk3fNr1ixgknT3nyv28O/uZ8H7v8FNy/+FyaPfSenn356jw8c7a7fO/XUj1WrVjFx4sQ6eiFJQ0OPZ7gy8+nMnJCZE4C/pBai7gDmAMsycyywrMwDnA2MLZ/ZwA0AEXEkcCUwGZgEXBkRI/q2Oxrqfv/73/Ob3/wGgFtvvZUPfOADnHbaafzkJz/h5Zdf5qWXXuKOO+7gtNNO47nnnuOQQw7hwgsv5NJLL+WRRx7h8MMP58UXX9y1vWnTprFo0SI2btwIwJYtW1i3bt0e29Dd/nrS2/Uee+yxXcFpzZo1LF68uMtLiv/2xz/y9iOG87a3HcJTTz3FAw880OX2Ovd9b/rd2XPPPcc73vGOuutLUqPr7SXFacAzmbkOmAHsPEO1ADi3TM8Abs6aB4DhEXEMcCawNDO3ZOZWYClw1j73QOrk+OOP57vf/S4nnngiW7du5ctf/jITJ07ks5/9LJMmTWLy5Ml84Qtf4NRTT+W3v/3trpvCv/a1r3HFFVcwcuRIpk6dyvjx47n00ksZN24cV199NdOnT+fkk0/mjDPO4Pnnn99jG7rbX096u97jjz/O66+/zimnnMJVV13FuHHjWPLPC99Ub+rp03htxw7O/fBk5syZ0+2lwM59v+mmm3rd787OPPNMZs2axS9/+cu616lKRPzXiHgyIp6IiB9FxLCIGBMRD0ZEW0TcFhEHl7pvLfNtZXlLp+1cXsqfjogzB6o/kganyMz6K0fcCDySmf8UEdsyc3gpD2BrZg6PiJ8C12bm/WXZMuAy4HRgWGZeXcr/D+DfM/Mfu9tfa2trLl++fC+7pv60evVqTjzxxAFtQ3t7Ox/72Md44oknBrQd/WXs2LG7zsrt1NvncA20rv67iYgVmdnaF9uPiFHA/cC4zPz3iLgduIvaLQ8/zsyFEfE94PHMvCEiLgZOzswvRcT5wCcy8zMRMQ74EbWz8+8EfgYcl5mv7Wn/Q+EY5nO4pD/b0/Gr7jNc5Rfgx4F/3n1Z1lJb/cltz/uZHRHLI2L5pk2b+mKTUsN58cUXiYg3hC1160DgbRFxIHAI8DzwEWBRWb77GfqdZ+4XAdPKD8oZwMLMfDUznwXaqIUvSapLby4pnk3t7NYLZf6FcqmQ8r2xlG8ARndar7mUdVf+Bpk5LzNbM7O1qampF83TUNfS0jJkzm4dfvjh/O53vxvoZuz3MnMD8I/A76kFre3ACmBbZu4o1TqAUWV6FLC+rLuj1B/ZubyLdSSpR70JXH9D7ZT6TkuAmWV6JrC4U/lFUTMF2J6ZzwP3ANMjYkS5WX56KZOkSpRjzQxgDLVLgYdS8b2jnqWX1JW6AldEHAqcAfy4U/G1wBkRsQb4qzIPtfsj1lI75f6/gIsBMnML8HXg4fK5qpRJUlX+Cng2Mzdl5p+oHcOmUhvMs/OxOJ3Ptu86E1+WHwFsps4z9OBZekldq+tJ85n5ErXT6p3LNlMbtbh73QQu6WY7NwI39r6ZkrRXfg9MiYhDgH+ndsxaDtwLnAcs5M1n6GcCvynLf56ZGRFLgFsj4lvUzpSNBR7qz45IGtx8tY/6TGbu8UGjGnh7GsXY3yMYezNCeh/28WBELAIeAXYAjwLzgDuBhRFxdSmbX1aZD/wgItqALcD5ZTtPlhGOq8p2LulphKIkdWbgUp8YNmwYmzdvZuTIkYYu9Sgz2bx5M8OGDeuPfV1J7aHLna2li1GGmfkK8KlutnMNcE2fN1DSkGDgUp9obm6mo6MDbxIeWC9s/fe9Xnf1i2/rw5b0bNiwYTQ3N/frPiVpoBi41CcOOuggxowZM9DNGPLO3oeHUPqQSUmqTm9f7SNJkqReMnBJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFfHm1JDW4ln14qbmkvuEZLkmSpIoZuCRJkipm4JIkSaqYgUuSJKliBi5JDSsijo+Ixzp9/hgR/xARR0bE0ohYU75HlPoREddHRFtErIyIiZ22NbPUXxMRMweuV5IGIwOXpIaVmU9n5oTMnAD8JfAycAcwB1iWmWOBZWUe4GxgbPnMBm4AiIgjgSuBycAk4MqdIU2S6lFX4IqI4RGxKCKeiojVEfE+fyFKGmSmAc9k5jpgBrCglC8Azi3TM4Cbs+YBYHhEHAOcCSzNzC2ZuRVYCpzVv82XNJjVe4brO8DdmXkCcAqwGn8hShpczgd+VKaPzszny/QfgKPL9Chgfad1OkpZd+WSVJceA1dEHAF8EJgPkJn/kZnb8BeipEEiIg4GPg788+7LMjOB7MN9zY6I5RGxfNOmTX21WUmDXD1Pmh8DbAJuiohTgBXAV/AXoqTB42zgkcx8ocy/EBHHZObz5QfhxlK+ARjdab3mUrYBOH238l90taPMnAfMA2htbe2zIDcUVfmE/PZrz6ls21JX6rmkeCAwEbghM08FXuLPlw+Bvv2F6K9DSRX4G/58ORFgCbDzPtKZwOJO5ReVe1GnANvLD8t7gOkRMaLcCjG9lElSXeoJXB1AR2Y+WOYXUQtgL5RfhvTiF2JX5W+QmfMyszUzW5uamnrTF0l6k4g4FDgD+HGn4muBMyJiDfBXZR7gLmAt0Ab8L+BigMzcAnwdeLh8riplklSXHi8pZuYfImJ9RByfmU9TG+mzqnxmUjtQ7f4L8W8jYiG1G+S3l9P29wD/s9ON8tOBy/u2O5L0Rpn5EjByt7LN1I5lu9dN4JJutnMjcGMVbZTU+Oq5hwvg74Bbyo2na4HPUTs7dntEzALWAZ8ude8CPkrtF+LLpS6ZuSUidv5CBH8hSpKkIaKuwJWZjwGtXSzyF6LUz6q8kViSVA2fNC9JklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXpIYWEcMjYlFEPBURqyPifRFxZEQsjYg15XtEqRsRcX1EtEXEyoiY2Gk7M0v9NRExc+B6JGkwMnBJanTfAe7OzBOAU4DVwBxgWWaOBZaVeYCzgbHlMxu4ASAijgSuBCYDk4Ard4Y0SaqHgUtSw4qII4APAvMBMvM/MnMbMANYUKotAM4t0zOAm7PmAWB4RBwDnAkszcwtmbkVWAqc1Y9dkTTIGbgkNbIxwCbgpoh4NCK+HxGHAkdn5vOlzh+Ao8v0KGB9p/U7Sll35ZJUFwOXpEZ2IDARuCEzTwVe4s+XDwHIzASyr3YYEbMjYnlELN+0aVNfbVbSIGfgktTIOoCOzHywzC+iFsBeKJcKKd8by/INwOhO6zeXsu7K3yQz52Vma2a2NjU19VlHJA1uBi5JDSsz/wCsj4jjS9E0YBWwBNg50nAmsLhMLwEuKqMVpwDby6XHe4DpETGi3Cw/vZRJUl0OrKdSRLQDLwKvATsys7WM2rkNaAHagU9n5taICGqjgj4KvAx8NjMfKduZCVxRNnt1Zi5Akqr1d8AtEXEwsBb4HLUfm7dHxCxgHfDpUvcuaseuNmrHr88BZOaWiPg68HCpd1Vmbum/Lkga7OoKXMWHM/NfO83vHFZ9bUTMKfOX8cZh1ZOpDaue3GlYdSu1+yVWRMSSMuJHkiqRmY9RO+7sbloXdRO4pJvt3Ajc2LetkzRU7MslRYdVS5Ik1aHewJXAv0TEioiYXcocVi1JklSHei8pfiAzN0TEXwBLI+KpzgszMyOiT4ZVl0A3G+DYY4/ti01KkiQNqLrOcGXmhvK9EbiD2qstKhlW7ZBqSZLUaHoMXBFxaEQcvnOa2nDoJ3BYtSRJUl3quaR4NHBH7WkPHAjcmpl3R8TDOKxakiSpRz0GrsxcC5zSRflmHFYtSZLUI580L0mSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckiRJFTNwSZIkVczAJamhRUR7RPw2Ih6LiOWl7MiIWBoRa8r3iFIeEXF9RLRFxMqImNhpOzNL/TURMXOg+iNpcDJwSRoKPpyZEzKztczPAZZl5lhgWZkHOBsYWz6zgRugFtCAK4HJwCTgyp0hTZLqYeCSNBTNABaU6QXAuZ3Kb86aB4DhEXEMcCawNDO3ZOZWYClwVn83WtLgZeCS1OgS+JeIWBERs0vZ0Zn5fJn+A3B0mR4FrO+0bkcp665ckupy4EA3QJIq9oHM3BARfwEsjYinOi/MzIyI7KudlVA3G+DYY4/tq81KGuQ8wyWpoWXmhvK9EbiD2j1YL5RLhZTvjaX6BmB0p9WbS1l35V3tb15mtmZma1NTU192RdIg5hkuSQC0zLlzj8vbrz2nn1rSdyLiUOAtmflimZ4OXAUsAWYC15bvxWWVJcDfRsRCajfIb8/M5yPiHuB/drpRfjpweT92RdIgZ+CS1MiOBu6ICKgd727NzLsj4mHg9oiYBawDPl3q3wV8FGgDXgY+B5CZWyLi68DDpd5Vmbml/7ohabAzcElqWJm5Fjili/LNwLQuyhO4pJtt3Qjc2NdtlDQ0eA+XJElSxQxckiRJFas7cEXEARHxaET8tMyPiYgHyyswbouIg0v5W8t8W1ne0mkbl5fypyPizL7ujCRJ0v6oN2e4vgKs7jT/TeC6zHw3sBWYVcpnAVtL+XWlHhExDjgfOInaE5rnRsQB+9Z8SZKk/V9dgSsimoFzgO+X+QA+AiwqVXZ/NcbOV2YsAqaV+jOAhZn5amY+S20U0KS+6IQkSdL+rN4zXN8Gvgq8XuZHAtsyc0eZ7/yai12vwCjLt5f6vhpDkiQNST0Groj4GLAxM1f0Q3uIiNkRsTwilm/atKk/dilJklSpes5wTQU+HhHtwEJqlxK/AwyPiJ3P8er8motdr8Aoy48ANlPnqzF8LYYkSWo0PQauzLw8M5szs4XaTe8/z8wLgHuB80q13V+NMbNMn1fqZyk/v4xiHAOMBR7qs55IkiTtp/blSfOXAQsj4mrgUWB+KZ8P/CAi2oAt1EIamflkRNwOrAJ2AJdk5mv7sH9JkqRBoVeBKzN/AfyiTK+li1GGmfkK8Klu1r8GuKa3jZQkSRrMfNK8JElSxQxckiRJFTNwSZIkVczAJUmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ekhhcRB0TEoxHx0zI/JiIejIi2iLgtIg4u5W8t821leUunbVxeyp+OiDMHpieSBisDl6Sh4CvA6k7z3wSuy8x3A1uBWaV8FrC1lF9X6hER46i9puwk4CxgbkQc0E9tl9QADFySGlpENAPnAN8v8wF8BFhUqiwAzi3TM8o8Zfm0Un8GsDAzX83MZ4E2uni1mSR1x8AlqdF9G/gq8HqZHwlsy8wdZb4DGFWmRwHrAcry7aX+rvIu1pGkHhm4JDWsiPgYsDEzV/TjPmdHxPKIWL5p06b+2q2k/ZyBS1Ijmwp8PCLagYXULiV+BxgeEQeWOs3AhjK9ARgNUJYfAWzuXN7FOm+QmfMyszUzW5uamvq2N5IGLQOXpIaVmZdnZnNmtlC76f3nmXkBcC9wXqk2E1hcppeUecryn2dmlvLzyyjGMcBY4KF+6oakBnBgz1UkqeFcBiyMiKuBR4H5pXw+8IOIaAO2UAtpZOaTEXE7sArYAVySma/1f7MlDVYGLklDQmb+AvhFmV5LF6MMM/MV4FPdrH8NcE11LZTUyLykKEmSVDHPcEn7mZY5dw50EyRJfcwzXJIkSRXzDJckacip+kxy+7XnVLp9DT6e4ZIkSaqYgUuSJKliBi5JkqSK9Ri4ImJYRDwUEY9HxJMR8bVSPiYiHoyItoi4LSIOLuVvLfNtZXlLp21dXsqfjogzq+qUJEnS/qSeM1yvAh/JzFOACcBZETEF+CZwXWa+G9gKzCr1ZwFbS/l1pR4RMY7aU5tPAs4C5kbEAX3ZGUmSpP1Rj4Era/6tzB5UPkntJbCLSvkC4NwyPaPMU5ZPi4go5Qsz89XMfBZoo4snPUuSJDWauu7hiogDIuIxYCOwFHgG2JaZO0qVDmBUmR4FrAcoy7cDIzuXd7GOJElSw6orcGXma5k5AWimdlbqhKoaFBGzI2J5RCzftGlTVbuRJEnqN70apZiZ24B7gfcBwyNi54NTm4ENZXoDMBqgLD8C2Ny5vIt1Ou9jXma2ZmZrU1NTb5onSZK0X6pnlGJTRAwv028DzgBWUwte55VqM4HFZXpJmacs/3lmZik/v4xiHAOMBR7qq45IkiTtr+p5tc8xwIIyovAtwO2Z+dOIWAUsjIirgUeB+aX+fOAHEdEGbKE2MpHMfDIibgdWATuASzLztb7tjiRJ0v6nx8CVmSuBU7soX0sXowwz8xXgU91s6xrgmt43U5IkafDySfOSJEkVM3BJkiRVzMAlSZJUMQOXJElSxQxckhpWRAyLiIci4vGIeDIivlbKx0TEgxHRFhG3RcTBpfytZb6tLG/ptK3LS/nTEXHmwPRI0mBl4JLUyF4FPpKZpwATgLMiYgrwTeC6zHw3sBWYVerPAraW8utKPSJiHLVH3JwEnAXMLY/KkaS6GLgkNays+bcye1D5JPARYFEpXwCcW6ZnlHnK8mkREaV8YWa+mpnPAm108VgcSeqOgUtSQ4uIAyLiMWAjsBR4BtiWmTtKlQ5gVJkeBawHKMu3AyM7l3exjiT1yMAlqaFl5muZOYHa+1snASdUub+ImB0RyyNi+aZNm6rclaRBxMAlaUjIzG3U3gH7PmB4ROx800YzsKFMbwBGA5TlRwCbO5d3sc7u+5mXma2Z2drU1NTn/ZA0OBm4JDWsiGiKiOFl+m3AGcBqasHrvFJtJrC4TC8p85TlP8/MLOXnl1GMY4CxwEP90wtJjaCel1dL0mB1DLCgjCh8C3B7Zv40IlYBCyPiauBRYH6pPx/4QUS0AVuojUwkM5+MiNuBVcAO4JLMfK2f+yJpEDNwSWpYmbkSOLWL8rV0McowM18BPtXNtq4BrunrNkoaGrykKEmSVDEDlyRJUsUMXJIkSRUzcEmSJFXMwCVJklQxA5ckSVLFDFySJEkVM3BJkiRVzMAlSZJUMQOXJElSxXoMXBExOiLujYhVEfFkRHyllB8ZEUsjYk35HlHKIyKuj4i2iFgZERM7bWtmqb8mImZ2t09JkqRGUs8Zrh3Af8/MccAU4JKIGAfMAZZl5lhgWZkHOBsYWz6zgRugFtCAK4HJ1N5hduXOkCZJktTIegxcmfl8Zj7y/7d3/7F213cdx58vqQznpsCoHePHyhJmBH8AVrpEzaawjkEcVcwGkVEXEjLH/ljM4qqYDCExBZMZDcYFt2bFmG04f6wJXZrSDMmSFSmMn5KtBVloV6CjC5PVTSdv/zif6qH09t7ec77fc+69z0dycr/n8/3cc96f7/ec733f7/fz+Xzb8n8ATwCnAZcDm1q1TcDatnw5cEcN7ABOTHIq8C5gW1UdqKrvANuAS8baGkmSpCl0TH24kqwEzgfuA1ZU1b626llgRVs+DXhm6Nf2tLKZyiVJkha1OSdcSV4H/APwkar67vC6qiqgxhFQkuuS7Eyyc//+/eN4SUmSpImaU8KV5EcZJFt/V1X/2Iqfa5cKaT+fb+V7gTOGfv30VjZT+StU1e1VtaqqVi1fvvxY2iJJkjSV5jJKMcCngSeq6hNDqzYDh0YargO+OFR+TRut+DbgxXbpcSuwJslJrbP8mlYmSZK0qC2bQ51fBt4PPJrkoVb2R8AG4M4k1wLfBN7b1m0BLgV2AweBDwBU1YEkNwP3t3o3VdWBsbRCkiRpis2acFXVV4DMsPqiI9Qv4PoZXmsjsPFYApQkSVronGle0qLlxM2SpoUJl6TFzImbJU0FEy5Ji5YTN0uaFiZckpYEJ26WNEkmXJIWvb4mbm7v5eTNkl7FhEvSotbnxM3g5M2SjsyES9Ki5cTNkqbFXCY+laSFyombJU0FEy5Ji5YTN0uaFl5SlCRJ6pgJlyRJUsdMuCRJkjpmwiVJktQxEy5JkqSOmXBJkiR1zIRLkiSpYyZckiRJHXPiU0maAivX3zXpECR1yDNckiRJHTPhkiRJ6pgJlyRJUsdMuCRJkjpmp3lJksasy0EQT2+4rLPXVndmPcOVZGOS55M8NlR2cpJtSXa1nye18iT5yyS7kzyS5IKh31nX6u9Ksq6b5kiSJE2fuVxS/AxwyWFl64HtVXU2sL09B3g3cHZ7XAf8NQwSNODjwGrgQuDjh5I0SZKkxW7WhKuq7gUOHFZ8ObCpLW8C1g6V31EDO4ATk5wKvAvYVlUHquo7wDZencRJkiQtSvPtNL+iqva15WeBFW35NOCZoXp7WtlM5ZIkSYveyJ3mq6qS1DiCAUhyHYPLkZx55pnjellJIzpaJ2A78UrS0c33DNdz7VIh7efzrXwvcMZQvdNb2Uzlr1JVt1fVqqpatXz58nmGJ0kDDvyRNA3me4ZrM7AO2NB+fnGo/MNJPsegg/yLVbUvyVbgT4c6yq8B/nD+YUsLm/fN69VngNuAO4bKDg382ZBkfXv+MV458Gc1g4E/q4cG/qwCCnggyebWJ1WSZjWXaSE+C3wV+Okke5JcyyDRemeSXcDF7TnAFuApYDfwN8CHAKrqAHAzcH973NTKJKlTDvyRNA1mPcNVVVfNsOqiI9Qt4PoZXmcjsPGYopOkbjjwR1KvvLWPpCWt/aM41oE/SXYm2bl///5xvaykBc6ES9JS5MAfSb0y4ZK0FB0a+AOvHvhzTRut+DbawB9gK7AmyUlt8M+aViZJc+LNqyUtam3gzzuAU5LsYTDacANwZxsE9E3gva36FuBSBgN/DgIfgMHAnySHBv6AA38kHSMTLkmLmgN/JE0DLylKkiR1zIRLkiSpYyZckiRJHTPhkiRJ6pgJlyRJUsdMuCRJkjpmwiVJktQxEy5JkqSOOfGpJEkLyMr1d3X22k9vuKyz117qPMMlSZLUMRMuSZKkjplwSZIkdcyES5IkqWMmXJIkSR0z4ZIkSeqYCZckSVLHnIdL6kiXc+VMm6O11Xl9JMkzXJIkSZ0z4ZIkSepY75cUk1wC/AVwHPCpqtrQdwySNB8ev7TYedug7vR6hivJccBfAe8GzgGuSnJOnzFI0nx4/JI0ir4vKV4I7K6qp6rqv4DPAZf3HIMkzYfHL0nz1vclxdOAZ4ae7wFW9xyDNBZLaRSiAI9f0kgW6jFzXJdCp25aiCTXAde1py8l+XqHb3cK8O0OX3+a2falq9f255Zj/pU3dxBGb0Y4hk3T53KaYgHjOZppigUWYTzHeAyb8fjVd8K1Fzhj6Pnprez/VNXtwO19BJNkZ1Wt6uO9po1tX5ptB9s/glmPXzD/Y9g07ZdpigWM52imKRYwnqPpuw/X/cDZSc5KcjxwJbC55xgkaT48fkmat17PcFXVD5N8GNjKYFj1xqp6vM8YJGk+PH5JGkXvfbiqaguwpe/3nUEvly6nlG1fupZ6++et4+PXNO2XaYoFjOdopikWMJ4ZpaomHYMkSdKi5q19JEmSOrakEq4kJyfZlmRX+3nSEeqcl+SrSR5P8kiS900i1nFJckmSryfZnWT9Eda/Jsnn2/r7kqzsP8puzKHtv5/k39p+3p5kQU9HMGy2tg/VuyJJJZmKUTyL0Xy/g0nekOTLSV5KctsUxPPOJA8kebT9/PUJx3Nhkofa4+EkvzmpWIbWn9n210dHjWWUeJKsTPKfQ9vnk5OMp637+aG/rY8mOWESsST5naHt8lCSl5OcN0osc1ZVS+YB3Aqsb8vrgVuOUOetwNlt+U3APuDEScc+z/YeBzwJvAU4HngYOOewOh8CPtmWrwQ+P+m4e2z7rwGvbcu/t5Ta3uq9HrgX2AGsmnTci/ExyncQ+HHgV4APArdNQTznA29qyz8L7J1wPK8FlrXlU4HnDz3vO5ah9V8A/h746IS3zUrgsSn6LC8DHgF+oT1/A3DcJPdVK/854MlxbqejPZbUGS4Gt+HY1JY3AWsPr1BV36iqXW35Wwy+xMt7i3C85nIrkuFt8gXgoiTpMcauzNr2qvpyVR1sT3cwmFdpMZjrLWhuBm4Bvt9ncEvMvL+DVfW9qvoK490/o8TztXZMBHgc+LEkr5lgPAer6oet/ARg1A7JIx0vk6wF/p3BthmHaTt+jxLPGuCRqnoYoKpeqKr/mVAsw65qv9uLpZZwraiqfW35WWDF0SonuZBB9vxk14F15Ei3IjltZLvBCAAAAzhJREFUpjrt4PUig/8+Frq5tH3YtcCXOo2oP7O2PckFwBlVtTDvtbFwTNt3cFzxXAE8WFU/mGQ8SVYneRx4FPjgUALWayxJXgd8DPiTEd5/bPG0dWcl+VqSf0nyqxOO561AJdma5MEkfzDBWIa9D/jsiLHM2dTd2mdUSe4G3niEVTcMP6mqSjLjf0RJTgX+FlhXVS+PN0pNkyRXA6uAt086lj4k+RHgE8DvTjgULUBJzmVwZnTNpGOpqvuAc5P8DLApyZeqahJnbG8E/ryqXpqSCwT7gDOr6oUkvwj8c5Jzq+q7E4pnGYPL478EHAS2J3mgqrZPKB6SrAYOVtVjfb3noku4qurimdYleS7JqVW1ryVUz89Q7yeAu4AbqmpHR6H2YS63IjlUZ0+SZcBPAi/0E16n5nQbliQXM0jG3z6G/9anxWxtfz2DPjj3tD8ObwQ2J3lPVe3sLcqlYdq+gyPFk+R04J+Aa6pqHGf+x7J9quqJJC8x+FzP9zM8Siyrgd9OcitwIvByku9X1SiDHeYdTw06KP0AoKoeSPIkg7NMo3y/R9k+e4B7q+rbAEm2ABcA8024xvG5uZIez24BS67T/J/xyk7ztx6hzvEMPgQfmXS8Y2jvMuAp4Cz+v2PhuYfVuZ5Xdiy8c9Jx99j28xlcLj570vH23fbD6t+DneYnti9m+w4yOBM5rk7z846HQSLxMPBb07B92u8c6jT/ZuBbwCmT3Fet/EbG02l+lG2znNYpnUHH8r3AyROM5yTgQdpAB+Bu4LJJ7SsG3an2Am8Z12d5TnH3+WaTfjC4frsd2NV2+MmtfBXwqbZ8NfDfwENDj/MmHfsIbb4U+AaDxOKGVnYT8J62fAKDUTW7gX/t+wM44bbfDTw3tJ83Tzrmvtp+WN17MOGa2L442ncQeBo4ALzE4CzBq0ab9hUP8MfA9w47Nv7UBON5P4MO6g8x+GO+dpL7aug1bmQMCdeI2+aKw7bNb0zBZ/nqFtNjHOFkR8+xvAPYMY5tciwPZ5qXJEnq2FIbpShJktQ7Ey5JkqSOmXBJkiR1zIRLkiSpYyZckiRJHTPhkiRJ6pgJlyRJUsdMuCRJkjr2v9Zuz5oZ5SBuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "before_mu_samples = mcmc.trace('mu')[:, 0]\n",
    "after_mu_samples = mcmc.trace('mu')[:, 1]\n",
    "before_sigma_samples = mcmc.trace('sigma')[:, 0]\n",
    "after_sigma_samples = mcmc.trace('sigma')[:, 1]\n",
    "\n",
    "tau_samples = mcmc.trace('tau')[:]\n",
    "\n",
    "f, axes = plt.subplots(2, 2, figsize=(10, 10), sharex='col')\n",
    "\n",
    "_ = axes[0][0].hist(before_mu_samples, label=r\"posterior of $\\mu$ before $\\tau$\")\n",
    "_ = axes[1][0].hist(after_mu_samples, label=r\"posterior of $\\mu$ after $\\tau$\")\n",
    "\n",
    "_ = axes[0][1].hist(before_sigma_samples)\n",
    "_ = axes[1][1].hist(after_sigma_samples)\n",
    "\n",
    "axes[0][0].legend(loc=\"upper right\")\n",
    "axes[1][0].legend(loc=\"upper right\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1321f5710>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(20, 5), nrows=2, sharex=True)\n",
    "years = tau_samples + annual.index[0]\n",
    "w = 1.0 / years.shape[0] * np.ones_like(years)\n",
    "ax[0].hist(years, bins=annual.shape[0], alpha=1, label=r\"posterior of $\\tau$\", color=\"#467821\", weights=w, rwidth=2.)\n",
    "ax[0].legend(loc=\"upper left\")\n",
    "ax[0].xaxis.set_major_locator(plt.MaxNLocator(10))\n",
    "_ = ax[1].plot(annual, label='temperature')\n",
    "ax[1].legend(loc=\"upper left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The width of these distributions shows how certain we should be\n",
    "\n",
    "Our analysis shows support for\n",
    "- a change in warming (mu0 != mu1)\n",
    "- a switchpoint occured in the late 1960's / 1970's\n",
    "\n",
    "## Statistical significance\n",
    "\n",
    "We can visually inspect the parameters above and see a clear trend (i.e. no overlap for the mean).  \n",
    "\n",
    "We can use our samples to determine this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6697666666666666"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(before_sigma_samples < after_sigma_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use a similar logic for a given size of effect:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4062"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "effect_size = 0.01\n",
    "\n",
    "np.mean(np.abs(before_sigma_samples - after_sigma_samples) >= effect_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Practical\n",
    "\n",
    "Extend the example above to model multiple switchpoints"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A bit more on PyMC\n",
    "\n",
    "### Parent & child relationships"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<pymc.distributions.new_dist_class.<locals>.new_class 'temperature' at 0x12dda6b70>,\n",
       " <pymc.distributions.new_dist_class.<locals>.new_class 'mu' at 0x12dceecc0>,\n",
       " <pymc.distributions.new_dist_class.<locals>.new_class 'sigma' at 0x12dceec50>)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observation, mu, sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'mu': <pymc.PyMCObjects.Deterministic 'mu_p' at 0x12dce5470>,\n",
       " 'tau': <pymc.PyMCObjects.Deterministic '(sigma_p_rtruediv_1)' at 0x12dda6320>}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observation.parents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{<pymc.PyMCObjects.Deterministic 'mu_p' at 0x12dce5470>}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu.children"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variables have values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.05, -0.01, -0.02, -0.07, -0.15, -0.25, -0.21, -0.29, -0.13,\n",
       "       -0.05, -0.33, -0.2 , -0.16, -0.16, -0.23, -0.16, -0.04, -0.07,\n",
       "       -0.28, -0.16, -0.08, -0.2 , -0.24, -0.38, -0.48, -0.24, -0.23,\n",
       "       -0.32, -0.42, -0.49, -0.44, -0.47, -0.26, -0.28, -0.13, -0.15,\n",
       "       -0.32, -0.37, -0.21, -0.22, -0.26, -0.28, -0.31, -0.32, -0.37,\n",
       "       -0.31, -0.23, -0.3 , -0.3 , -0.39, -0.3 , -0.22, -0.27, -0.33,\n",
       "       -0.27, -0.31, -0.27, -0.19, -0.19, -0.14,  0.08,  0.16,  0.  ,\n",
       "       -0.02,  0.13,  0.08, -0.18, -0.14, -0.21, -0.2 , -0.21, -0.19,\n",
       "       -0.04, -0.08, -0.26, -0.21, -0.16,  0.05, -0.02, -0.06, -0.12,\n",
       "        0.03, -0.06, -0.03, -0.21, -0.07, -0.09, -0.08, -0.09,  0.15,\n",
       "        0.09, -0.02,  0.2 ,  0.23,  0.04,  0.02,  0.01,  0.24,  0.12,\n",
       "        0.25,  0.35,  0.27,  0.23,  0.38,  0.27,  0.23,  0.24,  0.41,\n",
       "        0.4 ,  0.28,  0.38,  0.4 ,  0.31,  0.28,  0.26,  0.32,  0.39,\n",
       "        0.42,  0.52,  0.29,  0.29,  0.44,  0.54,  0.5 ,  0.43,  0.51,\n",
       "        0.47,  0.47,  0.41,  0.59,  0.55,  0.47,  0.48,  0.57,  0.58,\n",
       "        0.64,  0.73,  0.68,  0.67])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observation.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variables are stochastic or deterministic\n",
    "\n",
    "Deterministic\n",
    "- not random if parents values known\n",
    "- made using the `@pm.deterministic` decorator\n",
    "- elementary operations such as addition, exponentials etc\n",
    "\n",
    "Stochastic\n",
    "- even if you know all parent's values, it is is still random\n",
    "- Poisson, DiscreteUniform, Exponential\n",
    "\n",
    "We can call `.random()` on stochastic variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.1683512 , -1.15529729])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu.random()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How do we include data?\n",
    "\n",
    "Stochastic variables have kwarg `observed`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pymc.distributions.new_dist_class.<locals>.new_class 'fixed' at 0x132b1fd30>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.Poisson('fixed', 1, value=data, observed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using `pymc` to generate data\n",
    "\n",
    "A superpower of machine learning\n",
    "\n",
    "2.2.1 hacker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  sample a switchpoint\n",
    "tau = pm.rdiscrete_uniform(0, annual.shape[0])\n",
    "\n",
    "#  sample statitics for the Gaussian\n",
    "mu = pm.runiform(-2, 2, size=size)\n",
    "sigma = pm.rexponential(1 / annual.std(), size=size)\n",
    "\n",
    "mus = np.r_[\n",
    "    mu[0] * np.ones(tau), mu[1] * np.ones(annual.shape[0] - tau)\n",
    "]\n",
    "\n",
    "sigmas = np.r_[\n",
    "    sigma[0] * np.ones(tau), sigma[1] * np.ones(annual.shape[0] - tau)\n",
    "]\n",
    "\n",
    "data = pm.rnormal(mus, sigmas)\n",
    "\n",
    "plt.plot(data)\n",
    "_ = plt.axvline(tau, color='green')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Revisiting the temperature dataset\n",
    "\n",
    "If we have a look again at our dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = annual.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://link.springer.com/content/pdf/10.3758%2Fs13423-017-1281-0.pdf\n",
    "\n",
    "Let's sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 40000 of 40000 complete in 0.4 sec"
     ]
    }
   ],
   "source": [
    "size = 2\n",
    "\n",
    "mu = pm.Uniform('mu', size=size)\n",
    "beta = pm.Normal('beta', mu=mu, tau=0.5)\n",
    "\n",
    "@pm.deterministic\n",
    "def mu_p(mu=beta, count=annual.shape[0]):\n",
    "    out = np.full(count, mu[0])\n",
    "    out *= mu[1] * np.arange(count)\n",
    "    return out\n",
    "\n",
    "observation = pm.Normal('temperature', mu=mu_p, value=annual, observed=True)\n",
    "\n",
    "model = pm.Model([observation, mu_p])\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(40000, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x135020860>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "before_mu_samples = mcmc.trace('mu_p')[:, 0]\n",
    "after_mu_samples = mcmc.trace('mu_p')[:, 1]\n",
    "\n",
    "f, axes = plt.subplots(2, 2, figsize=(10, 10), sharex='col')\n",
    "\n",
    "_ = axes[0][0].hist(before_mu_samples, label=r\"posterior of $\\mu$ before $\\tau$\")\n",
    "_ = axes[1][0].hist(after_mu_samples, label=r\"posterior of $\\mu$ after $\\tau$\")\n",
    "\n",
    "#_ = axes[0][1].hist(before_sigma_samples)\n",
    "#_ = axes[1][1].hist(after_sigma_samples)\n",
    "\n",
    "axes[0][0].legend(loc=\"upper right\")\n",
    "axes[1][0].legend(loc=\"upper right\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to model this as a time series problem, using an autoregression model with two lags\n",
    "\n",
    "https://towardsdatascience.com/a-bayesian-approach-to-time-series-forecasting-d97dd4168cb7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}