{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "634cfda6",
   "metadata": {},
   "source": [
    "### Exercise 13"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b5c0952",
   "metadata": {},
   "source": [
    "#### Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7f667f81",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import gamma, dirichlet, multinomial\n",
    "from scipy.stats import gaussian_kde as kde\n",
    "from statsmodels.distributions.empirical_distribution import ECDF"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a9dc81d",
   "metadata": {},
   "source": [
    "#### Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4da63f60",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 30\n",
    "counts = np.array([2, 5, 3, 7, 5, 8])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a3708db",
   "metadata": {},
   "source": [
    "### (a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36beecae",
   "metadata": {},
   "source": [
    "#### Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4b96e3f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_posterior_sample(a, sim, counts):\n",
    "    aPost = a + counts\n",
    "    return dirichlet(aPost).rvs(sim)\n",
    "\n",
    "\n",
    "def get_posterior_sample_alt(a, sim, counts, m):\n",
    "    aPost = a + counts\n",
    "    x = gamma(a=aPost).rvs((sim, m))\n",
    "    return x / np.sum(x, axis=1).reshape((sim, 1))\n",
    "\n",
    "\n",
    "def get_posterior_param_sample(a, sim, counts):\n",
    "    result = np.zeros((4, sim))\n",
    "    posterior_sample = get_posterior_sample(a, sim, counts)\n",
    "    rho = posterior_sample[:, -1] / posterior_sample[:, 0]\n",
    "    alpha = (1/6)*np.sum((posterior_sample - 1/6)**2, axis=1)\n",
    "    beta = (1/6)*np.sum(np.abs(posterior_sample - 1/6), axis=1)\n",
    "    gamma = (posterior_sample[:, 3] * posterior_sample[:, 4] * posterior_sample[:, 5] \\\n",
    "            / posterior_sample[:, 0] * posterior_sample[:, 1] * posterior_sample[:, 2])**(1/3)\n",
    "    result[0] = rho\n",
    "    result[1] = alpha\n",
    "    result[2] = beta\n",
    "    result[3] = gamma\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0abcd398",
   "metadata": {},
   "source": [
    "#### Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "65fff5a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 6\n",
    "priora = np.row_stack((np.ones(m), 3*np.ones(m), .1*np.ones(m)))\n",
    "priornames = ['flat', 'symmetric but more confident', 'unwilling to guess']\n",
    "\n",
    "sim = 100_000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b996fb96",
   "metadata": {},
   "source": [
    "#### Simulations and plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0f6c7806",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for the flat prior:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for the symmetric but more confident prior:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for the unwilling to guess prior:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(3): # loop through each prior choice\n",
    "    print(f'Results for the {priornames[i]} prior:')\n",
    "    \n",
    "    a = priora[i]\n",
    "    posterior_param_sample = get_posterior_param_sample(a, sim, counts)\n",
    "    \n",
    "    fig, axs = plt.subplots(2, 2, figsize=(8, 6))\n",
    "    \n",
    "    rhospace = np.linspace(0, 7, 200)\n",
    "    alphaspace = np.linspace(-.01, .025, 200)\n",
    "    betaspace = np.linspace(0, .2, 200)\n",
    "    gammaspace = np.linspace(0, .3, 200)\n",
    "    \n",
    "    rho = posterior_param_sample[0]\n",
    "    gamma = posterior_param_sample[-1]\n",
    "    \n",
    "    alpha = posterior_param_sample[1]\n",
    "    beta = posterior_param_sample[2]\n",
    "    \n",
    "    axs[(0,0)].set_title(r'$\\rho$')\n",
    "    axs[(0,0)].plot(rhospace, kde(rho)(rhospace), color='black')\n",
    "    \n",
    "    axs[(0,1)].set_title(r'$\\alpha$')\n",
    "    axs[(0,1)].plot(alphaspace, kde(alpha)(alphaspace), color='black')\n",
    "    \n",
    "    axs[(1,0)].set_title(r'$\\beta$')\n",
    "    axs[(1,0)].plot(betaspace, kde(beta)(betaspace), color='black')\n",
    "    \n",
    "    axs[(1,1)].set_title(r'$\\gamma$')\n",
    "    axs[(1,1)].plot(gammaspace, kde(gamma)(gammaspace), color='black')\n",
    "    \n",
    "    plt.show()\n",
    "    plt.tight_layout()\n",
    "    plt.clf()\n",
    "    print('')\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef340db6",
   "metadata": {},
   "source": [
    "### (b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23a537f3",
   "metadata": {},
   "source": [
    "#### Posterior probability that $\\theta = p_0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cfdfc669",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Posterior probability that theta=p0 under the flat prior: 0.9173023072298073\n",
      "Posterior probability that theta=p0 under the symmetric but more confident prior: 0.6860334304835696\n",
      "Posterior probability that theta=p0 under the unwilling to guess prior: 0.9999369801066067\n"
     ]
    }
   ],
   "source": [
    "p0 = (1/6)*np.ones(m)\n",
    "\n",
    "for i in range(3):\n",
    "    a = priora[i]\n",
    "    dirichlet_logmarginal = dirichlet(a).logpdf(p0) + multinomial(n, p0).logpmf(counts) \\\n",
    "                            - dirichlet(a + counts).logpdf(p0)\n",
    "    dirichlet_marginal = np.exp(dirichlet_logmarginal)\n",
    "\n",
    "    degenerate_marginal = multinomial(n, p0).pmf(counts)\n",
    "    \n",
    "    full_marginal = .5*dirichlet_marginal + .5*degenerate_marginal\n",
    "    \n",
    "    posterior_prob_p0 = .5*degenerate_marginal / full_marginal\n",
    "                                      \n",
    "    print(f'Posterior probability that theta=p0 under the {priornames[i]} prior: {posterior_prob_p0}')\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adb54f2e",
   "metadata": {},
   "source": [
    "#### Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9ced5c2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_posterior_param_sample_new(a, sim, counts, p0):\n",
    "    # this is a simple test SSH key comment\n",
    "    dirichlet_logmarginal = dirichlet(a).logpdf(p0) + multinomial(n, p0).logpmf(counts) \\\n",
    "                            - dirichlet(a + counts).logpdf(p0)\n",
    "    dirichlet_marginal = np.exp(dirichlet_logmarginal)\n",
    "\n",
    "    degenerate_marginal = multinomial(n, p0).pmf(counts)\n",
    "    \n",
    "    full_marginal = .5*dirichlet_marginal + .5*degenerate_marginal\n",
    "    \n",
    "    posterior_prob_p0 = .5*degenerate_marginal / full_marginal\n",
    "    \n",
    "    \n",
    "    result = np.zeros((4, sim))\n",
    "    posterior_dirichlet_sample = get_posterior_sample(a, sim, counts)\n",
    "    U = np.random.random(sim)\n",
    "    posterior_sample = (U < posterior_prob_p0).reshape((sim, 1)) * p0 \\\n",
    "                            + (U >= posterior_prob_p0).reshape((sim, 1)) * posterior_dirichlet_sample\n",
    "    \n",
    "    rho = posterior_sample[:, -1] / posterior_sample[:, 0]\n",
    "    alpha = (1/6)*np.sum((posterior_sample - 1/6)**2, axis=1)\n",
    "    beta = (1/6)*np.sum(np.abs(posterior_sample - 1/6), axis=1)\n",
    "    gamma = (posterior_sample[:, 3] * posterior_sample[:, 4] * posterior_sample[:, 5])**(1/3) \\\n",
    "            / (posterior_sample[:, 0] * posterior_sample[:, 1] * posterior_sample[:, 2])**(1/3)\n",
    "    result[0] = rho\n",
    "    result[1] = alpha\n",
    "    result[2] = beta\n",
    "    result[3] = gamma\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53fe7488",
   "metadata": {},
   "source": [
    "#### Simulation and plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7924d82b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for the flat prior:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for the symmetric but more confident prior:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ngUnO5Q7gsfiXa/oiGMg2GzxxWFgnge3bt8d0CBzshB5+ICJ5wMXAkwCq2qyq1cC1wNNOs6eB65zr1wLPaMBKYLCIFMS1aNMn1rNOPBbWCa6pqYny8vKYTS4LGj9+PJmZmdaz9rbxQBXwGxH5UESeEJFsYKSqBs9xehAY6VwvBPaFPL7CWXYKOz+9t1hYJx4L6wT30Ucf0dbWFvOedVpaGpMnT7aetbelATOAx1R1OnCCT4a8AXBOvBPxyXfs/PTe0lVYB4fELaz9ycI6wcV6t61QdkIPz6sAKlR1lXP7ZQLhfSg4vO38POzcXwmMCXl8kbPMeFxPu25ZWPuThXWCi3dY79q1i/r6+pi/lomcqh4E9olI8MMwH9gKLAYWOssWAouc64uBLzqzwmcDNSHD5cbDbBg88UR0ikzjP9u3b6eoqIicnJyYv9bUqVNRVbZv38706dNj/nqmT+4GnheRDKAcuI3Al/aXROR2YA9wo9P2TeAqoAyod9oaH7DZ4InHwjrBlZaWxqVXDR1P6GFh7U2quh6Y2cVd87toq8BXY12TiT7rWSceGwZPYMFebqwnlwVNmjSJ1NRUm2RmjMu6Cuu0tDRSU1MtrH3KwjqBHTp0iJqamrj1rDMyMpg4caKFtTEu62oYHALhbWHtTxbWCSwexwTvzGaEG+O+pqYm0tLSSEvruKUzKyvLTuThUxbWCWz79u1AfGaCB02dOpWdO3fS3Nwct9c0xnTU2NjYYQg8yHrW/mVhncBKS0sZOHAgRUVFcXvNkpISWltbKSsri9trGmM6srBOPBbWCWz79u1MmTIlpifw6MyOEW6M+xobG0/ZXg0W1n5mYZ3A4rnbVtCUKVMQEQtrY1xkPevEE1FYi8hTInJYRDZ3c7+d/9YjGhoa2L17d1wnlwEMHDiQ4uJim2RmjIssrBNPpD3r3wJX9nC/nf/WI8rKylDVuPesITAUbj1rY9zT1NTUZVhnZmZaWPtURGGtqn8FPu6hiZ3/1iPc2G0raOrUqWzfvp3W1ta4v7YxxnrWiSja26zt/LceEdxta9KkSXF/7ZKSEpqamti1a1fcX9sYY2GdiFybYGbnv42tLVu2UFxcTHZ2dtxfe+rUqYDNCDfGLTYbPPFEO6zt/LcesWXLFs444wxXXjsY1jbJzBh3WM868UQ7rO38tx7Q0tLC9u3bXQvrvLw8CgsLrWdtjEssrBNPRKfIFJEXgLnAMBGpAB4A0gFU9ZfY+W89oaysjObmZtfCGgK9awtrY9zRU1jbscH9KaKwVtUv9HK/nf/WA7Zs2QLgaliXlJTw5JNPoqqIiGt1GJOMutt1y3rW/mVHMEtAW7ZsQUTatx27oaSkhBMnTrBv377eGxtjoqqnnnVLSwstLS0uVGX6w8I6AW3ZsoXx48czcOBA12qwSWbeJSKpIvKhiLzh3B4vIqucIw++KCIZzvJM53aZc3+xq4WbsDU0NHQ5G3zAgAHt9xt/sbBOQJs3b3Z1CBw+OaHH5s1dHpnWuOvrQOi3qB8BP1XVicAx4HZn+e3AMWf5T512xuNOnjxJa2trl1/Wg8vq6+vjXZbpJwvrBNPc3MyOHTtcD+thw4ZRWFjIhx9+6GodpiMRKQL+DnjCuS3APOBlp8nTwHXO9Wud2zj3zxebgOB5wSDuKaytZ+0/FtYJZufOnbS0tLge1gDTp0+3sPae/wa+A7Q5t/OBalUNbsQMPepg+xEJnftrnPansCMSekcwiIND3qGCy6xn7T8W1gnGCzPBg6ZPn05paan9Y/AIEbkaOKyqa6P93HZEQu8Ip2dt66T/WFgnmI0bN5KamurqTPCg6dOn09bWxqZNm9wuxQRcCFwjIruB3xEY/v4ZgRPuBHfjDD3qYPsRCZ3784Cj8SzYRC7Ys7Zh8MRiYZ1g1q9fz+mnn97lbhvxNmNG4HTmNhTuDap6n6oWqWoxcBOwTFVvBpYDNzjNFgKLnOuLnds49y9zjqVgPCzYa7Zh8MRiYZ1gNmzYwDnnnON2GQCMHTuWIUOGWFh73z3AN0WkjMA26Sed5U8C+c7ybwL3ulSfiUA4PWsLa/+J6AhmxtuOHDlCRUWFZ8JaRJg+fTrr1q1zuxTTiaquAFY418uB87to0wh8Pq6FmX7rqWdtw+D+ZT3rBLJhwwYApk2b5nIln5g+fTqbNm3i5MmTbpdiTFLoaYKZDYP7l4V1AvFqWDc1NVFaWup2KcYkBRsGT0wW1glk/fr1jB49mhEjRrhdSruZM2cC8MEHH7hciTHJIZxhcAtr/7GwTiBemlwWNGnSJIYMGcLKlSvdLsWYpNBTzzq4l4hts/YfC+sE0dTUxNatWz01BA6QkpLCrFmz+Nvf/uZ2KcYkhZ561iLCgAEDrGftQxbWCWLr1q20tLR4LqwB5syZw5YtW6itrXW7FGMSXrDX3N2xFgYOHGhh7UMW1gkiuE34vPPOc7mSU82ZMwdVZfXq1W6XYkzCq6+vZ+DAgXR3zpUBAwbYMLgPWVgniFWrVjFs2DDGjx/vdimnOP/88xERGwo3Jg7q6+u7HAIPsp61P1lYJ4hVq1a1h6LX5OXlUVJSYpPMjImDhoaGLieXBVlY+5OFdQKoq6tj69atnH/+KQeh8ozZs2ezcuVK7NDSxsRWbz1rGwb3JwvrBLBmzRpUlVmzZrldSrfmzJnDxx9/bAdHMSbGrGedmCysE8CqVasAPN2zvvTSSwFYtmyZy5UYk9iCE8y6Y2HtTxGHtYhcKSLbRaRMRE45C4+I3CoiVSKy3rl8OTqlmu6sXr2aiRMnMnToULdL6daECRMoLi7m7bffdrsUYxJaQ0ODDYMnoIjCWkRSgUeBTwMlwBdEpKSLpi+q6jnO5Yko1Gl6sGrVKk8PgQfNnz+fFStW0Nra6nYpxiQs61knpkh71ucDZaparqrNwO+Aa6NflgnX3r172b9/vy/C+rLLLqO6utpOmWlMDNmuW4kp0rAuBPaF3K5wlnX2ORHZKCIvi8iYPldnerVixQoALrnkEncLCcO8efMAbCjcmBjqbYJZdnY2x48fj2NFJhpiMcHsdaBYVc8GlgBPd9VIRO4QkTUisqaqqioGZSSHFStWMHToUM4880y3S+nViBEjOOuss1i6dKnbpRiTsI4fP052dna39+fl5dHU1ERTU1McqzL9FWlYVwKhPeUiZ1k7VT2qqsFPwRPAuV09kao+rqozVXXm8OHDIyzDBC1fvpxLLrmElBR/TOy/7LLLePfddzlx4oTbpSQdERkjIstFZKuIbBGRrzvLh4rIEhHZ6fwc4iwXEfm5M5l0o4jMcPc3ML1RVWpqasjLy+u2TfC+mpqaeJVloiDS//AfAJNEZLyIZAA3AYtDG4hIQcjNa4Bt/SvRdGf37t3s3r27fbcoP/jMZz5DU1MTf/zjH90uJRm1AN9S1RJgNvBVZ4LovcBSVZ0ELHVuQ2Ai6STncgfwWPxLNpFoaGigtbXVwjoBRRTWqtoCfA34E4EQfklVt4jIQyJyjdPsn5xv7RuAfwJujWbB5hPB7dVz5851tY5IfOpTn2LYsGG8+uqrbpeSdFT1gKquc67XEViHCwlMEg1urnoauM65fi3wjAasBAZ3+jJuPCYYwIMGDeq2jYW1P6VF+gBVfRN4s9Oy+0Ou3wfc1//STG9WrFjBsGHDOOOMM9wuJWxpaWlce+21vPTSSzQ1NZGZmel2SUlJRIqB6cAqYKSqHnDuOgiMdK53N6H0AMaTggFsPevE448NneYUquq77dVBn/3sZ6mrq7OJZi4RkRzgFeAbqtrhJOMaOHh7xAdwtwmj3mBhnbj89V/etNu8eTN79+7liiuucLuUiM2fP5/c3FxeeeUVt0tJOiKSTiCon1fV4LaIQ8HhbefnYWd5rxNKg2zCqDfU1ga+e9kweOKxsPapRYsWAYEJW36TmZnJNddcw6uvvmoHZ4gjCZw/9Ulgm6r+JOSuxcBC5/pCYFHI8i86s8JnAzUhw+XGg6xnnbgsrH1q0aJFzJo1i1GjRrldSp98+ctfprq6mpdeesntUpLJhcAtwLyQY/dfBfwQuFxEdgKXObchMDelHCgDfg3c5ULNJgLhhHWw121h7S8RTzAz7qusrGTNmjX84Ac/cLuUPrvkkkuYMmUKv/rVr7j11lvdLicpqOq7gHRz9/wu2ivw1ZgWZaIqnNngaWlpZGdnW1j7jPWsfej1118H4JprrumlpXeJCF/5yldYuXIl69evd7scYxJCcJt1bm5uj+3y8vIsrH3GwtqH/vCHPzBhwgRKSro64Zl/fPGLXyQrK4tf/OIXbpdiTEKoqakhNzeX1NTUHttZWPuPhbXP7N+/nyVLlnDjjTcSmC/kX0OHDuXWW2/lt7/9Lbt27XK7HGN8r6ampsch8CALa/+xsPaZZ599lra2Nr70pS+5XUpU/Mu//Aupqak88MADbpdijO/V1tb2OLksyMLafyysfURVeeqpp/jUpz7FpEmT3C4nKgoLC7n77rt57rnn2LJli9vlGONrvZ3EIygvL4/q6urYF2SixsLaR95//3127NiRML3qoHvuuYdBgwZx55130tra6nY5xvhWuMPgI0eO5NChQ3GoyESLhbWPPP744+Tk5HDDDTe4XUpU5efn8/Of/5x33nmHH//4x26XY4xvHT16lCFDhvTarqioiNra2vbZ48b7LKx9oqKighdeeIHbbruNnJwct8uJultuuYUbb7yR+++/n/fff9/tcozxHVWlsrKSoqKiXtuOGRM4imxlZZdHjzUeZGHtEz/5yU9oa2vjm9/8ptulxISI8Mtf/pJx48Zx1VVXsW7dOrdLMsZXPv74Y5qamigsLOy1bTDQKyoqYl2WiRILax+oqKjgF7/4BbfccgvFxcVulxMzQ4YMYenSpeTl5XH55ZezfPlyt0syxjeCveRIwnrfvn29tDReYWHtA9/97ndRVR588EG3S4m5cePGsXz5coYNG8b8+fP57ne/y/Hjx90uyxjPiySsR48eDVjP2k8srD3uL3/5C88++yzf/va3GTdunNvlxMWECRNYu3Ytt956K//5n//J+PHj+bd/+zd27tzpdmnGeFYweMMJ68zMTEaOHGlh7SN2Ig8Pq62t5dZbb2XChAl897vfdbucuMrJyeGpp57ijjvu4KGHHuL+++/n/vvvZ/LkyZx//vmUlJQwZswYCgsLycvLY+DAgQwYMICsrKz251DV9kvwdqjQI8AFr3f3My0t7ZRLSop91zXeUVlZiYhQUFAQVvuioiILax+xsPaotrY2br31Vvbu3cs777zDwIED3S7JFbNnz+bNN99k7969vPrqqyxfvpylS5fy3HPPuV0aItJliIdzyczMJCMjo8PP66+/PuF2yzPxU1lZyYgRI8jIyAir/YQJE1i9enWfX6+1tZVDhw6xd+9e9u7dS0VFBceOHaO6upqamhqqq6upr69v/5I8YMAAhg4dypAhQxg6dCgjR46koKCAUaNGtf8Mt/ZkZGHtQarKt7/9bV577TUefvhhLrjgArdLct3YsWP5xje+wTe+8Q0ATpw4QWVlJRUVFdTV1dHQ0EB9fT2NjY1Ax55x8BK6PLSX3bnn3dXP1tZWWlpaonI5efIkzc3N1NTU0NzcTFNTE83NzcycOTPG76JJZBUVFWENgQddfPHF/P73v2fXrl2MHz++x7Z1dXW88847rF27lq1bt7J161a2b99OU1NTh3YiQl5eHoMHD2bw4MEMHDiwfZ2rrq5my5YtHDt2rNtDnebn51NUVMTkyZNPuQwdOjTs3y0RWVh7THNzM3fddRdPPvkkd999N//8z//sdkmelJ2d3b4SG5PsVJX169czb968sB9z6aWXArB8+fIuwzp4bIfXXnuN1atX09raiohQXFxMSUkJCxYs4LTTTmPs2LGMGTOGoqIi8vLywto81NLSwuHDhzlw4AAHDx7kwIED7Zc9e/awfv16Xn311Q5HNMzPz2fy5MlMmjSpQ4hPnDiR7OzssH9vv7Kw9pCysjK+9KUv8c477/D973+fBx980Pdn1jLGxF55eTkHDx7kU5/6VNiPKSkpYcSIEbz++uvthzCurq7mlVde4fnnn2fFihWoKjNnzuSee+5h3rx5zJ49OyrBmJaWxujRo9tnpXfl5MmT7Nq1ix07dnS4LF26lGeeeaZD28698WCgjx8/nvT09H7X6wUW1h6wf/9+HnnkEX7yk5+QkZHB888/zz/8wz+4XZYxxifee+89AC666KKwHyMifOUrX+Ghhx7i1ltvpbKykr/85S+cPHmSSZMm8cADD3DzzTczceLEWJXdo/T09G5Hz06cOEFZWdkpQf7iiy9y7Nix9napqalMmDDhlCH1SZMmUVhY6KtJohGHtYhcCfwMSAWeUNUfdro/E3gGOBc4Cvy9qu7uf6mJQ1XZs2cPy5cvZ/Hixbzxxhu0trbyhS98gf/6r//q8dumMfHW2zpv3Lds2TIGDx5MSUlJRI/7/ve/T3l5Oa+88gpjxozh61//Op///Oc577zzPD2ql52dzbRp05g2bdop9x09erQ9vHfu3Nl+fdmyZTQ0NLS3S01NZejQoeTn5zNs2DDy8/PbL93dHjp0KGlp7vRxI3pVEUkFHgUuByqAD0RksapuDWl2O3BMVSeKyE3Aj4C/j1bBXtbc3ExdXR21tbXU1dVRV1dHTU0NBw4coKKigoqKCsrLy/nwww/bv/0VFRVx991389WvfpXTTjvN5d/AmI7CXOeNizZt2sRzzz3Hl7/85Yh7imlpaTz77LMxqswd+fn5zJkzhzlz5nRY3tbWxv79+9mxYwfbt2+noqKCo0ePtl/Ky8v54IMPOHr06CkT50IFJ9Dl5uaSm5tLTk5O+/XQ29/5zneiGuyRPtP5QJmqlgOIyO+Aa4HQFfda4EHn+svAIyIi2nkn1wgsWbKEl19+ucN+sz1d2trawm7b06W1tZXm5ub22bs9/WxoaKC5ubnH32PUqFGMHTuWz3/+88yYMYNZs2Yxbdo0T3+DNUkvnHU+InfffXe360pv/yZ6ut+Pj+3vcx8/fpwlS5YwePBg/v3f/73HtskuJSWFoqIiioqKepyIp6rU19dz5MiRDmF+9OjR9mU1NTXtHbLa2loqKys5fvx4+7K2tjbuu+++qNYfaVgXAqEHk60AZnXXRlVbRKQGyAeOhDYSkTuAOyCwW05PysrKWLRoUYfdcLq7pKSkhNUunEtqaioZGRlkZWWRm5tLRkYG6enpp/xMT08nKyuLQYMGtX+7Cl4fNGgQBQUFFBQU2D6Exo/CWecjWp/feOON9l3sutLbl9ee7nfrsW7VlZWVxec+9zm+//3vM2zYsB5fw4RHRMjOziY7O7tPR41UVZqamqLeCXNtgpmqPg48DjBz5swevz7eeeed3HnnnXGpyxgTuUjW5127dsWlJmPcICIdjqQYLZFOhasExoTcLnKWddlGRNKAPAITzYwx/hPOOm+MibFIw/oDYJKIjBeRDOAmYHGnNouBhc71G4Bl/dlebYxxVTjrvDEmxiIaBne2QX8N+BOB3TieUtUtIvIQsEZVFwNPAs+KSBnwMYGV2xjjQ92t8y6XZUzSiXibtaq+CbzZadn9Idcbgc/3vzRjjBd0tc4bY+LLP4dvMcYYY5KUeGFzsohUAXt6aTaMTrt/+YRf6wb/1p7IdY9T1eHxKKavbH32JKs7vqK+LnsirMMhImtU1XfnEPRr3eDf2q1u7/Pr72p1x5fV/QkbBjfGGGM8zsLaGGOM8Tg/hfXjbhfQR36tG/xbu9XtfX79Xa3u+LK6Hb7ZZm2MMcYkKz/1rI0xxpik5LmwFpErRWS7iJSJyL1d3J8pIi86968SkWIXyjxFGHXfKiJVIrLeuXzZjTo7E5GnROSwiGzu5n4RkZ87v9dGEZkR7xq7Ekbdc0WkJuT9vr+rdvEmImNEZLmIbBWRLSLy9S7aePI9D4eIDBWRJSKy0/k5pJt2C502O0VkYcjy/xCRfSJyvFP7mK73Uaj7XBHZ5NT3c3FOuSQiD4pIZcjn8Koo1dvn/5Micp+zfLuIXBHuc3q47t3Oe79eRNZ4qW4RyXfW9+Mi8kinx3T5melWNM77HK0LgcMZfgRMADKADUBJpzZ3Ab90rt8EvOiTum8FHnG71i5qvxiYAWzu5v6rgD8CAswGVrldc5h1zwXecLvOLuoqAGY413OBHV18Vjz5nof5+/0YuNe5fi/woy7aDAXKnZ9DnOtDnPtmO+/R8U6Piel6H4W6Vzu1i/O3+7Sz/EHg/4tyrX3+PwmUOO0zgfHO86SG85xerNu5bzcwLIaf6f7UnQ1cBHyFTv//u/vMdHfxWs+6/UT3qtoMBE90H+pa4Gnn+svA/F6/kcReOHV7kqr+lcAx3LtzLfCMBqwEBotIQXyq614YdXuSqh5Q1XXO9TpgG4FzRofy5HseptD182ngui7aXAEsUdWPVfUYsAS4EkBVV6rqgV6eNxbrfZ/rdv42g5zaFXimm8dHS3/+T14L/E5Vm1R1F1DmPF88/ofFou546HPdqnpCVd8FOpzAvS+fGa+FdVcnuu/8j6y9jaq2ADVAflyq6144dQN8zhnWfFlExnRxvxeF+7t50RwR2SAifxSRM9wupjNnqGw6sKrTXX5+z0eGhO1BYGQXbfry+8V6ve9P3YXO9c7Lg77mrPdPdTe8HqH+/J/s6XeI9WcuFnUDKPBnEVkrIndEueb+1t3Tc/b0mTlFxCfyMH32OvCCqjaJyD8S+BY2z+WaEtk6AofzO+5sJ/wDMMndkj4hIjnAK8A3VLXW7XoiISJvA6O6uOt7oTdUVUXEM7ubuFT3Y8C/EQiUfwMeBr4Upec2ARepaqWIjACWiEipM/KWULwW1uGc6D7YpkJE0oA84Gh8yutWr3WramiNTxDYRuYH4fxNPCc0AFX1TRH5hYgMU1XXjzMsIukEgvp5VX21iyaefs9V9bLu7hORQyJSoKoHnKG+w100qyQwpyCoCFjRy8v2e72PYd2VzvXQ5ZXOax4KeY1fA29EUnM3+vN/sqfHxvozF5O6VTX487CIvEZg2DqaYR2LXOr2M9Mdrw2Dh3Oi+8VAcBbmDcAyZ8zfTb3W3Wmb4zUEtlX6wWLgixIwG6jpZpuip4jIqJAZuecT+Ky7/aUOp6YngW2q+pNumvnyPXeErp8LgUVdtPkTsEBEhjjDwgucZeE+byzW+z7X7fxtakVktvP3/WLw8Z3W++uBLvdeiFB//k8uBm5yZi+PJzDatDrM5/Rc3SKSLSK5ACKSTeBvEo33OFp1d6mnz0y3YjWDrq8XAjNhdxCYffc9Z9lDwDXO9Szg9wQmGKwGJrhdc5h1/yewhcBMwuXA6W7X7NT1AnAAOElgu8ntBGYufsW5X4BHnd9rEzDT7ZrDrPtrIe/3SuACt2t26rqIwJDoRmC9c7nKD+95mL9fPrAU2Am8DQx1ls8Enghp9yVnHS4DbgtZ/mPn79nm/HzQWR7T9T4Kdc8kEBIfAY/wyQGnnnX+hhsJ/EMviFK9ff4/SWDY/yNgOyEzkLt6zhh8PqJaN4EZ2hucyxaP1r2bwGTY485nuqSnz0x3FzuCmTmF8831FwR2K6gH/kVVf+NuVcYYk7y8NgxuvOFlArulDAP+N/Av7pZjjDHJzcLadCAiZwP5qvoTVW11Fle5WZMxJjIikiUiJ0Tkvk7LV4nIP7hVl+k7C2vT2YXAuyKSIiLnAj8hsPuJMcYnVLWRwEE2Qg+J+nkgncB8D+MzFtams3OANQQmwa0hsM36NTcLMsb0yXvAeBFJc3YX/AFwj9pEJV+ysDadnUNgV4VLgYkEZjH+yM2CjDGRU9V6ArsrjgfuAHar6hJ3qzJ95bWDohgXiUgqMBX4UFXbgI9E5D1ghLuVGWP6qIzACW/+Bfg7l2sx/WA9axNqCjAQ+LSIpIrIOQT2X366x0cZY7yqDPgvYLk6J5Ax/mRhbUJNB7YSOH5xNfBb4J80cOYnY4z/lBE4Kcn3emtovM2GwU2ocwicbOQ/3S7EGBMVx4HFGjitpPEx61mbUNPxzzHLjTG9O4PAIW2Nz1lYm1DTgFK3izDGRM1ZBI5NbnzOjg1ujDHGeJz1rI0xxhiPs7A2xhhjPM4Ts8GHDRumxcXFbpdhjOetXbv2iKoOd7uOntj6bEzvIl2Xew1rEXkKuBo4rKpnOsuGAi8CxQROrH2jqh4TEQF+RuBE3fXAreHsiF9cXMyaNWvCrdmYpCUie9yuoTe2PhvTu0jX5XCGwX8LXNlp2b3AUlWdBCx1bgN8GpjkXO7AztZkjDHG9FuvYa2qfyVwModQ1/LJISifJnAqtuDyZzRgJTBYRAqiVKsxxhiTlPo6wWykqh5wrh8kcDg7gEJgX0i7CmfZKUTkDhFZIyJrqqqq+liGMcYYk/j6PRvcOTdqxDtrq+rjqjpTVWcOH+7p+TJJZ9OmTfzoRz+y7Y7G+FxbWxsvvfQSjz76KM3NzW6XY/qhr7PBD4lIgaoecIa5DzvLK4ExIe2KnGXGR77//e+zaNEi5s6dy/Lly90uxxjTR8899xwLFy4EoLGxkW9961suV2T6qq8968XAQuf6QmBRyPIvSsBsoCZkuNz4xLFjxwCorq52txBjTJ+1tLTw0EMPMX36dK644gr+4z/+g9raWrfLMn0Uzq5bLwBzgWEiUgE8APwQeElEbgf2ADc6zd8ksNtWGYFdt26LQc0mxoIrtK3YxvjXypUr+eijj3jhhRcoKChg7ty5vP3223z2s591uzTTB72Gtap+oZu75nfRVoGv9rco4666ujrAwtoYP1u6dCkiwoIFC8jNzSU3N5c///nPFtY+5YkjmBlvCYZ0MLSNMf7z9ttvM2PGDIYOHQrA3LlzWbJkictVmb6yY4ObUwTDuqmpiaamJperMcZEqr6+npUrVzJ//icDoPPnz6e8vJyKigoXKzN9ZWFtOggG9MiRgV3nrXdtRGSwiLwsIqUisk1E5rhdk+nZli1baGlpYdasWe3LZs6cCcD69etdqsr0h4W16SAYzkVFRYBttzZA4Hj/b6nq6cA0YJvL9ZhebNiwAYCzzz67fVnwuoW1P1lYmw4srE0oEckDLgaeBFDVZlWtdrUo06uNGzeSk5PDhAkT2pfl5uZy2mmntQe58RcLa9NBMJyDYW3D4ElvPFAF/EZEPhSRJ0Qk2+2iTM82bNjAWWedRUpKx3/x06ZNs561T1lYmw46h7X1rJNeGjADeExVpwMn+OQse+3sWP/eoaps3LixwxB40LRp0ygrK6O+vt6Fykx/WFibDoLhXFhY2OG2SVoVQIWqrnJuv0wgvDuwY/17R1VVFdXV1UydOvWU+6ZMmQLARx99FO+yTD9ZWJsOLKxNKFU9COwTkSnOovnAVhdLMr0oKysDYNKkSafcF1y2Y8eOuNZk+s8OimI66DzBzLZZG+Bu4HkRyQDKscMIe9rOnTsBmDhx4in3BcM62Mb4h4W16SDYky4oKEBErGdtUNX1wEy36zDhKSsrIzU1leLi4lPuy83NZdSoURbWPmTD4KaD2tpaRIScnBwGDRpkYW2Mz+zcuZNx48aRkZHR5f2TJk2ysPYhC2vTQW1tLYMGDUJELKyN8aGdO3d2ub06aPLkybbN2ocsrE0HdXV15OTkAIEhM9tmbYy/fPTRR5x22mnd3j9+/HgOHTpEQ0NDHKsy/WVhbTpobGxk4MCBAAwYMMBWaGN8pKamhpqami63VweNHTsWwE7o4TMW1qaDhoYGsrKyAMjKyrKwNsZH9uzZA8C4ceO6bRMM671798alJhMdFtamg8bGxvawHjBgAI2NjS5XZIwJl4V14rKwNh10DmvrWRvjH7t37wbocRi8sLAQEbGw9pl+hbWI/LOIbBGRzSLygohkich4EVklImUi8qJzIAXjE6FhnZWVZT1rY3xkz549ZGVlMWLEiG7bZGRkMGrUKAtrn+lzWItIIfBPwExVPRNIBW4CfgT8VFUnAseA26NRqIkP61kb41979uxh7NixiEiP7caOHWth7TP9HQZPAwaISBowEDgAzCNwsH+Ap4Hr+vkaJo4aGxsZMGAAYD1rY/xmz549PW6vDrKw9p8+h7WqVgL/B9hLIKRrgLVAtaq2OM0qgML+FmniJ3Q2uPWsjfGXiooKxowZ02u7YFirahyqMtHQn2HwIcC1BE5OPxrIBq6M4PF2/lsP6rzN2sLaGH9oaWnh0KFDjB49ute2Y8eOpbGxkSNHjsShMhMN/RkGvwzYpapVqnoSeBW4EBjsDIsDFAGVXT3Yzn/rTZ23WTc3N9PW1uZyVcaY3hw+fJi2trb209v2xHbf8p/+hPVeYLaIDJTAbIbgeW6XAzc4bRYCi/pXoomnzmEdXGaM8bb9+/cDhN2zBgtrP+nPNutVBCaSrQM2Oc/1OHAP8E0RKQPygSejUKeJA1U9ZRgcLKyN8QML68TWr/NZq+oDwAOdFpcD5/fneY07mpubgU961MGftt3aGO+rrAxscQwnrPPz8xkwYICFtY/YEcxMu2AoW8/aGP/Zv38/KSkpPR4QJUhEbPctn7GwNu2Codx5m7X1rI3xvv379zNy5EjS0sIbMB0zZoyFtY9YWJt2ncM6+NPC2hjv279/f1gzwYOKiorah86N91lYm3bd9axtGNwY79u/f39Y26uDCgsLOXjwIK2trTGsykSLhbVpZ8PgxvhXpGE9evRoWltbOXToUAyrMtFiYW3aBcM69NjgocuNMd7U1NTEkSNHIu5ZAzYU7hMW1qZd59ng1rM2xh8OHDgAhLfbVlAwrIP7Zxtvs7A27bqbYGY9a2O8LZIDogRZz9pfLKxNO9tmbYw/BcM6ktngI0aMIDU11cLaJyysTTvbdcsYf+pLzzo1NZWCggILa5+wsDbtbNctY/xp//79pKenk5+fH9HjRo8ebWHtExbWpl3nCWYZGRmIiPWsjfG4yspKRo8eTeAEiOErLCy0CWY+YWFt2nXedUtEyMrKsp61MR4X6T7WQYWFhdaz9gkLa9Ou8zA4BILbetbGeFt/wrqmpoYTJ07EoCoTTRbWpl1jYyMiQnp6evsy61kb432RHhc8yHbf8g8La9OusbGRrKysDtu9rGdtjLcdP36c2traPveswcLaDyysTbtgWIeynrUx3taXo5cFBR9jk8y8z8LatGtoaDglrK1nbQBEJFVEPhSRN9yuxXQU7BVbzzqxWVibdo2Nje0zwYOysrIsrA3A14FtbhdhTtWXA6IE5ebmkpuba2HtA/0KaxEZLCIvi0ipiGwTkTkiMlRElojITufnkGgVa2Krq2HwAQMG2DB4khORIuDvgCfcrsWcqi+HGg1lu2/5Q3971j8D3lLV04FpBL553wssVdVJwFLntvGB7sLaetZJ77+B7wBt3TUQkTtEZI2IrKmqqopbYSYQ1tnZ2eTm5vbp8RbW/tDnsBaRPOBi4EkAVW1W1WrgWuBpp9nTwHX9K9HEi00wM52JyNXAYVVd21M7VX1cVWeq6szhw4fHqToDn+xjHenRy4IsrP2hPz3r8UAV8Btn4skTIpINjFTVA06bg8DIrh5s38S9x3rWpgsXAteIyG7gd8A8EXnO3ZJMqL4eECVo9OjRHDhwgLa2bgdOjAf0J6zTgBnAY6o6HThBpyFvVVVAu3qwfRP3nq5mg1vPOrmp6n2qWqSqxcBNwDJV/V8ul2VCBI8L3leFhYW0tLRgnSZv609YVwAVqrrKuf0ygfA+JCIFAM7Pw/0r0cRLV7PBrWdtjHepar971rb7lj/0OaxV9SCwT0SmOIvmA1uBxcBCZ9lCYFG/KjRx0902awtrA6CqK1T1arfrMJ+orq6msbGxzzPBwcLaL9L6+fi7gedFJAMoB24j8AXgJRG5HdgD3NjP1zBx0t0265MnT9La2kpqaqpLlRljutKffayDLKz9oV9hrarrgZld3DW/P89r3NFdWAfvy87OdqMsY0w3ohHWI0eOJCUlxQ456nF2BDPTrrth8OB9xhhviUZYp6WlMXLkSOtZe5yFtQECE1W6OzY4YNutjfGgYMAWFBT063lsX2vvs7A2ALS0tNDW1mY9a2N8ZP/+/QwePJiBAwf263ksrL3PwtoAn4RxV7tugfWsjfGi/fv392smeJCFtfdZWBvgk7DurmdtYW2M9/R3H+ugwsJCjh07Zuu5h1lYG6D7sA6dDW6M8ZZohnXw+Yw3WVgb4JOes00wM8Yf2traOHDgQFTCOvgcNhTuXRbWBuh9GNx61sZ4S1VVFS0tLVHtWVtYe5eFtQF6Hwa3nrUx3hKNfayDLKy9z8LaAN3PBreetTHeFAzraMwGHzRoENnZ2RbWHmZhbQDrWRvjN9HsWYsIhYWFNsHMwyysDWC7bhnjN5WVlYgIo0aNisrz2b7W3mZhbYDeZ4PbMLgx3lJRUcGoUaNIT0+PyvONHj3awtrDLKwN0H3POj09nZSUFOtZG+MxFRUVFBUVRe35gsPgqhq15zTRY2FtgO7DWkTIysqynrUxHhOLsG5ububIkSNRe04TPRbWBug+rCEwFG49a2O8Zd++fVEPa7Ddt7zKwtoA3W+zDi6znrUx3lFbW0ttbW1MwtpmhHuThbUBeg5r61kb4y3B3q/1rJNHv8NaRFJF5EMRecO5PV5EVolImYi8KCIZ/S/TxFpDQwNZWVmkpJz6kbCetTHeUlFRAUQ3rEeNGoWIWFh7VDR61l8HtoXc/hHwU1WdCBwDbo/Ca5gYq6+v7/YE9tazNsZbYhHW6enpjBgxwsLao/oV1iJSBPwd8IRzW4B5wMtOk6eB6/rzGiY+GhoaTjnUaFBWVpaFtTEesm/fPiA6hxoNZQdG8a7+9qz/G/gO0ObczgeqVbXFuV0BdPlpEpE7RGSNiKypqqrqZxmmv3rrWdswuDHeUVFRwYgRI8jMzIzq89ohR72rz2EtIlcDh1V1bV8er6qPq+pMVZ05fPjwvpZhoqSnnrUNgxvjLdHexzrIetbeldaPx14IXCMiVwFZwCDgZ8BgEUlzetdFgP3lfaCnnrVNMDPGWyoqKhg/fnzUn7ewsJAjR47Q1NQU9V676Z8+96xV9T5VLVLVYuAmYJmq3gwsB25wmi0EFvW7ShNz1rM2xj9i1bMOnsHLhsK9Jxb7Wd8DfFNEyghsw34yBq9hosx61sb4w4kTJzh27FjMhsHB9rX2ov4Mg7dT1RXACud6OXB+NJ7XxI/1rI3xh1jsthVkYe1ddgQzA/Tes7awNsYbgmE9ZsyYqD/3uHHjANi9e3fUn9v0j4W1AXrvWbe0tNDS0tLl/caY+NmzZw8Qm7DOzc1l+PDhlJeXR/25Tf9YWBug9/2sAdtubYwH7Nq1i5SUFMaOHRuT558wYQIfffRRTJ7b9J2FtUFVez2CGVhYG+MF5eXljB07lvT09Jg8/4QJE6xn7UEW1oaTJ0/S2tra4zA4YNutk5CIjBGR5SKyVUS2iMjX3a4p2ZWXl8dkH+ug0047jb1793Ly5MmYvYaJnIW1aQ/hniaYgfWsk1QL8C1VLQFmA18VkRKXa0pqu3btYsKECTF7/gkTJtDa2tp+/HHjDRbWhvr6egDrWZtTqOoBVV3nXK8jcIa96J49woTtxIkTHDp0KOZhDdhQuMdYWJuwe9YW1slNRIqB6cCqLu6zE/PEQXCXqlgOg1tYe5OFtQm7Z23D4MlLRHKAV4BvqGpt5/vtxDzxEQzQWPasR48eTUZGhoW1x1hYm1571jYMntxEJJ1AUD+vqq+6XU8y27VrFxDbnnVqairFxcUW1h5jYW3aQ9h23TKdiYgQOL7/NlX9idv1JLvy8nKys7OJ9eiF7b7lPRbWpn0Y3HrWpgsXArcA80RkvXO5yu2iklVwJnjgO1TsWFh7T1RO5GH8zXrWpjuq+i4Q22QwYSsvL4/p9uqgCRMmcOzYMY4dO8aQIUNi/nqmd9azNtazNsYHVDWuYQ3YYUc9xMLahD0bPNjOGBN/VVVV1NfXx3RyWdCUKVMAKC0tjflrmfBYWBvq6uoAGDRoUJf3Z2dnA3D8+PG41WSM6aisrAwIHA401iZOnEhqairbtm2L+WuZ8FhYG2prA7vN5uTkdHl/SkoKubm57e2MMfEX7OVOnTo15q+VkZHBxIkTLaw9xMLaUFtbS05ODqmpqd22GTRokIW1MS4qLS0lMzOTcePGxeX1pk6damHtIX0O6+7OxiMiQ0VkiYjsdH7aVEKPq62t7XYIPMjC2hh3bdu2jcmTJ/f4pTqapk6dSllZmZ19yyP607Pu7mw89wJLVXUSsNS5bTzMwtoY7ystLeX000+P2+uVlJTQ0tLCjh074vaapnt9DusezsZzLfC00+xp4Lp+1mhizMLaGG9ramqivLw8Lturg84++2wANmzYELfXNN2LyjbrTmfjGamqB5y7DgIjo/EaJnbCCWubYGaMe7Zv305bW1tcw/r0008nIyPDwtoj+h3WPZ2NR1UV0G4eZ6fU84i6ujrrWRvjYcHAnDZtWtxeMyMjg5KSEtavXx+31zTd61dYd3M2nkMiUuDcXwAc7uqxdko977BhcGO8bcOGDWRmZjJp0qS4vu4555xjPWuP6M9s8O7OxrMYWOhcXwgs6nt5Jh5qa2vJzc3tsc2gQYOoq6sjMFhijImnjRs3cuaZZ5KWFt/TOZxzzjkcOnSI/fv3x/V1zan607Pu7mw8PwQuF5GdwGXObeNRqhp2z7qtrc0OOWqMCzZs2NA+4SueZs2aBcCqVavi/tqmoz5/TevlbDzz+/q8Jr7q6+tpa2sLK6wh0AsPHn7UGBN7lZWVHD58OK7bq4OmT59ORkYGf/vb37j++uvj/vrmE3YEsyQX3A4dSVgbY+Jn9erVwCe93HjKzMxk+vTprFy5Mu6vbTqysE5yFtbGeNvq1atJT0/nnHPOceX1Z8+ezZo1a2hubnbl9U2AhXWSs7A2xttWrVrFtGnTyMrKcuX1L7nkEhoaGmy7tcssrJNcuGEdnC1uYW1M/LS0tPDBBx+4MgQeNHfuXFJSUnj77bddq8FYWCe9mpoaoPewzsvLA6C6ujrWJRljHGvXruX48eNccsklrtUwZMgQzj33XJYuXepaDcbCOukdOnQIgJEjez4qbPDANYcPd3mMG2NMDCxfvhwI9G7dtGDBAlauXMnRo0ddrSOZWVgnuYMHDyIi9HYUuZycHHJycjh48GCcKjPGLFu2jDPPPLPX9TPWrr/+elpbW3n99dddrSOZWVgnuYMHDzJ8+PCwjoxUUFDAgQMHem1njOm/EydO8M477zB/vvuHrZgxYwZjx47llVdecbuUpGVhneQOHDhAQUFBWG1HjRplPWtj4uTPf/4zjY2NXHPNNW6Xgojw93//97z11lvtm85MfFlYJ7mDBw8yatSosNpaz9qY+Fm0aBGDBw/mU5/6lNulAPDlL3+ZlpYWfvOb37hdSlKysE5ykYS19ayNiY/6+npee+01PvOZz5Cenu52OQBMnjyZSy+9lEcffZSmpia3y0k68T2Fi/EUVeXgwYMRDYPX1tZSX1/PwIEDY1xdeIK/w6ZNm9i6dSuVlZUcOHCA/fv38/HHH9PY2EhaWhpDhw5lwoQJzJgxg7lz53LWWWcROHGcMd7z2muvUVtby2233eZ2KR3cd999LFiwgCeffJK77rrL7XKSioV1Evv44485efJkRMPgEOiNT5gwIZal9ejo0aP86U9/4q233mLJkiUdevtZWVkUFBRQUFDAuHHjyMrK4uTJkxw9epQ//vGPPP300wCMGTOGq666iquuuor58+fbyUmMpzz++OMUFxe7un91Vy677DIuvvhi7r//fm644QZGjBjhdklJw8I6iQVDLpKedfBx8Q7r+vp6Xn/9dZ577jneeustWlpaGDZsGAsWLGD27NmcffbZnHHGGeTn53fbY1ZVKioq+POf/8ybb77J888/z69+9SsyMjKYO3cuV199Nddffz1FRUVx/d2MCfX+++/z17/+lZ/+9KekpHhrS6WI8NhjjzF9+nS+9KUvsWjRIlJTU90uKzmoquuXc889V038vfHGGwrou+++G1b7zZs3K6DPPfdcjCv7xMaNG/Uf//EfNScnRwEtLCzU73znO7p69WptbW3t13M3NTXp22+/rd/85jd1ypQpCiigs2bN0ocfflj3798fpd8ieoA16oF1tqeLrc9919bWpvPmzdP8/Hw9fvy42+V069FHH1VAb7vtNm1ubna7HF+KdF22nnUS+/DDDwE466yzwmo/ZcoUsrKy+PDDD7n55ptjVldLSwuLFi3ikUceYcWKFWRlZXHTTTexcOFCLr744qj1NjIyMpg/fz7z58/n4YcfZvv27bzyyiu88sorfOtb3+Lb3/42l112GbfccgvXX3+9DZWbmHvxxRdZtmwZjzzyiKc/b3fddReHDh3ioYceYvPmzTz88MNcdNFFMZ8Hoqo0NzfT0NBAY2MjJ0+ebL80Nzd3uN3dspaWlj69dkpKCikpKaSmprZf72nZZZddFtX3QwIB766ZM2fqmjVr3C4j6Xz2s59ly5YtbN++PezHzJo1i+zsbJYtWxb1eqqqqnjiiSd47LHH2LdvH+PGjeOuu+7i9ttvJz8/P+qv15PS0lKee+45nnvuOfbs2UN2djaf/exnueWWW5g3b55rQ38islZVZ7ry4mGy9blvdu7cyXnnnceUKVN4//33fTG8/NJLL3H33Xdz+PBhCgsLmTdvHpMmTaKgoICMjIz2mezBcG1sbGy/Hvqz86Wr5cFlXsiscLS1tfUY1pGuyxbWSay4uJg5c+bwwgsvhP2YO++8kxdeeIFjx45F5VujqrJy5Up+8Ytf8NJLL9Hc3Mz8+fO5++67ufrqq13/h9XW1sZ7773Hs88+y0svvURNTQ2jRo3i6quv5qqrruKyyy5rPyNZPFhYJ6YdO3Zw+eWXc+LECdasWUNxcbHbJYWtvr6e3/3ud/zxj3/k3XffDWv3ThEhKyuLAQMGdLh0tay75ZmZme1fCNLT0ztc72lZWlpaxP+7gkPRra2ttLW1dbh0t+yiiy7q7T2IbF2OZMw8VhfbxhV/VVVVCuiPf/zjiB73+OOPK6A7d+7s1+tXVlbqz3/+c502bZoCmpubq3fddZdu3ry5X88bSw0NDfryyy/rDTfcoIMGDVJA09PTde7cufqv//qvumLFCm1oaIhpDdg264TS2NiojzzyiObm5mp+fr6uW7fO7ZL6raGhQffu3asfffSRbtu2Tbdt26a7d+/WgwcPak1NjTY1NWlbW5vbZbou0nU5JtusReRK4GdAKvCEqv4wFq9j+u6ZZ54B4NJLL43ocfPmzUNEeOqpp/jBD34Q9uPq6+tZvXo17777Lm+99Rbvv/8+qso555zDL3/5S26++WZycnIiqiXesrKy+NznPsfnPvc5Tp48yXvvvcf/+3//j6VLl/Lggw+iqmRmZjJnzhwuueQSZsyYwRlnnMH48eM9N6s3ErY+R09dXR07d+5k27ZtLF26lDfeeIOqqirmzZvHb37zG8aOHet2if2WlZXFmDFj3C4j4UR9GFxEUoEdwOVABfAB8AVV3drdY2zYLL7279/Peeedx+TJk9tPwReJG2+8kT/96U/87W9/o6SkpH25qlJbW8vhw4cpKytj27ZtbN26lU2bNrFu3TpaWloQEaZNm9YeelOnTo3mr+aaY8eO8c477/CXv/yFFStWsH79etra2oDAP6+ioiIKCws7XEaNGkV+fj75+fkMHTqUESNGMGDAgB5fJ97D4Im+Pre2ttLS0tJ+CU5ACr1+8uTJLre1dresvr6empoaqqurqa6u7nD92LFj7a89ZMgQFixYwO233x71yUjG+1zfZi0ic4AHVfUK5/Z9AKr6n909preV+w9/+EOH49F2VXPnZX1pE6/HuFlLa2srmzZtoq2tjSVLlnDBBRec8pjebNu2jblz51JVVUVRURFpaWk0NjZy5MgRTp482aHt8OHDKSkpYc6cOVx00UVccMEFDBkyJOLX9Jva2lq2bNnCli1bKC0tpaKigsrKyvZLc3PzKY+57777eh2tcCGso74+33jjjTQ2NqKqtLW1xeRna2trl8Hb+Xq0//+lp6czYMAABg8eTF5eHoMHD26/npeXR1FRERMnTmTy5MmUlJSEdbY7k5giXZdj8UkpBPaF3K4AZnVuJCJ3AHcAvQ791NTUsHfv3s6PP6Vd52V9aROvx0TjeUWkT89788038/Wvf73PvdqpU6eyYcMGfv3rX1NWVoaqkpGRwfDhwxk2bBjDhg1jwoQJTJ06lWHDhvXpNfxu0KBBzJkzhzlz5pxyn6py9OhRDh06xMcff8zRo0c5evQoZ599tguV9irq6/PevXtpamoiJSUFEen1Z2pqaljtgj9FhLS0NNLS0tonFHV3vbf7g9eDk5yCE51CfwavZ2Zmuj4h0iSuWPSsbwCuVNUvO7dvAWap6te6e4yfhs2McZMLPWtbn42JgUjX5VjMeqkEQmcXFDnLjDH+Y+uzMR4Qi7D+AJgkIuNFJAO4CVgcg9cxxsSerc/GeEDUt1mraouIfA34E4FdPZ5S1S3Rfh1jTOzZ+myMN8RkKqKqvgm8GYvnNsbEl63PxrjPv0dqMMYYY5KEJ44NLiJVwJ5emg0DjsShnGjza93g39oTue5xqjo8HsX0VZjrc7R48W9tNYUn2WuKaF32RFiHQ0TWxHOXlWjxa93g39qt7uThxffMagqP1RQZGwY3xhhjPM7C2hhjjPE4P4X1424X0Ed+rRv8W7vVnTy8+J5ZTeGxmiLgm23WxhhjTLLyU8/aGGOMSUqeCmsRGSoiS0Rkp/Ozy3MpishbIlItIm90Wj5eRFaJSJmIvOgcHtFLdS902uwUkYUhy1eIyHYRWe9cRsS43iud1ysTkXu7uD/Tef/KnPezOOS++5zl20XkiljWGa26RaRYRBpC3t9feqzui0VknYi0OCfOCL2vy89MsuntPXTa3CgiW0Vki4j8j9s1ichYEVkuIh+KyEYRuSrG9TwlIodFZHM394uI/Nypd6OIzIhlPWHWdLNTyyYReV9EprldU0i787paJ12jqp65AD8G7nWu3wv8qJt284HPAG90Wv4ScJNz/ZfAnV6pGxgKlDs/hzjXhzj3rQBmxqnWVOAjYAKQAWwASjq1uQv4pXP9JuBF53qJ0z4TGO88T6oP6i4GNsfzsxxh3cXA2cAzwA3hfGaS6RLmezgJ+DBknRrhgZoeD/4Pctad3TGu6WJgRnefdeAq4I+AALOBVXH42/VW0wUhf7NPe6GmkL/vMgJH7rsh1jWFc/FUzxq4Fnjauf40cF1XjVR1KVAXukxEBJgHvNzb42MgnLqvAJao6seqegxYAlwZn/I6OB8oU9VyVW0Gfkeg/lChv8/LwHzn/b0W+J2qNqnqLqDMeT6v1+2mXutW1d2quhFo6/RYr3xm3BbO3/5/A4867xOqetgDNSkwyLmeB+yPZUGq+lfg4x6aXAs8owErgcEiUuBmTar6fvBvBqwkcFa3mArjfQK4G3gFiPXnKGxeC+uRqnrAuX4QGBnBY/OBalVtcW5XAIXRLK4H4dRdCOwLud25vt84Q7Tfj3HA9FZHhzbO+1lD4P0N57Gx0p+6AcY7w5F/EZFPxbrYrmpyRPKeufl+e0k478NkYLKIvCciK0Uk1l9qwqnpQeB/iUgFgR7a3TGuqTde/zzdTqDn7yoRKQSuBx5zu5ZQMTmRR09E5G1gVBd3fS/0hqqqiHhmqnqM675ZVStFJJfAt7lbCAyJmug4AIxV1aMici7wBxE5Q1Vr3S7MRE0agaHwuQR6Z38VkbNUtdrFmr4A/FZVHxaROcCzInKmqnYeQUl6InIpgbC+yO1agP8G7lHVNvcH5j4R97BW1cu6u09EDolIgaoecIZnIhmCOEpgWCfN6VUVAZX9LLddFOquJPCPJKiIwLZqVLXS+VnnTIw5n9iFdSUwplMdnd+nYJsKEUkjMIR3NMzHxkqf69bARqgmAFVdKyIfEeiJrYl51f17z7r9zCSZcN7DCgLbO08Cu0RkB4Hw/sDFmm7H2Wyhqn8TkSwCx552a2jVzfW3WyJyNvAE8GlVPep2PcBM4HdOUA8DrhKRFlX9g5tFeW0YfDEQnPG6EFgU7gOdf8jLgeDMvYge30/h1P0nYIGIDJHAbPEFwJ9EJE1EhgGISDpwNdDjLMV++gCYJIGZ8xkEJmIt7tQm9Pe5AVjmvL+LgZucWdfjCfwzXB3DWqNSt4gMF5FUABGZ4NRd7qG6u9PlZyZGdXpZOO/hH3C+2Djr02Ri+zcOp6a9BCbDIiJTgSygKoY19WYx8EVnVvhsoCZk850rRGQs8Cpwi6rucLOWIFUdr6rFqlpMYO7LXW4HNeC52eD5wFJgJ/A2MNRZPhN4IqTdOwQ+9A0EvlFf4SyfQCA8yoDfA5keq/tLTm1lwG3OsmxgLbAR2AL8jBjPsCYwK3QHgdms33OWPQRc41zPct6/Muf9nBDy2O85j9tO4JtwPD8ffaob+Jzz3q4H1gGf8Vjd5zmf4xMERjC29PSZScZLGO+hAD8BtgKbcPYKcbmmEuA9AjPF1wMLYlzPCwQ2+Zx0Pk+3A18BvhLyHj3q1LuJOOyBEkZNTwDHnPdnPbDG7Zo6tf0tHpkNbkcwM8YYYzzOa8PgxhhjjOnEwtoYY4zxOAtrY4wxxuMsrI0xxhiPs7A2xhhjPM7C2hhjjPE4C2tjjDHG4yysjTHGGI/7/wFKUnn2QnSGQQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for the unwilling to guess prior:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(3): # loop through each prior choice\n",
    "    print(f'Results for the {priornames[i]} prior:')\n",
    "    \n",
    "    a = priora[i]\n",
    "    posterior_param_sample = get_posterior_param_sample_new(a, sim, counts, p0)\n",
    "    \n",
    "    fig, axs = plt.subplots(2, 2, figsize=(8, 6))\n",
    "    \n",
    "    rhospace = np.linspace(0, 2, 200)\n",
    "    alphaspace = np.linspace(-.01, .01, 200)\n",
    "    betaspace = np.linspace(-.1, .1, 200)\n",
    "    gammaspace = np.linspace(.5, 1.5, 200)\n",
    "    \n",
    "    rho = posterior_param_sample[0]\n",
    "    gamma = posterior_param_sample[-1]\n",
    "    \n",
    "    alpha = posterior_param_sample[1]\n",
    "    beta = posterior_param_sample[2]\n",
    "    \n",
    "    axs[(0,0)].set_title(r'$\\rho$')\n",
    "    axs[(0,0)].plot(rhospace, kde(rho)(rhospace), color='black')\n",
    "    \n",
    "    axs[(0,1)].set_title(r'$\\alpha$')\n",
    "    axs[(0,1)].plot(alphaspace, kde(alpha)(alphaspace), color='black')\n",
    "    \n",
    "    axs[(1,0)].set_title(r'$\\beta$')\n",
    "    axs[(1,0)].plot(betaspace, kde(beta)(betaspace), color='black')\n",
    "    \n",
    "    axs[(1,1)].set_title(r'$\\gamma$')\n",
    "    axs[(1,1)].plot(gammaspace, kde(gamma)(gammaspace), color='black')\n",
    "    \n",
    "    plt.show()\n",
    "    plt.tight_layout()\n",
    "    plt.clf()\n",
    "    print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "158f8dd0",
   "metadata": {},
   "source": [
    "#### With CDFs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f0c1a3ec",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results for the flat prior:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for the symmetric but more confident prior:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Results for the unwilling to guess prior:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(3): # loop through each prior choice\n",
    "    print(f'Results for the {priornames[i]} prior:')\n",
    "    \n",
    "    a = priora[i]\n",
    "    posterior_param_sample = get_posterior_param_sample_new(a, sim, counts, p0)\n",
    "    \n",
    "    fig, axs = plt.subplots(2, 2, figsize=(8, 6))\n",
    "    \n",
    "    rhospace = np.linspace(0, 2, 200)\n",
    "    alphaspace = np.linspace(-.01, .01, 200)\n",
    "    betaspace = np.linspace(-.1, .1, 200)\n",
    "    gammaspace = np.linspace(.5, 1.5, 200)\n",
    "    \n",
    "    rho = posterior_param_sample[0]\n",
    "    gamma = posterior_param_sample[-1]\n",
    "    \n",
    "    alpha = posterior_param_sample[1]\n",
    "    beta = posterior_param_sample[2]\n",
    "    \n",
    "    axs[(0,0)].set_title(r'$\\rho$')\n",
    "    axs[(0,0)].plot(rhospace, ECDF(rho)(rhospace), color='black')\n",
    "    \n",
    "    axs[(0,1)].set_title(r'$\\alpha$')\n",
    "    axs[(0,1)].plot(alphaspace, ECDF(alpha)(alphaspace), color='black')\n",
    "    \n",
    "    axs[(1,0)].set_title(r'$\\beta$')\n",
    "    axs[(1,0)].plot(betaspace, ECDF(beta)(betaspace), color='black')\n",
    "    \n",
    "    axs[(1,1)].set_title(r'$\\gamma$')\n",
    "    axs[(1,1)].plot(gammaspace, ECDF(gamma)(gammaspace), color='black')\n",
    "    \n",
    "    plt.show()\n",
    "    plt.tight_layout()\n",
    "    plt.clf()\n",
    "    print('')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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