{ "cells": [ { "cell_type": "markdown", "id": "7056df7c-5606-4920-a0c4-0f23e97e9cb3", "metadata": {}, "source": [ "# Optimal acceptance thresholds" ] }, { "cell_type": "markdown", "id": "7e61a1f0-7adb-4b76-abd7-76f31b0114cb", "metadata": {}, "source": [ "
\n", "Note: The SilkOptimalEpsilon threshold schedule is work in progress and may or may not work. Contact us if you are interested.\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "id": "321f713e-01b2-41b3-b743-95abe07e6b94", "metadata": {}, "outputs": [], "source": [ "# install if not done yet\n", "#!pip install pyabc[autograd] --quiet" ] }, { "cell_type": "code", "execution_count": 2, "id": "acdecd17-4cda-467f-8b50-82c8525bd0b4", "metadata": {}, "outputs": [], "source": [ "import logging\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import pyabc\n", "\n", "pyabc.settings.set_figure_params(\"pyabc\") # for beautified plots\n", "\n", "# debug\n", "for debugger in [\"ABC.Distance\", \"ABC.Epsilon\"]:\n", " logging.getLogger(\"ABC.Distance\").setLevel(logging.DEBUG)" ] }, { "cell_type": "raw", "id": "16cb1ada-c1d4-44e1-9777-78bd09a238ed", "metadata": { "raw_mimetype": "text/restructuredtext", "tags": [] }, "source": [ "In this notebook:\n", "\n", "* :class:`ListEpsilon `\n", "* :class:`QuantileEpsilon `\n", "* :class:`SilkOptimalEpsilon `" ] }, { "cell_type": "markdown", "id": "35af3933-8723-4189-9df0-0e8a97513934", "metadata": {}, "source": [ "## Issues of quantile-based acceptance thresholds\n", "\n", "Approximate Bayesian Computation with a Sequential Monte Carlo scheme (ABC-SMC) generates a sequence of populations constituting sequentially better posterior approximations\n", "\n", "$$\\pi_{\\text{ABC},\\varepsilon}(\\theta|y_\\text{obs}) \\propto \\int I[d(y,y_\\text{obs})\\leq\\varepsilon]\\pi(y|\\theta)\\pi(\\theta)\\operatorname{dy},$$\n", "\n", "corresponding to reduced acceptance thresholds $\\varepsilon$. Under mild conditions, the ABC posterior converges to the true Bayesian posterior for $\\varepsilon\\rightarrow 0$, i.e.\n", "\n", "$$\\pi_{\\text{ABC},\\varepsilon}(\\theta|y_\\text{obs})\\rightarrow\\pi(\\theta|y_\\text{obs}).$$\n", "\n", "(Note that the use of insufficient summary statistics adds another layer of approximation, which we abstract from here.)\n", "\n", "However, in practice $\\varepsilon\\rightarrow 0$ is not guaranteed, or rather small-enough levels are not known, raising the question of how to determine the sequence of thresholds $\\{\\varepsilon_t\\}$.\n", "Often, values are pre-defined (`ListEpsion`), which is however overall impractical, as it requires manual tuning of at least the initial threshold can yield excessively low or high acceptance rates.\n", "A common strategy is to set the threshold of generation $t$ as a quantile of the (weighted) distances $\\{d_i=d(y_i,y_\\text{obs})\\}_{i\\leq N}$ accepted in generation $t-1$. However, such an approach may fail to focus on small domains of attraction. Consider the following (deterministic) example, discussed in [Silk et al. 2012](https://doi.org/10.1515/sagmb-2012-0043), which possesses a wide local optimum and a small global optimum:" ] }, { "cell_type": "code", "execution_count": 3, "id": "526298bd-dde4-444b-8607-aaca08c907ee", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def model(p):\n", " theta = p[\"theta\"]\n", " return {\"y\": (theta - 10) ** 2 - 100 * np.exp(-100 * (theta - 3) ** 2)}\n", "\n", "\n", "p_true = {\"theta\": 3}\n", "y_obs = model(p_true)\n", "\n", "bounds = {\"theta\": (0, 20)}\n", "prior = pyabc.Distribution(\n", " **{\n", " key: pyabc.RV(\"uniform\", lb, ub - lb)\n", " for key, (lb, ub) in bounds.items()\n", " }\n", ")\n", "\n", "# plot observables over parameters\n", "_, ax = plt.subplots()\n", "xs = np.linspace(0, 20, 1000)\n", "ys = model({\"theta\": xs})[\"y\"]\n", "ax.plot(xs, ys, color=\"grey\")\n", "ax.set_xlabel(r\"$\\theta$\")\n", "ax.set_ylabel(\"y\");" ] }, { "cell_type": "markdown", "id": "01046f64-0360-4e82-9a0c-35dd974f5d5d", "metadata": {}, "source": [ "Some more utilities:" ] }, { "cell_type": "code", "execution_count": 4, "id": "173a5da0-7b4b-4afa-b8ad-cf2a4af37441", "metadata": {}, "outputs": [], "source": [ "pop_size = 200\n", "n_samples = pop_size * 20\n", "db_path = pyabc.create_sqlite_db_id()\n", "\n", "\n", "def plot_posterior(history, show_history=False, ax=None):\n", " \"\"\"Plot 1d posteriors.\"\"\"\n", " if ax is None:\n", " _, ax = plt.subplots(figsize=(10, 6))\n", " t0 = 0\n", " if not show_history:\n", " t0 = history.max_t\n", " for t in range(t0, history.max_t + 1):\n", " df, w = history.get_distribution(t=t)\n", " pyabc.visualization.plot_kde_1d(\n", " df,\n", " w,\n", " xmin=bounds[\"theta\"][0],\n", " xmax=bounds[\"theta\"][1],\n", " numx=1000,\n", " x=\"theta\",\n", " ax=ax,\n", " label=f\"t={t}\" if show_history else None,\n", " refval=p_true,\n", " refval_color=\"grey\",\n", " kde=pyabc.GridSearchCV(),\n", " )\n", "\n", "\n", "def plot_pars_over_data(history):\n", " \"\"\"Plot parameters over data background.\"\"\"\n", " _, ax = plt.subplots(figsize=(10, 6))\n", " ax.plot(xs, ys - y_obs[\"y\"], color=\"grey\")\n", " for t in range(history.max_t + 1):\n", " df, _ = history.get_distribution(t=t)\n", " eps = history.get_all_populations().set_index(\"t\").loc[t, \"epsilon\"]\n", " ax.plot(\n", " df[\"theta\"],\n", " eps * np.ones_like(df[\"theta\"]),\n", " \".\",\n", " markersize=1,\n", " color=pyabc.visualization.colors.RED900,\n", " )\n", " ax.set_xlabel(r\"$\\theta$\")\n", " ax.set_ylabel(r\"$d(y,y_ {obs})$\")" ] }, { "cell_type": "markdown", "id": "255034dd-4527-4a7e-ae92-b1966e1fa972", "metadata": {}, "source": [ "Let us first try a quantile-based threshold strategy:" ] }, { "cell_type": "code", "execution_count": 5, "id": "4183286b-a5c4-47f3-9a4c-880d30452ab5", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ABC.Sampler INFO: Parallelize sampling on 4 processes.\n", "ABC.History INFO: Start \n", "ABC INFO: Calibration sample t = -1.\n", "ABC INFO: t: 0, eps: 1.16338545e+02.\n", "ABC INFO: Accepted: 200 / 255 = 7.8431e-01, ESS: 2.0000e+02.\n", "ABC INFO: t: 1, eps: 9.08304741e+01.\n", "ABC INFO: Accepted: 200 / 266 = 7.5188e-01, ESS: 1.9438e+02.\n", "ABC INFO: t: 2, eps: 7.24305556e+01.\n", "ABC INFO: Accepted: 200 / 249 = 8.0321e-01, ESS: 1.8418e+02.\n", "ABC INFO: t: 3, eps: 6.48220804e+01.\n", "ABC INFO: Accepted: 200 / 303 = 6.6007e-01, ESS: 1.7112e+02.\n", "ABC INFO: t: 4, eps: 5.96357401e+01.\n", "ABC INFO: Accepted: 200 / 272 = 7.3529e-01, ESS: 1.9748e+02.\n", "ABC INFO: t: 5, eps: 5.69131917e+01.\n", "ABC INFO: Accepted: 200 / 271 = 7.3801e-01, ESS: 1.9841e+02.\n", "ABC INFO: t: 6, eps: 5.51356743e+01.\n", "ABC INFO: Accepted: 200 / 261 = 7.6628e-01, ESS: 1.9802e+02.\n", "ABC INFO: t: 7, eps: 5.36904752e+01.\n", "ABC INFO: Accepted: 200 / 262 = 7.6336e-01, ESS: 1.9887e+02.\n", "ABC INFO: t: 8, eps: 5.27431393e+01.\n", "ABC INFO: Accepted: 200 / 256 = 7.8125e-01, ESS: 1.9775e+02.\n", "ABC INFO: t: 9, eps: 5.20129556e+01.\n", "ABC INFO: Accepted: 200 / 251 = 7.9681e-01, ESS: 1.9930e+02.\n", "ABC INFO: t: 10, eps: 5.16910309e+01.\n", "ABC INFO: Accepted: 200 / 275 = 7.2727e-01, ESS: 1.9856e+02.\n", "ABC INFO: t: 11, eps: 5.14267838e+01.\n", "ABC INFO: Accepted: 200 / 261 = 7.6628e-01, ESS: 1.9883e+02.\n", "ABC INFO: t: 12, eps: 5.12757551e+01.\n", "ABC INFO: Accepted: 200 / 270 = 7.4074e-01, ESS: 1.9832e+02.\n", "ABC INFO: t: 13, eps: 5.11674471e+01.\n", "ABC INFO: Accepted: 200 / 270 = 7.4074e-01, ESS: 1.9940e+02.\n", "ABC INFO: t: 14, eps: 5.11068315e+01.\n", "ABC INFO: Accepted: 200 / 252 = 7.9365e-01, ESS: 1.9894e+02.\n", "ABC INFO: Stop: Total simulations budget.\n", "ABC.History INFO: Done \n" ] } ], "source": [ "abc = pyabc.ABCSMC(\n", " model,\n", " prior,\n", " pyabc.PNormDistance(p=2),\n", " population_size=pop_size,\n", " eps=pyabc.QuantileEpsilon(alpha=0.8),\n", ")\n", "\n", "abc.new(db_path, y_obs)\n", "\n", "h = abc.run(max_total_nr_simulations=n_samples)" ] }, { "cell_type": "markdown", "id": "4aacdb6e-e02e-4173-a4b0-e96a93eb5878", "metadata": {}, "source": [ "The posterior should converge to a point estimate at $\\theta=3$, however when repeating the above analysis, in many cases does not do so, but converges to a bimodal distribution, or one with a single mode at $\\theta=10$.\n", "This is because the majority of samples is from the local optimum, such that a focus on a small subset is required to push the sample towards the global mode." ] }, { "cell_type": "code", "execution_count": 6, "id": "5975c319-9086-48ee-8533-696d1ae5d35d", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ABC.Transition INFO: Best params: {'scaling': 0.2875}\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_posterior(h)\n", "plot_pars_over_data(h);" ] }, { "cell_type": "markdown", "id": "746a1ddd-b6bc-423b-9b0a-4f3aa7b5a19f", "metadata": {}, "source": [ "As observed in Silk et al., for large quantile values, the chance of completely missing the global optimum increases, which can be explained by more populations being generated until a similar point is reached, each providing an opportunity to miss the global optimum (and from there on ever after with high probability).\n", "This can be circumvented by a lower quantile, which increases the focus on the global optimum. Upon repetition, this analysis is less likely to solely focus on the local optimum, and more likely to correctly only sample from the global one." ] }, { "cell_type": "code", "execution_count": 7, "id": "e3931d11-eaeb-4336-8c60-05d92cd3982b", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ABC.Sampler INFO: Parallelize sampling on 4 processes.\n", "ABC.History INFO: Start \n", "ABC INFO: Calibration sample t = -1.\n", "ABC INFO: t: 0, eps: 6.98156111e+01.\n", "ABC INFO: Accepted: 200 / 444 = 4.5045e-01, ESS: 2.0000e+02.\n", "ABC INFO: t: 1, eps: 5.44899082e+01.\n", "ABC INFO: Accepted: 200 / 522 = 3.8314e-01, ESS: 1.9843e+02.\n", "ABC INFO: t: 2, eps: 5.16041676e+01.\n", "ABC INFO: Accepted: 200 / 488 = 4.0984e-01, ESS: 1.9887e+02.\n", "ABC INFO: t: 3, eps: 5.11285054e+01.\n", "ABC INFO: Accepted: 200 / 501 = 3.9920e-01, ESS: 1.9861e+02.\n", "ABC INFO: t: 4, eps: 5.10206082e+01.\n", "ABC INFO: Accepted: 200 / 526 = 3.8023e-01, ESS: 1.9906e+02.\n", "ABC INFO: t: 5, eps: 5.10030070e+01.\n", "ABC INFO: Accepted: 200 / 508 = 3.9370e-01, ESS: 1.9819e+02.\n", "ABC INFO: t: 6, eps: 5.10006094e+01.\n", "ABC INFO: Accepted: 200 / 520 = 3.8462e-01, ESS: 1.9871e+02.\n", "ABC INFO: t: 7, eps: 5.10000988e+01.\n", "ABC INFO: Accepted: 200 / 513 = 3.8986e-01, ESS: 1.9733e+02.\n", "ABC INFO: Stop: Total simulations budget.\n", "ABC.History INFO: Done \n", "ABC.Transition INFO: Best params: {'scaling': 0.05}\n" ] }, { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# smaller alpha\n", "\n", "abc = pyabc.ABCSMC(\n", " model,\n", " prior,\n", " pyabc.PNormDistance(p=2),\n", " population_size=pop_size,\n", " eps=pyabc.QuantileEpsilon(alpha=0.4),\n", ")\n", "\n", "abc.new(db_path, y_obs)\n", "\n", "h = abc.run(max_total_nr_simulations=n_samples)\n", "\n", "plot_posterior(h)\n", "plot_pars_over_data(h);" ] }, { "cell_type": "code", "execution_count": 8, "id": "461acd3e-d43a-415d-9522-0edf75623747", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ABC.Sampler INFO: Parallelize sampling on 4 processes.\n", "ABC.History INFO: Start \n", "ABC INFO: Calibration sample t = -1.\n", "ABC INFO: t: 0, eps: 5.53074395e+01.\n", "ABC INFO: Accepted: 200 / 1065 = 1.8779e-01, ESS: 2.0000e+02.\n", "ABC INFO: t: 1, eps: 5.11276404e+01.\n", "ABC INFO: Accepted: 200 / 1164 = 1.7182e-01, ESS: 1.0078e+02.\n", "ABC INFO: t: 2, eps: 5.10006655e+01.\n", "ABC INFO: Accepted: 200 / 6825 = 2.9304e-02, ESS: 1.1171e+02.\n", "ABC INFO: Stop: Total simulations budget.\n", "ABC.History INFO: Done \n", "ABC.Transition INFO: Best params: {'scaling': 0.05}\n" ] }, { "data": { "image/png": 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\n", 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IY3XprPPZ2dlu165dXscIS19//TVLly7l2Wef5bnnnvM6joiI1GHnzp3jvffeIz09nRkzZuh8Z1Wr8oA8z49Bk9rRu3dvevbsyZYtWzh48KDXcUREpI4qLCzk008/JSEhgRdffFHlLEAqaPWEmTF27Fhat27NggULOH/+vNeRRESkjikpKWHevHncuHGDadOmkZyc7HWkiKWCVo/ExMQwbdo04uPj+fTTT7l9+7bXkUREpA5Zu3YteXl5jBkzhoyMjIc/QaqkglbPNGrUiGnTpnH9+nXmzp2rSQMiIhIU3377Ldu2bSM7O5vevXt7HSfiqaDVQ23atGHs2LHk5eWxZs0ar+OIiEiEO3v2LIsXL6Zt27aMGnX/ZbclEDFeBxBv9OrVi4KCArZv3056ejo9evTwOpKIiESgskkBDRo00KSAINIIWj02cuRI2rVrx5IlS3SlARERqbGyKwXcvHmTl156iYYNG3odqc5QQavHoqOjefHFF2nYsCGffvopN2/e9DqSiIhEkJUrV3L8+PHyswRI8Kig1XOJiYm8/PLL3L59mzlz5uDz6YINIiLycLt27eKrr75iwIAB9OrVy+s4dY4KmpCens7EiRM5deoUy5Ytoy5dXUJERILv+PHjLF++nE6dOjF8+HCv49RJmiQgAHTr1o1z586xZcsW0tLSeOqpp7yOJCIiYejSpUvMmTOHZs2aMWXKFKKiNNYTCipoUm7o0KFcunSJ1atXk5qaSufOnb2OJCIiYeTOnTvMnj0bM2P69OnEx8d7HanOUu2VcmbGxIkTadmyJfPmzePs2bNeRxIRkTBRNmPzypUrvPTSSzRp0sTrSHWaCpp8T2xsLNOnTychIYHZs2drZqeIiACwatUqjh07xtixY3nssce8jlPnqaDJDyQnJzN9+nRu377Np59+SlFRkdeRRETEQ7t27WLnzp0MGDBAl3GqJSpoUqmWLVsyefJkTp8+zaJFizSzU0Sknjp+/DgrVqzQjM1apoImVerSpQvDhg0jJyeHTZs2eR1HRERq2cWLF5kzZw5NmzbVjM1aplmc8kDPPPMMly5dYtOmTTRt2pQnnnjC60giIlILbt26xSeffEJ0dDSvvPKKZmzWMlVheSAzY9y4cbRt25ZFixaRn5/vdSQREQmxoqKi8oli06dPp3Hjxl5HqndU0OShoqOjeemll2jUqBGffvopV69e9TqSiIiESElJCfPnz+f06dNMmTJF19j0iAqaVEtiYiKvvPIKxcXFzJ49m7t373odSUREQmDNmjUcOnSIUaNG0aVLF6/j1FsqaFJtzZo1Y9q0aVy4cIF58+ZRUlLidSQREQminTt3sn37dvr370///v29jlOvqaBJjbRv354xY8aQm5vL6tWrvY4jIiJBcvjwYVauXEnnzp0ZMWKE13HqPc3ilBrLzs7m4sWL7Nixg6ZNm9K3b1+vI4mIyCM4c+YM8+bNKz8Hpk6n4T0VNAnIiBEjuHz5MitWrCA1NZUOHTp4HUlERAJw9epV/t//+38kJiYyffp04uLivI4kaBenBCgqKoopU6aQlpbG559/zoULF7yOJCIiNVRYWMjHH39McXExP/rRj2jYsKHXkcRPBU0CFh8fz/Tp04mJiWHOnDmaNCAiEkHu3bvH7NmzuXr1KtOnTyctLc3rSFKBCpo8ksaNGzNu3DguXrzIgQMHvI4jIiLV4PP5mDt3bvm5zh577DGvI8l9VNDkkXXu3JmGDRty8OBBr6OIiMhDOOdYunQpubm5jBkzhqysLK8jSSVU0OSRmRmdOnUiLy8P55zXcURE5AHWr1/P3r17GTx4MNnZ2V7HkSrUWkEzs/fN7LyZ7a9wX6qZrTGzXP/nJv77zcz+1cyOmtk3Zta7tnJKYFq2bMmdO3e4fv2611FERKQKO3bs4IsvvqB3794MHjzY6zjyALU5gvYhMOq++34OrHPOdQLW+b8GGA108n+8Dfy2ljJKgFq0aAHAuXPnPE4iIiKVycnJKT8R7dixYzEzryPJA9RaQXPObQYu33f3BGCW//YsYGKF+//gSm0HGptZy1oJKgFp1qwZAJcuXfI4iYiI3O/48eMsWLCAtm3bMmXKFJ2INgJ4/Qq1cM4V+G+fBVr4b7cGTlVYLt9/n4SpBg0aEB0dzc2bN72OIiIiFeTn5/Ppp5+SmprKyy+/TGxsrNeRpBq8LmjlXOnR5TU+wtzM3jazXWa2SydL9Y6ZkZyczI0bN7yOIiIifufPn+eTTz4hKSmJ1157jQYNGngdSarJ64J2rmzXpf/zef/9p4E2FZbL8N/3A865d5xz2c65bJ1kz1sqaCIi4ePy5ct89NFHxMbG8tprr5GcnOx1JKkBrwvaYmCG//YMYFGF+3/sn805ALhWYVeohKnk5GTt4hQRCQPXr1/no48+wufz8dprr9GkSROvI0kN1drF0s1sNjAEaGZm+cA/AL8C5pjZm8B3wDT/4suBMcBRoBB4vbZySuCSkpJU0EREPHbr1i0++ugjCgsLmTFjhi7hFKFqraA556ZX8dCwSpZ1wJ+FNpEEW3x8PHfv3sU5p+nbIiIeuHPnDp988glXr17l1VdfpVWrVl5HkgB5vYtT6pCEhASccxQVFXkdRUSk3ikqKmL27NmcO3eOadOm6fqaEa7WRtCk7ouPjwdK/wcXFxdX5XIFBQXMmTOHhg0bMnnyZB0bISLyiIqLi/nss884efIkU6ZMoVOnTl5HkkekETQJmoSEBADu3r37wOU2b97M1atXuXDhAu+99x7nz59/4PIiIlI1n8/HnDlzOHbsGOPHj6d79+5eR5IgUEGToKk4glaVkpIScnNz6devH2+99RZRUVHMmjVLl4gSEQmAz+dj7ty55ObmMnbsWHr16uV1JAkSFTQJmuqMoF25cgWfz0fLli1p1qwZM2bMIDo6mj/84Q8qaSIiNVBSUsL8+fM5dOgQo0ePJjs72+tIEkQqaBI01RlBK7vaQ9m1O5s2bcrMmTNV0kREaqCkpIQFCxZw4MABRowYQb9+/byOJEGmgiZBU50RtMuXLwN/LGgAqamp5SVNuztFRB6spKSExYsXs3//foYNG8ZTTz3ldSQJARU0CZqymZv37t2rcplbt24RHR1dPtpWpqykxcbGMmvWLM6ePRvSrCIikcg5x9KlS9m3bx9Dhw5l4MCBXkeSEFFBk6CJiSk9a0txcXGVyxQWFpKYmFjpiWxTU1OZMWMGsbGx/OEPf1BJExGpwDnHsmXL2LNnD4MGDWLQoEFeR5IQUkGToImOjgZ44IlqCwsLSUpKqvJxlTQRkR9yzrFkyRK+/vprBg4cyJAhQ7yOJCGmgiZBY2bExsY+sKDdunWLxMTEB36firs7VdJEpL4rKSlh0aJF5SNnzz33nC6nVw+ooElQxcbGVmsX58M0adLkeyWtoKAgmDFFRCJC2WzNsmPOhg4dqnJWT6igSVDFxMQ8dBdndQoa/LGkxcXFqaSJSL3j8/mYN29e+WxNHXNWv6igSVA9aATNOcfdu3d/MIPzQZo0acKMGTOIj49XSROReqPsCgFl5znTbM36RwVNgupBx6CVFbcHXUi9MveXtDNnzjxyThGRcFV24fOyKwToPGf1kwqaBNWDdnGWnR+tpgUN/ri7s6yknTp16pFyioiEo6KiIj799NPya2vqCgH1lwqaBNWDdnE+SkEDaNy4Ma+//jpJSUl89NFHHDt2LOCcIiLh5s6dO3z00Ufk5eUxfvx4XVuznlNBk6B60C7ORy1oACkpKbz++uukpqYye/ZsDh48GPD3EhEJF7du3WLWrFmcPn2aqVOn0qtXL68jicdU0CSoQl3QABo2bMiMGTNo2bIln3/+OXv37n2k7yci4qVr167xwQcfcPHiRaZPn07Xrl29jiRhQAVNgiomJiZkuzgratCgAa+99hqZmZksWrSI7du3P/L3FBGpbRcvXuT999/n5s2bvPbaa3Ts2NHrSBImVNAkqEI1SaAycXFxTJ8+naysLFatWsWmTZtwzgXle4uIhFpBQQEffPABPp+PmTNn0rZtW68jSRhRQZOgiomJwefzVfpYWXGLjY0N6s+bOnUqPXv2ZOPGjaxatUolTUTC3smTJ5k1axaxsbG8/vrrpKenex1JwkyM1wGkbomOjq6VXZwVRUVFMX78eOLj49mxYwe3bt1i4sSJ5RdvFxEJJ4cPH2bu3LmkpKTw2muvkZKS4nUkCUM1LmhmlgTccc5VPkwi9Vp0dDQ+nw/n3A+uFxeqggalF2ofOXIkDRs2ZN26ddy6dYuXXnqpRlctEBEJtV27drF8+XJatmzJK6+8QlJSkteRJEw9dBenmUWZ2StmtszMzgOHgAIzO2BmvzEzHdEo5WJiSjt/ZbsZQ7GLsyIzY+DAgUycOJHvvvuODz74gBs3boTkZ4mI1IRzjg0bNrBs2TI6duzIjBkzVM7kgapzDNoGoAPwt0C6c66Nc645MBDYDvzazF4NYUaJIGW7FSvbzenz+TAzoqJCe+hjjx49mD59OpcvX+a9997j4sWLIf15IiIP4vP5WLx4MZs3b6Znz568/PLLIdmTIHVLdbaUzzvn/j/n3DfOuZKyO51zl51z85xzU4DPQhdRIklZQatsokBxcXH5CFuodezYkZkzZ1JcXMz777+vS0OJiCfu3bvHZ599xt69exk0aBDjx48P+X9SpW546G+Jc+4H50wws+f8n1uaWXRly0j9FC4FDaBVq1a88cYbJCQk8Ic//IHDhw/X2s8WESm7OsDRo0cZN24cQ4cO/cGxuSJVCbTGjzKzDOB3wD8FMY9EuIcVtNqeWZmamsqbb75J8+bN+eyzz9ixY0et/nwRqZ8uXbrEe++9x/nz53nppZfo06eP15EkwgRa0BoDfwP8NXA3aGkk4pWNkFVW0Hw+X62OoJVJSkpixowZPP7446xcuZLly5dTUlLy8CeKiATg+PHj/Pu//zt3797lxz/+MZ07d/Y6kkSgQAvaL4GNzrnDwCOfbsPM/tLMcsxsv5nNNrMEM8s0sx1mdtTMPjMzHVEZAR40SaC2d3FWFBcXx7Rp03jqqaf46quvmD17Nnfv6v8WIhJce/bs4eOPPyY5OZm33nqLNm3aeB1JIlSgBe03wHAzmwUsf5QAZtYa+I9AtnOuOxANvAz8Gvgn51xH4Arw5qP8HKkdD9rF6dUIWpmoqChGjBjBuHHjOHbsGO+//z7Xrl3zLI+I1B3OOdasWcPixYvJzMzkjTfeoEmTJl7HkggWaEE76Jz7qXNuBqVl6lHFAA3MLAZIBAqA54C5/sdnAROD8HMkxMLtGLTK9OnThx/96Edcu3aNd999l9OnT3sdSUQi2L1795gzZw5ffvkl2dnZvPLKKyQkJHgdSyJcjQuamb0LjDCz/2hmQ4CrjxLAOXca+B/ASUqL2TXga+Cqc65sP1k+0PpRfo7UjnCaxfkgHTp04M033yQ2NpYPP/yQAwcOeB1JRCLQjRs3+PDDDzl8+DAjR45kzJgxOo2GBEWNf4uccz8Bnge+AnoATR8lgJk1ASYAmUArIAkYVYPnv21mu8xs14ULFx4ligRBpBQ0gLS0NN566y3S09P5/PPP2bhxoy60LiLVdubMGd59910uXbrEyy+/zIABA3QaDQmaQGv+3wH/GegF/J9HzPA8cNw5d8F/PrX5wDNAY/8uT4AMoNL9UM65d5xz2c657LS0tEeMIo/qQbM4w62gwR9nePbo0YNNmzYxZ84cTR4QkYf65ptv+OCDD4iKiuL111/n8ccf9zqS1DGBFrRE59yLwNvAzx4xw0lggJklWul/PYYBByi9xNRU/zIzgEWP+HOkFjzsUk/hcAza/WJiYpgwYQIjR47k8OHDvPfee1y+fNnrWCIShkpKSli1ahULFiwgIyODn/zkJ6Snp3sdS+qgQAtagpn1ds7dAx5pPNc5t4PSyQC7gW/9md6h9Dxr/9nMjlK6G/W9R/k5UjsiaRdnRWbGgAEDePXVV7l58ybvvvsux44d8zqWiISRwsJCPv74Y7Zv306/fv149dVXdcFzCZlAC9pfAc+Z2fsEYWTLOfcPzrkuzrnuzrnXnHN3nXN5zrl+zrmOzrkXnXPa7xQBImEW54O0b9+en/zkJ6SkpPDJJ5/w5Zdf6rg0EeHcuXO8++67nDx5kvHjxzN69Oiw/3smka3aBc3M1phZDwDn3G3n3P9wzr3hnFsRungSaSJ1BK2iJk2a8MYbb5CVlcWaNWtYsGABRUW63KxIfZWTk8N7772Hz+dj5syZ9OrVy+tIUg/UZGv5N8A/m9kJ4O+ccwWhiSSRLBwv9RSIuLg4pk6dyhdffMH69es5d+4c06ZNo2nTR5q0LCIRxOfzsWbNGnbs2EFGRgbTpk0jOTnZ61hST1R7BM05t9s5NxRYCqw0s38wswahiyaRqOz8P1UVtEjaJWBmPPvss7z66qvcuHGDd955h5ycHK9jiUgtuHbtGh9++CE7duygX79+zJw5U+VMalWNjkHzz7I8DPwW+HMg18xeC0UwiUxlBez+i5E75ygpKYnIEzh26NCBP/mTP6F58+bMnTuXFStWVFpARaRuOHbsGO+88w7nz59n6tSpOt5MPFHt/U1mtpXSk8nmANuBmcAh4C/M7Fnn3NshSSgRpaoRtLID7SP1j1xKSgozZ84s391x5swZpk6dSkpKitfRRCRISkpK2Lx5M5s2bSItLY1p06bRrFkzr2NJPVWTA4LeBg64H05p+3MzOxjETBLBygra/SNoZYUtEkfQykRHRzNq1Cjatm3LokWL+P3vf8/kyZPp2LGj19FE5BHdunWLBQsWcOzYMZ588knGjh1LXFyc17GkHqt2QXPOPejgm7FByCJ1QNllTu4vaGVfR3JBK9O1a1datGjBnDlz+OSTT3j66ad57rnnInZ0UKS+y8vLY8GCBdy+fZtx48bRu3dvXbJJPBeUKXXOubxgfB+JfGZGVFRUnS5oAE2bNuWtt95i1apVfPnll5w4cYLJkydrlqdIBPH5fGzYsIGtW7fSrFkzfvSjH+mqABI2Ai5oZtYSuKwTyMr96kNBA4iNjWXcuHF06NCBxYsX88477zBmzBh69OjhdTQReYgrV64wb948Tp8+Te/evRk5cqR2aUpYeZQRtI+ADmY2zzn3X4MVSCLfgwpaXdwNmJWVRatWrZg/fz4LFy7k2LFjjB07lvj4eK+jiUglvv32W5YuXUpUVBQvvvgiXbt29TqSyA8EXNCcc8/7T7uh32z5nqioqB/M4qwLkwQeJCUlhRkzZrBlyxY2bdpEfn4+kydPJiMjw+toIuJ39+5dVqxYwb59+2jTpg2TJ0+mcePGXscSqVRAl3oq40rpzJ3yPdHR0fViF+f9oqKiGDx4MDNnzqSkpIT333+fdevW6ZxpImHg+PHj/Pa3v+Wbb75h0KBBzJw5U+VMwpou9SRBV1+OQatK27Zt+elPf8qqVav44osvyM3NZdKkSbRo0cLraCL1TlFREevWrWPHjh2kpqbyxhtvaGRbIkJNTrOxGxhqZlMovdTTfOAfnXO3Q5ZOIlJ9L2gACQkJTJgwgS5durBkyRLeffddhgwZwtNPP11v/g1EvHb69GkWLFjApUuX6Nu3L88//7wmAkjEqNExaPdd6um/Az8xs791zn0UinASmerbJIEH6dy5MxkZGSxbtox169Zx5MgRJk6cSGpqqtfRROosn8/H5s2b2bJlC8nJybz22mu0b9/e61giNaJLPUnQVVbQ6vokgQdJSkrixRdf5Ntvv2X58uX87ne/Y+jQofTv379e/nuIhNKZM2dYvHgx586do0ePHowaNYqEhASvY4nUmC71JEGnXZw/ZGY8+eSTtGvXjqVLl7J69WpycnJ44YUXdGyaSBAUFRWxceNGtm3bRlJSEi+99BJdunTxOpZIwB5a0MzMqjFbU5d6knL1dRZndTRq1Ijp06ezf/9+Vq5cyTvvvMPAgQN59tlniYkJyoU9ROqd48ePs2TJEq5cuUKvXr0YMWKERs0k4lVni7DBzOYBi5xzJ8vuNLM4YCAwA9gA6HJPAlR+HjQVtD8yM5544gk6dOjAqlWr2Lx5MwcOHGD8+PG0adPG63giEePOnTusXr2aPXv20KRJE3784x+TmZnpdSyRoKhOQRsFvAHMNrP2wBWgAaXnUFsN/LNzbk/oIkqk0SSB6klMTGTSpEl0796dpUuX8v7775Odnc1zzz1HgwYNvI4nEracc+Tk5LBq1Spu3brF008/zZAhQ4iNjfU6mkjQVKegPQcsdM79m5nFAs2A2865qyFNJhFLkwRqplOnTvzsZz9j/fr1fPXVVxw4cIDhw4fTo0cPSidOi0iZixcvsmLFCvLy8khPT2f69Om0atXK61giQVedgjYJ+KWZtaB01uY+YK+Z7QUOOud0mnT5Hk0SqLn4+HhGjx5Nz549Wb58OYsWLWLPnj2MGTNGkwhEgHv37rF582a2bdtGbGwsY8aMoU+fPvqbInXWQwuac+4nAGb2d0BrSo81Gwq8A1wGdEpm+Z7o6GiKi4u/d58KWvW0bNmSN954gz179rB27Vp+//vf069fP4YOHaqLr0u95Jzj0KFDrFq1imvXrtGjRw+GDx9OUlKS19FEQqom08Zecs6VX4vTzP4N+KvgR5JIpxG0R2Nm9O7dmy5dupRfoiYnJ4dhw4Zpt6fUKxcuXGD16tUcPXqU5s2bM3PmTB577DGvY4nUipoUtOtm1sc59zWAc+5rM3s8RLkkgj1oFqcmCVRfYmIiL7zwAr1792bFihUsWrSInTt3MmLECNq1a+d1PJGQuXXrFhs3buTrr78mLi6OESNG0K9fP/39kHqlJgXtTWC+mX0FfA08ARSFJJVENE0SCK7WrVvz5ptvsn//ftauXcusWbPo0qULw4cP1yWjpE4pLi5m586dbN68mXv37pGdnc3gwYO1O1PqpZpcLP2ImfUGJlJazg4CfxeiXBLBtIsz+MrOndalSxe2bdvGF198wZEjR+jXrx+DBw/WSTklojnnOHjwIGvXruXKlSt06tSJ4cOHk5aW5nU0Ec/U6NTlzrl7wBz/h0ilVNBCJzY2lkGDBtGrVy82bNjA9u3b2bt3LwMHDqRfv346D5REnOPHj7N+/Xry8/Np3rw5r776Kh06dPA6lojndG0ZCboHXepJx5AER3JyMuPHj6dfv36sX7+etWvXsn37dgYNGkTv3r317yxh7/Tp06xfv568vDwaNWrECy+8QM+ePfWfOBE/FTQJOjPTCFotSU9P55VXXuHkyZOsW7eO5cuX8+WXXzJkyBCeeOIJ/XtL2Dl//jwbNmzg0KFDJCYmMnLkSLKzs3UtWpH76B0hQVfZLE5NEgittm3bMnPmTI4dO8a6detYuHAhW7duZfDgwWRlZenfXTx38eJFtmzZwjfffEN8fDxDhgxhwIABOr+fSBXCoqCZWWPg34HugKP02p+Hgc+AdsAJYJpz7oo3CaUmHrSLU0UhdMyMjh070qFDBw4ePMiGDRuYO3cuTZs25dlnn6V79+7a9Sm17ty5c2zZsoWcnBxiYmJ4+umneeaZZ0hMTPQ6mkhYC4uCBvwLsNI5N9XM4oBESmeIrnPO/crMfg78HPgbL0NK9WiSgLfMjK5du9KlSxcOHjzIli1bWLhwIRs3buSZZ56hZ8+e2p0kIXf69Gm2bNnC4cOHiYuLY+DAgQwYMECnzBCpJs//SptZCjAImAnlM0XvmdkEYIh/sVnARlTQIkJVBc3MdBb8WhQVFUW3bt3o2rUrubm5bN68mWXLlrF582aefvppevXqpd1LElTOOY4fP86XX37JsWPHSEhIYMiQIfTr148GDRp4HU8konhe0IBM4ALwgZn1oPQkuH8BtHDOFfiXOQtUesVoM3sbeBtKj8MR71V1olqNnnnDzHj88cfp1KkTx48fZ/PmzaxatYqNGzfSp08f+vXrR0pKitcxJYL5fD7279/Ptm3bOHfuHElJSQwbNoy+ffvqPwEiAQqHghYD9Ab+3Dm3w8z+hdLdmeWcc87MXGVPds69Q+mF28nOzq50GaldZQXNOVc+YlZSUqKC5jEzo3379rRv3578/Hy2b9/Otm3b2LZtG926dWPAgAG0bt3a65gSQW7fvs2uXbvYuXMnN2/eJC0tjfHjx/PEE09oN7rIIwqHd1A+kO+c2+H/ei6lBe2cmbV0zhWYWUvgvGcJpUbKitj9BU0HqIePjIwMpk6dyrVr19ixYwe7d+9m//79tGnThr59+5KVlaUNrFSpoKCAXbt28e2331JUVET79u2ZMGECHTp00GEMIkHi+V9g59xZMztlZp2dc4eBYcAB/8cM4Ff+z4s8jCk1UFbEKo6aaQQtPKWkpDBixAgGDx7Mnj172LlzJ/PnzycxMZFevXrRp08fmjRp4nVMCQNFRUXk5OSwa9cuTp8+TUxMDN27d2fAgAG0aFHpESgi8gg8L2h+fw584p/BmQe8DkQBc8zsTeA7YJqH+aQGyoqYz+crH4VRQQtv8fHxDBgwgP79+5OXl8euXbv48ssv2bp1Kx06dCA7O5tOnTppFLQeunDhArt372bfvn3cvn2bpk2bMnLkSHr06KED/0VCKCwKmnNuL5BdyUPDajmKBEHFUbMyKmiRwczo0KEDHTp04Pr16+zevZvdu3fz2WefkZSURPfu3enZsyfp6eleR5UQun37Nvv372fv3r2cOXOGqKgounTpQnZ2Nu3atdNuTJFaEBYFTeoWFbS6oVGjRgwZMoRBgwaRm5vLvn372LVrFzt27KBFixY8+eSTPPnkkzRs2NDrqBIEPp+PY8eOsW/fPg4fPozP56NFixaMGDGCJ554Qq+zSC1TQZOgq6qgafdYZIqKiqJz58507ty5fGRl3759rFmzhrVr15KZmVl+YlydhDSylJSUcPz4cXJycjh06BC3b98mMTGR7OxsjZSKeEwFTYIuOjoaSkooWLKEs5cukTZ4ML6iIhIuXPjezE6JPA0aNKBv37707duXixcvsm/fPg4cOMDSpUtZtmwZmZmZZGVlkeEcDRo0oFG3bpSUlJD3b/+Gc46mgwZxecsW4lq2pOjsWTL/9E9xznHkl7+kxeTJxMTE0DAri7NLluCco0FmJvlz5lB0+TLt/uRPuJ2Xx/U9e+j093/PhWXLKMzPp8nAgVzdupWmzz6LRUVhZjTMyuLc0qUktm9Pcteu5bdTunenpKSE7373Ox776U8xMwoWLaLw1ClSBw3iypYtNB08GIBbx46Vr3dS+/bcOHqUG3v30uEXv+Dof//vpPTuDZTuFm7YsSONunXj5sGDJHXpwplFi7j69dfENW9O2pAhGHBh0ybunD1Lqxdf5NrWrbR5+22++/3vcUDjp57ixD/9Ex3+6q9I6d6dk7//PW3efpsLy5cT26YNJ995h+jGjYmKiqLl1KmcX7CAFpMnc2nTJm4cPEiLkSNJ6tCBwrw8nCs929DVXbtonJ1Nw44dMTOcc9w8dow7p05hY8Zw6NAhDh48SGFhIXFxcXTu3Jlu3brRsWNH/WdKJAxY2Zu5LsjOzna7du3yOka9t2/fPjb/z/9Jp40bwTliGzfm6pgxxC1fzuBPP6VRt25eR5Qgcs5x7tw5cnJyOHDgAHdyc3l81Sqio6Np9Itf0Pj0ac787/8NQFRCAiV37pQ/9/Gf/5w7585x8oMPiGrQgNiUFB6bOZMj//iP4BxR8fHly1tcHO7ePQCaDh7MpS1boKQEi4/H3b1LTMOGWHw8UbGxpd/jN78htnFjMn/yE4785jfENW5M9iefcHHjRo786lc8/vOf06BNG/b9+Z9DSUl5tpiGDSE6muLr18tzxiQlUXzzJgANs7K4efAgmIFzEBVFbJMmdP3lLzny61/T5pVXOPKrX5U/N7phQwzKnx8VF0fJvXul67Bpk3+haPD5iIqPJ+OVVzj5wQekjx/P2WXLICoKiorKv5/FxuKKiso/V/w5vsJCKCn5YzYgJiUFi4mh6O5dnD/DyexsLvXtS+fOnenatSsdO3YkNjY2KL8PIlIjVY5YaARNgi4qKorLmZk89vzzxFy7RtrgwSz/5huuJyWR3LWr1/EkyMyM9PR00tPTee655zh79iw5PXty8rvv+Do3F0pKyHzmGdKaNqX5qFE0OHaMhIwMis6e5bGf/rR8xKfiCFp869aPPIKWkJFRPoJW8XZSly4A5SNoT/h8QRtBS+rQgaQuXYht2fKRRtASWrSgzdtv03zEiIBG0JxzFGzdys3mzTnr81Fw9iyupIRGt2/TKj6ep3/2M7p06aJSJhLGNIImQZeTk8PcuXP50z/9U5o3bw7Axx9/zJ07d3jrrbc8Tie16dq1a+Tm5pKbm0teXh7FxcVER0fTtm1b2rVrR2ZmJq1bt9YEkiC4du0aeXl5HD9+nOPHj3PTP1rWvHlzHn/8cR5//HH9W4uEH42gSe3RJAEpk5KSQnZ2NtnZ2RQVFXHixAny8vI4ceIEGzZsYMOGDcTFxfHYY4/Rtm1b2rRpQ6tWrTSy8xDOOS5dusSpU6c4deoU3333HZcvXwYgKSmJzMxMMjMzad++PY0bN/Y2rIgERAVNgq6ygqaLpUtsbCydOnWiU6dOABQWFnLixInyEZ/c3Fzgj7tMMzIyyMjIoHXr1jRp0qRe//7cunWLs2fPcvr0afLz88nPz+f27dsAJCQk0LZtW/r27UtmZibNmzfXRByROkAFTYKu4qWeypSUlOjajvI9iYmJdO3ala7+4xILCwvJz8/n1KlT5Ofns3fvXr766iugtNw1b96c9PR0WrRoQXp6Os2bNyc+Pt7LVQg6n8/HlStXOH/+PGfPni3/uHHjRvkyaWlpdOnShTZt2pCRkUGzZs1UyETqIG0xJegqXuqpjE5UKw+TmJhYfqwUlP7OnD9/noKCAs6ePVs+U/Trr78uf05SUhJNmzaladOmpKamln9u1KgRCQkJYVlcioqKuH79OtevX+fy5ctcvHix/POVK1fKJ02YGWlpaWRmZpZPwkhPT9fllUTqCRU0CTodgybBEBUVVV5KyjjnuH79OmfPnuXChQtcunSJy5cvc+TIEW7duvW958fGxtKoUaPyj4YNG5KYmEiDBg1o0KBB+e2EhARiY2OJjY0lyj8LtLpKSkooLi6mqKiIe/fucfv2bQoLC8s/l33cuHGDa9eucf36dQoLC7/3PWJiYkhNTSU9PZ2uXbvSrFkz0tLSaN68uUadReoxvfsl6KKiouDqVQ4PGsTh0jtoVVICycncmTiRhIQEryNKhDIzUlJSSElJoXPnzt977M6dO1y+fJkrV66Uj1DduHGD69evc+LECW7cuPG9/zQA4POR/vXXpB49SnxhIUVRURAXR9ydOxTzwz+Q14CERo2Iv34dB/iAkqgo4kpKuJOUxIFJk+C+3+8GDRqQnJxMo0aNaNWqFSkpKTRq1IiUlBSaNGlCSkpKWI70iYi3dJoNCbr8/Hz2PP00sRV+t8puJWdlMXD1am+CSb3mnCsf5Sob4To7axY3Pvjgh8tW4/tVVqliMjN5/OOPSUxMJDExkYSEBO3aF5EH0Wk2pPZERUWxe8oU+s+dW3YHxf4RtOzFi70NJ/WWmREfH098fHz5qSfa/cM/cKRJE/IXLMB35gykpBCdmIivoKB0JOzate9/k6wsYs0oOnq09Ez9DRtCbCxcvEhc+/Y8vWKFRohFJChU0CTooqOjoXFjHlu9mqysLAD++Z//mXbt2mnjJWElOjqarL/8S7L+8i+9jiIi8j0ae5eg0yxOERGRR6MtpgSdTlQrIiLyaLTFlKCr6jQbKmgiIiLVoy2mBJ3OgyYiIvJoVNAk6Kq61JNG0ERERKpHW0wJOu3iFBEReTTaYkrQ3T+L0zmngiYiIlID2mJK0N0/glZ2tQoVNBERkerRFlOC7v6CVvZZkwRERESqRwVNgu7+gla2q1MjaCIiItWjLaYEnVnptV/vH0FTQRMREakebTEl6MyMqKgoFTQREZEAaYspIVFZQdMxaCIiItWjgiYhoRE0ERGRwGmLKSFRsaBpkoCIiEjNhM0W08yizWyPmS31f51pZjvM7KiZfWZmcV5nlOrTCJqIiEjgwmmL+RfAwQpf/xr4J+dcR+AK8KYnqSQgKmgiIiKBC4stppllAGOBf/d/bcBzwFz/IrOAiZ6Ek4BokoCIiEjgwqKgAf8M/DVQdnXtpsBV51yx/+t8oHVlTzSzt81sl5ntunDhQsiDSvXoGDQREZHAeb7FNLNxwHnn3NeBPN85945zLts5l52WlhbkdBIo7eIUEREJXIzXAYBngPFmNgZIABoB/wI0NrMY/yhaBnDaw4xSQypoIiIigfN8i+mc+1vnXIZzrh3wMrDeOfcjYAMw1b/YDGCRRxElACpoIiIigQvnLebfAP/ZzI5Sekzaex7nkRrQJAEREZHAhcMuznLOuY3ARv/tPKCfl3kkcJokICIiEjhtMSUktItTREQkcNpiSkiooImIiAROW0wJCRU0ERGRwGmLKSGhSQIiIiKBU0GTkNAkARERkcBpiykhoV2cIiIigdMWU0JCBU1ERCRw2mJKSKigiYiIBE5bTAkJTRIQEREJnAqahIQmCYiIiAROW0wJCe3iFBERCZy2mBISKmgiIiKB0xZTQuL+gmZmmJnHqURERCKDCpqExP0FTaNnIiIi1aetpoTE/ZMEVNBERESqT1tNCYn7R9B0ig0REZHqU0GTkNAuThERkcBpqykhUVbQnHMqaCIiIjWkraaERFkhU0ETERGpOW01JSTKCllJSYkKmoiISA1pqykhcX9B0yQBERGR6lNBk5CoWNB0mg0REZGa0VZTQkK7OEVERAKnraaEhAqaiIhI4LTVlJBQQRMREQmctpoSEpokICIiEjgVNAmJskKmSQIiIiI1p62mhIR2cYqIiAROW00JCRU0ERGRwGmrKSGhgiYiIhI4z7eaZtbGzDaY2QEzyzGzv/Dfn2pma8ws1/+5iddZpfo0SUBERCRwnhc0oBj4L865rsAA4M/MrCvwc2Cdc64TsM7/tUQIXUlAREQkcJ5vNZ1zBc653f7bN4CDQGtgAjDLv9gsYKInASUg2sUpIiISuLDaappZO6AXsANo4Zwr8D90FmjhVS6pORU0ERGRwIXNVtPMGgLzgP/knLte8THnnANcFc9728x2mdmuCxcu1EJSqQ4VNBERkcCFxVbTzGIpLWefOOfm++8+Z2Yt/Y+3BM5X9lzn3DvOuWznXHZaWlrtBJaHUkETEREJnOdbTTMz4D3goHPuf1V4aDEww397BrCotrNJ4DRJQEREJHAxXgcAngFeA741s73++/4O+BUwx8zeBL4DpnkTTwKh02yIiIgEzvOC5pz7ArAqHh5Wm1kkeMoKms/n0y5OERGRGtJWU0JCx6CJiIgETltNCQkVNBERkcBpqykhUVbIiouLv/e1iIiIPJy2mhISZYWsqKgIgJgYzw93FBERiRgqaBIS9xc0zeIUERGpPhU0CYn7C5p2cYqIiFSftpoSEhpBExERCZwKmoSECpqIiEjgVNAkJMoKmQqaiIhIzamgSUiUjaDdu3cPUEETERGpCRU0CQkzIzo6WgVNREQkACpoEjIqaCIiIoFRQZOQUUETEREJjAqahEzFgqbzoImIiFSftpoSMjExMRpBExERCYAKmoSMdnGKiIgERgVNQiY6Opri4uLy2yIiIlI9KmgSMhVLmQqaiIhI9amgScjExMSU31ZBExERqT4VNAkZjaCJiIgERgVNQkYFTUREJDAqaBIyKmgiIiKBUUGTkKl4DJpOVCsiIlJ92mpKyGgETUREJDAqaBIyZaXMzDSCJiIiUgPaakrIlBW0uLg4j5OIiIhEFhU0CZmyghYfH+9xEhERkciigiYho4ImIiISGBU0CZmyYlZxNqeIiIg8nAqahExSUhIAPp/P4yQiIiKRRQVNQqasoBUXF3ucREREJLKEfUEzs1FmdtjMjprZz73OI9WngiYiIhKYsC5oZhYN/F9gNNAVmG5mXb1NJdWlgiYiIhKYsC5oQD/gqHMuzzl3D/gUmOBxJqmmxMREoPREtSIiIlJ94T69rjVwqsLX+UD/iguY2dvA2wBt27atvWTyUAkJCQwcOJBu3bp5HUVERCSihPsI2kM5595xzmU757LT0tK8jiMVmBnDhg0jPT3d6ygiIiIRJdwL2mmgTYWvM/z3iYiIiNRZ4V7QvgI6mVmmmcUBLwOLPc4kIiIiElJhfQyac67YzP4DsAqIBt53zuV4HEtEREQkpMK6oAE455YDy73OISIiIlJbwn0Xp4iIiEi9o4ImIiIiEmZU0ERERETCjAqaiIiISJhRQRMREREJMypoIiIiImFGBU1EREQkzKigiYiIiIQZFTQRERGRMGPOOa8zBI2ZXQC+q4Uf1Qy4WAs/Jxxp3euv+rz+9XndoX6vv9a9/qqN9b/onBtV2QN1qqDVFjPb5ZzL9jqHF7Tu9XPdoX6vf31ed6jf6691r5/rDt6vv3ZxioiIiIQZFTQRERGRMKOCFph3vA7gIa17/VWf178+rzvU7/XXutdfnq6/jkETERERCTMaQRMREREJMypoVTCzUWZ22MyOmtnPK3k83sw+8z++w8zaeRAzJMysjZltMLMDZpZjZn9RyTJDzOyame31f/y9F1lDwcxOmNm3/vXaVcnjZmb/6n/tvzGz3l7kDAUz61zhNd1rZtfN7D/dt0ydee3N7H0zO29m+yvcl2pma8ws1/+5SRXPneFfJtfMZtRe6uCpYv1/Y2aH/L/bC8yscRXPfeD7JNxVse7/zcxOV/jdHlPFcx+4fQh3Vaz7ZxXW+4SZ7a3iuRH9ukPV27iwe+875/Rx3wcQDRwD2gNxwD6g633L/Az4nf/2y8BnXucO4vq3BHr7bycDRypZ/yHAUq+zhmj9TwDNHvD4GGAFYMAAYIfXmUP07xANnAUeq6uvPTAI6A3sr3DfPwI/99/+OfDrSp6XCuT5Pzfx327i9foEaf1HADH+27+ubP39jz3wfRLuH1Ws+38D/utDnvfQ7UO4f1S27vc9/j+Bv6+Lr7t/HSrdxoXbe18jaJXrBxx1zuU55+4BnwIT7ltmAjDLf3suMMzMrBYzhoxzrsA5t9t/+wZwEGjtbaqwMgH4gyu1HWhsZi29DhUCw4BjzrnaOPmzJ5xzm4HL991d8b09C5hYyVNHAmucc5edc1eANUClJ5sMZ5Wtv3NutXOu2P/ldiCj1oPVgipe++qozvYhrD1o3f3bsWnA7FoNVYsesI0Lq/e+ClrlWgOnKnydzw8LSvky/j9m14CmtZKuFvl33fYCdlTy8FNmts/MVphZt9pNFlIOWG1mX5vZ25U8Xp3fj7rgZar+I11XX3uAFs65Av/ts0CLSpapL78Db1A6WlyZh71PItV/8O/efb+KXVx1/bV/FjjnnMut4vE69brft40Lq/e+CppUycwaAvOA/+Scu37fw7sp3fXVA/jfwMJajhdKA51zvYHRwJ+Z2SCvA9U2M4sDxgOfV/JwXX7tv8eV7tOol1PdzewXQDHwSRWL1MX3yW+BDkBPoIDSXX31zXQePHpWZ173B23jwuG9r4JWudNAmwpfZ/jvq3QZM4sBUoBLtZKuFphZLKW/uJ845+bf/7hz7rpz7qb/9nIg1sya1XLMkHDOnfZ/Pg8soHSXRkXV+f2IdKOB3c65c/c/UJdfe79zZbus/Z/PV7JMnf4dMLOZwDjgR/4N1Q9U430ScZxz55xzPudcCfAula9TnX3t/duyycBnVS1TV173KrZxYfXeV0Gr3FdAJzPL9I8kvAwsvm+ZxUDZ7I2pwPqq/pBFGv8xCO8BB51z/6uKZdLLjrkzs36U/i5FfEE1syQzSy67TekB0/vvW2wx8GMrNQC4VmFYvK6o8n/RdfW1r6Die3sGsKiSZVYBI8ysiX832Aj/fRHPzEYBfw2Md84VVrFMdd4nEee+Y0knUfk6VWf7EKmeBw455/Ire7CuvO4P2MaF13vfy5kU4fxB6Uy9I5TO1vmF/75fUvpHCyCB0t0/R4GdQHuvMwdx3QdSOrT7DbDX/zEG+CnwU/8y/wHIoXQG03bgaa9zB2nd2/vXaZ9//cpe+4rrbsD/9f9ufAtke507yP8GSZQWrpQK99XJ157SEloAFFF6LMmblB5Lug7IBdYCqf5ls4F/r/DcN/zv/6PA616vSxDX/yilx9iUvffLZqu3Apb7b1f6PomkjyrW/SP/e/obSjfWLe9fd//XP9g+RNJHZevuv//Dsvd5hWXr1OvuX4+qtnFh9d7XlQREREREwox2cYqIiIiEGRU0ERERkTCjgiYiIiISZlTQRERERMKMCpqIiIhImFFBExEREQkzKmgiIiIiYUYFTUSkCmYWbWb/YmY5ZvatmbX3OpOI1A8qaCIiVftbIM851w34V+BnHucRkXoixusAIiLhyH+twUnOuT7+u44DYz2MJCL1iAqaiEjlngfamNle/9eplF6fT0Qk5LSLU0Skcj2Bv3fO9XTO9QRWU3pRZRGRkFNBExGpXBOgEMDMYoARwBJPE4lIvaGCJiJSuSPAAP/tvwSWOeeOe5hHROoRc855nUFEJOyYWRNgBdAM2Aa87Zy77W0qEakvVNBEREREwox2cYqIiIiEGRU0ERERkTCjgiYiIiISZlTQRERERMKMCpqIiIhImFFBExEREQkzKmgiIiIiYUYFTURERCTM/P9E8MLzxJSs8AAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# even smaller alpha\n", "\n", "abc = pyabc.ABCSMC(\n", " model,\n", " prior,\n", " pyabc.PNormDistance(p=2),\n", " population_size=pop_size,\n", " eps=pyabc.QuantileEpsilon(alpha=0.2),\n", ")\n", "\n", "abc.new(db_path, y_obs)\n", "\n", "h = abc.run(max_total_nr_simulations=n_samples)\n", "\n", "plot_posterior(h)\n", "plot_pars_over_data(h);" ] }, { "cell_type": "markdown", "id": "d60abaa2-7267-4413-b144-31689a6166a1", "metadata": {}, "source": [ "## Optimal threshold based on predicting the acceptance rate\n", "\n", "In general, an appropriate quantile in situations as sketeched above, as well as a sufficiently large population size, are problem-dependent. Silk et al. thus propose a strategy that tries to identify the problem of local optima and propose appropriate values automatically. It does so by predicting the acceptance rate in the next population as a function of the threshold. In the first place, it then chooses a threshold maximizing the Hessian of that function, yielding appropriate values for convex shapes, indicative of local optima. If such potential problems cannot be found (i.e. the function is mostly concave), instead a threshold is chosen as a trade-off of acceptance rate and threshold decrease, minimizing a combined objective. See the paper or the API documentation for further details.\n", "\n", "In pyABC, the `SilkOptimalEpsilon` is based on the above-mentioned approach:" ] }, { "cell_type": "code", "execution_count": 9, "id": "a653958d-cf3d-48bd-8bd4-f79d5e84f199", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ABC.Sampler INFO: Parallelize sampling on 4 processes.\n", "ABC.History INFO: Start \n", "ABC INFO: Calibration sample t = -1.\n", "ABC.Epsilon INFO: Optimal threshold for t=0: eps=1.1162e+02, estimated rate=7.6606e-01 (discontinuous=7.6000e-01)\n", "ABC.Population INFO: Recording also rejected particles: True\n", "ABC INFO: t: 0, eps: 1.11620488e+02.\n", "ABC INFO: Accepted: 200 / 261 = 7.6628e-01, ESS: 2.0000e+02.\n", "ABC.Epsilon INFO: Optimal threshold for t=1: eps=4.5116e+01, estimated rate=5.6816e-02 (discontinuous=7.0895e-03)\n", "ABC INFO: t: 1, eps: 4.51162085e+01.\n", "ABC INFO: Accepted: 200 / 29393 = 6.8043e-03, ESS: 1.9995e+02.\n", "ABC.Epsilon INFO: Optimal threshold for t=2: eps=1.6576e+01, estimated rate=5.2353e-01 (discontinuous=5.1976e-01)\n", "ABC INFO: Stop: Total simulations budget.\n", "ABC.History INFO: Done \n", "ABC.Transition INFO: Best params: {'scaling': 0.05}\n" ] }, { "data": { "image/png": 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\n", 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4Ccdq0lnn8/Ly3JYtW7yOEZd++OEHFi1axNNPP80zzzzjdRwREanBzpw5w/vvv09OTg4zZszQ+c7KV+4OeZ7vgybVo0+fPvTq1Yuvv/6aPXv2eB1HRERqqJs3b/LFF1+QkZHBiy++qHIWIRW0WsLMGDduHK1atWLevHmcPXvW60giIlLD+P1+5syZw7Vr15g2bRr16tXzOlLCUkGrRVJSUpg2bRrp6el88cUX3Lp1y+tIIiJSg6xatYrDhw/z3HPPkZub+/AHSLlU0GqZ+vXrM23aNK5evcrs2bN10ICIiETFrl272LBhA3l5efTp08frOAlPBa0Wat26NePGjePw4cOsXLnS6zgiIpLgTp8+zYIFC2jTpg1jxpS97LZEIsXrAOKN3r17c+rUKTZu3EhOTg49e/b0OpKIiCSg4EEBderU0UEBUaQ1aLXY6NGjadeuHQsXLtSVBkREpMqCVwq4fv06L730EnXr1vU6Uo2hglaLJScn8+KLL1K3bl2++OILrl+/7nUkERFJIMuWLePIkSOlZwmQ6FFBq+UyMzN5+eWXuXXrFrNmzcLn0wUbRETk4bZs2cL333/PwIED6d27t9dxahwVNCEnJ4dJkyZx/PhxFi9eTE26uoSIiETfkSNHWLJkCZ07d2bkyJFex6mRVNAEgB49evD000+zbds2Nm7ceN99zjmuFBRwedcurhQUPFDggveXvS90uN/v52phIc45nHNc2rmTQ//yL/etsfP7/ZzMz+fyrl34fD5OzJ/Pifnz8fl8pY/1+/2cmD+f43PncmL+/EqfJiSY5dLOnZzMzy99XPD5gs/lnCv9XcHHXS0sxO/3PzAtodMUmv/Szp0PvBZ+v59TCxaU/o5glhPz53N5166w4/p8vvte19Bs4V7z0KxlM1c0ztXCQnw+X+lrH3xc6PwO97qEPnfovCv73MHnCze9D3vecO/BYC6fz1f6mpY3v0PHKy4u5mR+Phe3b+fgO+9waefOcnOUHRbudtn5X/b3X961q3R6y45b3nNX9JpUND/CTXNwfpT3D1dFGcKNV/b9VN68CuXz+Tgc8jkv+9oF503Zz3jo34Gy87i8rKGfm4pe27LvI7/fXzqvwn12H/Zal/28hHu/V/ReDf3b8LB5Ge49V958KPuZLJsxdJ6GvrfC/f0pO/6xb75h1pdf0qRJE6ZMmUJSkqpETATfxDXhq2/fvk4i5/f73axZs9zf/M3fuL1795YOv1JQ4Nbk5blVPXu6NXl57kpBwX2PC95f9r7Q4Sfz8926p55yVwoK3JWCAreyRw+3NDfXHXrnndLxT+bnu6Vt27pVPXu6Q++845a2aeOWtmnjDr3zTuljT+bnlwxv3dotbdPGnczPr9S0BbOs7NHDLW3btvRxpc8XeK4rBQWlvyv4uHVPPeVO5uc/MC2h0xSaf2WPHg+8Fifz892ydu1Kf0dpljZt3OqePcOOe+idd+57XUOzhXvNQ7OWzVzROOueeqrk9W7b1q3u2bP0caHzO9zrEvrcofOu7HMHny84vatCpvdhzxvuPbg6kOvQO++Uvqblze/Q8Qr/6391S9u2dSs6d3ZLc3Pdyh49ys1Rdli422Xnf9nfv6pnz9LpLTtuec9d0WtS0fwIN83B+REu38MyhBuv7PupvHkV6tA779z3OS/72gXnzQOf8ZC/A2XncXlZQz83Fb22wdcy+HqezM8vnVfhPrsPe63Lfl7Cvd8req+G/m142LwM954rbz6U/UyWzRg6T0PfW+H+/oSOv7pvX7ega1f3T3/2Z+7ixYth57tUSbmdxvNSFc0vFbRHd/fuXffrX//a/ff//t/dqVOnnHMlxe3yrl3u0s6d7vKuXc7v99/3mOD9Ze8LHe7z+dyVggLn9/ud3+93F3fscAffeccVFxeXju/z+dyJ+fPdpZ07XXFxsSuaN88VzZvniouLSx/r8/lc0bx57ticOa5o3jzn8/kqNV3BLBd37HAn5s8vfVzw+YLP5ff7S39X8HFXCgqcz+d7YFpCpyk0/8UdOx54LXw+nzuZn1/6O4JZiubNc5d27gw7bnFx8X2va2i2cK95aNaymSsa50pBgSsuLi597YOPC53f4V6X0OcOnXdlnzv4fOGm92HPW3b+Xdq5szRXcXFx6Wta3vwOHe/evXvuxPz57sK2be7A//k/7uKOHeXmKDss3O2y87/s77+0c2fp9JYdt7znrug1qWh+hJvm4PwIl+9hGcKNV/b9VN68ClVcXOwOhXzOy752wXlT9jMe+neg7DwuL2vo56ai17bs+8jn85XOq3Cf3Ye91mU/L+He7xW9V0P/NjxsXoZ7z5U3H8p+JstmDJ2noe+tcH9/guPfu3fP/dvf/Z37hz/5E3fkyJGw81yqrNxOY87VnP2N8vLy3JYtW7yOkfCuXbvGe++9h5nx85//XIdNi4gIS5cuZfPmzTz//PO6UkD0WHl3aMOxPKBevXpMnz6dW7du8cUXX3Dv3j2vI4mIiIe2bNnC5s2bGThwoMpZNVFBk7BatGjB5MmTOXHiBPn5+Q/skCsiIrXDkSNHWLp0qY7YrGYqaFKurl27MmLECAoLC/nqq6+8jiMiItXs/PnzzJo1i8aNG+uIzWqma3FKhQYNGsSFCxf46quvaNy4MU888YTXkUREpBrcuHGDzz77jOTkZF555RXS09O9jlSrqApLhcyM8ePH06ZNG/Lz8ykqKvI6koiIxNi9e/f4/PPPuX79OtOnT6dBgwZeR6p1VNDkoZKTk3nppZeoX78+X3zxBZcvX/Y6koiIxIjf72fu3LmcOHGCKVOm6BqbHlFBk0rJzMzklVdeobi4mM8//5w7d+54HUlERGJg5cqV7N27lzFjxtC1a1ev49RaKmhSaU2aNGHatGmcO3eOOXPmVPoySyIikhg2b97Mxo0bGTBgAAMGDPA6Tq2mgiZV0qFDB5577jkOHDjAihUrvI4jIiJRsm/fPpYtW0aXLl0YNWqU13FqPR3FKVWWl5fH+fPn2bRpE40bN6Zfv35eRxIRkUdw8uRJ5syZU3oOTJ1Ow3sqaBKRUaNGcfHiRZYuXUqjRo3o2LGj15FERCQCly9f5t/+7d/IzMxk+vTppKWleR1J0CZOiVBSUhJTpkyhadOm/O53v+PcuXNeRxIRkSq6efMmv/3tbykuLuanP/2prr0cR1TQJGLp6elMnz6dlJQUZs2apYMGREQSyN27d/n888+5fPky06dPp2nTpl5HkhAqaPJIGjRowPjx4zl//jy7d+/2Oo6IiFSCz+dj9uzZpec6a9u2rdeRpAwVNHlkXbp0oW7duuzZs8frKCIi8hDOORYtWsSBAwd47rnn6Natm9eRJAwVNHlkZkbnzp05fPgwzjmv44iISAXWrFnD9u3bGTp0KHl5eV7HkXJUW0Ezsw/M7KyZFYQMa2RmK83sQOB7w8BwM7N/NrODZrbTzPpUV06JTIsWLbh9+zZXr171OoqIiJRj06ZNfPPNN/Tp04ehQ4d6HUcqUJ1r0D4CxpQZ9ktgtXOuM7A68DPAWKBz4Ott4FfVlFEi1Lx5cwDOnDnjcRIREQmnsLCw9ES048aNw8y8jiQVqLaC5pxbD1wsM3gi8HHg9sfApJDhn7gSG4EGZtaiWoJKRJo0aQLAhQsXPE4iIiJlHTlyhHnz5tGmTRumTJmiE9EmAK/nUHPn3KnA7dNA88DtVsDxkPGKAsMkTtWpU4fk5GSuX7/udRQREQlRVFTEF198QaNGjXj55ZdJTU31OpJUgtcFrZQr2bu8ynuYm9nbZrbFzLboZKneMTPq1avHtWvXvI4iIiIBZ8+e5bPPPiMrK4vXXnuNOnXqeB1JKsnrgnYmuOky8P1sYPgJoHXIeLmBYQ9wzr3rnMtzzuXpJHveUkETEYkfFy9e5NNPPyU1NZXXXnuNevXqeR1JqsDrgrYAmBG4PQPIDxn+s8DRnAOBKyGbQiVO1atXT5s4RUTiwNWrV/n000/x+Xy89tprNGzY0OtIUkXVdrF0M/scGAY0MbMi4L8BfwfMMrM3gR+BaYHRlwDPAQeBm8Dr1ZVTIpeVlaWCJiLisRs3bvDpp59y8+ZNZsyYoUs4JahqK2jOuenl3DUizLgO+KPYJpJoS09P586dOzjndPi2iIgHbt++zWeffcbly5d59dVXadmypdeRJEJeb+KUGiQjIwPnHPfu3fM6iohIrXPv3j0+//xzzpw5w7Rp03R9zQRXbWvQpOZLT08HSv6DS0tLK3e8U6dOMWvWLOrWrcvkyZO1b4SIyCMqLi7myy+/5NixY0yZMoXOnTt7HUkekdagSdRkZGQAcOfOnQrHW79+PZcvX+bcuXO8//77nD17tsLxRUSkfD6fj1mzZnHo0CEmTJjA448/7nUkiQIVNIma0DVo5fH7/Rw4cID+/fvz1ltvkZSUxMcff6xLRImIRMDn8zF79mwOHDjAuHHj6N27t9eRJEpU0CRqKrMG7dKlS/h8Plq0aEGTJk2YMWMGycnJfPLJJyppIiJV4Pf7mTt3Lnv37mXs2LHk5eV5HUmiSAVNoqYya9CCV3sIXruzcePGzJw5UyVNRKQK/H4/8+bNY/fu3YwaNYr+/ft7HUmiTAVNoqYya9AuXrwI/L6gATRq1Ki0pGlzp4hIxfx+PwsWLKCgoIARI0bwk5/8xOtIEgMqaBI1wSM37969W+44N27cIDk5uXRtW1CwpKWmpvLxxx9z+vTpmGYVEUlEzjkWLVrEjh07GD58OIMHD/Y6ksSICppETUpKyVlbiouLyx3n5s2bZGZmhj2RbaNGjZgxYwapqal88sknKmkiIiGccyxevJht27YxZMgQhgwZ4nUkiSEVNIma5ORkgApPVHvz5k2ysrLKvV8lTUTkQc45Fi5cyA8//MDgwYMZNmyY15EkxlTQJGrMjNTU1AoL2o0bN8jMzKzweUI3d6qkiUht5/f7yc/PL11z9swzz+hyerWACppEVWpqaqU2cT5Mw4YN7ytpp06dimZMEZGEEDxaM7jP2fDhw1XOagkVNImqlJSUh27irExBg9+XtLS0NJU0Eal1fD4fc+bMKT1aU/uc1S4qaBJVFa1Bc85x586dB47grEjDhg2ZMWMG6enpKmkiUmsErxAQPM+ZjtasfVTQJKoq2gctWNwqupB6OGVL2smTJx85p4hIvApe+Dx4hQCd56x2UkGTqKpoE2fw/GhVLWjw+82dwZJ2/PjxR8opIhKP7t27xxdffFF6bU1dIaD2UkGTqKpoE+ejFDSABg0a8Prrr5OVlcWnn37KoUOHIs4pIhJvbt++zaeffsrhw4eZMGGCrq1Zy6mgSVRVtInzUQsaQHZ2Nq+//jqNGjXi888/Z8+ePRE/l4hIvLhx4wYff/wxJ06cYOrUqfTu3dvrSOIxFTSJqlgXNIC6desyY8YMWrRowe9+9zu2b9/+SM8nIuKlK1eu8OGHH3L+/HmmT59O9+7dvY4kcUAFTaIqJSUlZps4Q9WpU4fXXnuN9u3bk5+fz8aNGx/5OUVEqtv58+f54IMPuH79Oq+99hqdOnXyOpLECRU0iapYHSQQTlpaGtOnT6dbt24sX76cr776CudcVJ5bRCTWTp06xYcffojP52PmzJm0adPG60gSR1TQJKpSUlLw+Xxh7wsWt9TU1Kj+vqlTp9KrVy/WrVvH8uXLVdJEJO4dO3aMjz/+mNTUVF5//XVycnK8jiRxJsXrAFKzJCcnV8smzlBJSUlMmDCB9PR0Nm3axI0bN5g0aVLpxdtFROLJvn37mD17NtnZ2bz22mtkZ2d7HUniUJULmpllAbedc+FXk0itlpycjM/nwzn3wPXiYlXQoORC7aNHj6Zu3bqsXr2aGzdu8NJLL1XpqgUiIrG2ZcsWlixZQosWLXjllVfIysryOpLEqYdu4jSzJDN7xcwWm9lZYC9wysx2m9k/mJn2aJRSKSklnT/cZsZYbOIMZWYMHjyYSZMm8eOPP/Lhhx9y7dq1mPwuEZGqcM6xdu1aFi9eTKdOnZgxY4bKmVSoMvugrQU6An8J5DjnWjvnmgGDgY3A35vZqzHMKAkkuFkx3GZOn8+HmZGUFNtdH3v27Mn06dO5ePEi77//PufPn4/p7xMRqYjP52PBggWsX7+eXr168fLLL8dkS4LULJVZUj7rnPt/nHM7nXP+4EDn3EXn3Bzn3BTgy9hFlEQSLGjhDhQoLi4uXcMWa506dWLmzJkUFxfzwQcf6NJQIuKJu3fv8uWXX7J9+3aGDBnChAkTYv5PqtQMD32XOOceOGeCmT0T+N7CzJLDjSO1U7wUNICWLVvyxhtvkJGRwSeffMK+ffuq7XeLiASvDnDw4EHGjx/P8OHDH9g3V6Q8kdb4MWaWC/wr8I9RzCMJ7mEFrbqPrGzUqBFvvvkmzZo148svv2TTpk3V+vtFpHa6cOEC77//PmfPnuWll16ib9++XkeSBBNpQWsA/AXw58CdqKWRhBdcQxauoPl8vmpdgxaUlZXFjBkzeOyxx1i2bBlLlizB7/c//IEiIhE4cuQIv/nNb7hz5w4/+9nP6NKli9eRJAFFWtD+FljnnNsHPPLpNszsP5hZoZkVmNnnZpZhZu3NbJOZHTSzL81Me1QmgIoOEqjuTZyh0tLSmDZtGj/5yU/4/vvv+fzzz7lzR/9biEh0bdu2jd/+9rfUq1ePt956i9atW3sdSRJUpAXtH4CRZvYxsORRAphZK+DfAXnOuceBZOBl4O+Bf3TOdQIuAW8+yu+R6lHRJk6v1qAFJSUlMWrUKMaPH8+hQ4f44IMPuHLlimd5RKTmcM6xcuVKFixYQPv27XnjjTdo2LCh17EkgUVa0PY45/7QOTeDkjL1qFKAOmaWAmQCp4BngNmB+z8GJkXh90iMxds+aOH07duXn/70p1y5coX33nuPEydOeB1JRBLY3bt3mTVrFt999x15eXm88sorZGRkeB1LElyVC5qZvQeMMrN/Z2bDgMuPEsA5dwL4n8AxSorZFeAH4LJzLridrAho9Si/R6pHPB3FWZGOHTvy5ptvkpqaykcffcTu3bu9jiQiCejatWt89NFH7Nu3j9GjR/Pcc8/pNBoSFVV+Fznnfg48C3wP9AQaP0oAM2sITATaAy2BLGBMFR7/tpltMbMt586de5QoEgWJUtAAmjZtyltvvUVOTg6/+93vWLdunS60LiKVdvLkSd577z0uXLjAyy+/zMCBA3UaDYmaSGv+XwH/EegNvPOIGZ4FjjjnzgXOpzYXGAQ0CGzyBMgFwm6Hcs6965zLc87lNW3a9BGjyKOq6CjOeCto8PsjPHv27MlXX33FrFmzdPCAiDzUzp07+fDDD0lKSuL111/nscce8zqS1DCRFrRM59yLwNvALx4xwzFgoJllWsm/HiOA3ZRcYmpqYJwZQP4j/h6pBg+71FM87INWVkpKChMnTmT06NHs27eP999/n4sXL3odS0TikN/vZ/ny5cybN4/c3Fx+/vOfk5OT43UsqYEiLWgZZtbHOXcXeKT1uc65TZQcDLAV2BXI9C4l51n7j2Z2kJLNqO8/yu+R6pFImzhDmRkDBw7k1Vdf5fr167z33nscOnTI61giEkdu3rzJb3/7WzZu3Ej//v159dVXdcFziZlIC9p/Bp4xsw+Iwpot59x/c851dc497px7zTl3xzl32DnX3znXyTn3onNO250SQCIcxVmRDh068POf/5zs7Gw+++wzvvvuO+2XJiKcOXOG9957j2PHjjFhwgTGjh0b93/PJLFVuqCZ2Uoz6wngnLvlnPufzrk3nHNLYxdPEk2irkEL1bBhQ9544w26devGypUrmTdvHvfu6XKzIrVVYWEh77//Pj6fj5kzZ9K7d2+vI0ktUJWl5V8A/9vMjgJ/5Zw7FZtIksji8VJPkUhLS2Pq1Kl88803rFmzhjNnzjBt2jQaN36kg5ZFJIH4fD5WrlzJpk2byM3NZdq0adSrV8/rWFJLVHoNmnNuq3NuOLAIWGZm/83M6sQumiSi4Pl/yitoibRJwMx4+umnefXVV7l27RrvvvsuhYWFXscSkWpw5coVPvroIzZt2kT//v2ZOXOmyplUqyrtgxY4ynIf8CvgT4ADZvZaLIJJYgoWsLIXI3fO4ff7E/IEjh07duQP/uAPaNasGbNnz2bp0qVhC6iI1AyHDh3i3Xff5ezZs0ydOlX7m4knKr29ycy+peRksoXARmAmsBf4UzN72jn3dkwSSkIpbw1acEf7RP0jl52dzcyZM0s3d5w8eZKpU6eSnZ3tdTQRiRK/38/69ev56quvaNq0KdOmTaNJkyZex5Jaqio7BL0N7HYPHtL2J2a2J4qZJIEFC1rZNWjBwpaIa9CCkpOTGTNmDG3atCE/P59f//rXTJ48mU6dOnkdTUQe0Y0bN5g3bx6HDh3iySefZNy4caSlpXkdS2qxShc051xFO9+Mi0IWqQGClzkpW9CCPydyQQvq3r07zZs3Z9asWXz22Wc89dRTPPPMMwm7dlCktjt8+DDz5s3j1q1bjB8/nj59+uiSTeK5qBxS55w7HI3nkcRnZiQlJdXoggbQuHFj3nrrLZYvX853333H0aNHmTx5so7yFEkgPp+PtWvX8u2339KkSRN++tOf6qoAEjciLmhm1gK4qBPISlm1oaABpKamMn78eDp27MiCBQt49913ee655+jZs6fX0UTkIS5dusScOXM4ceIEffr0YfTo0dqkKXHlUdagfQp0NLM5zrk/i1YgSXwVFbSauBmwW7dutGzZkrlz5zJ//nwOHTrEuHHjSE9P9zqaiISxa9cuFi1aRFJSEi+++CLdu3f3OpLIAyIuaM65ZwOn3dA7W+6TlJT0wFGcNeEggYpkZ2czY8YMvv76a7766iuKioqYPHkyubm5XkcTkYA7d+6wdOlSduzYQevWrZk8eTINGjTwOpZIWBFd6inIldCZO+U+ycnJtWITZ1lJSUkMHTqUmTNn4vf7+eCDD1i9erXOmSYSB44cOcKvfvUrdu7cyZAhQ5g5c6bKmcQ1XepJoq627INWnjZt2vCHf/iHLF++nG+++YYDBw7wwgsv0Lx5c6+jidQ69+7dY/Xq1WzatIlGjRrxxhtvaM22JISqnGZjKzDczKZQcqmnucD/cM7dilk6SUi1vaABZGRkMHHiRLp27crChQt57733GDZsGE899VSteQ1EvHbixAnmzZvHhQsX6NevH88++6wOBJCEUaV90Mpc6un/BX5uZn/pnPs0FuEkMdW2gwQq0qVLF3Jzc1m8eDGrV69m//79TJo0iUaNGnkdTaTG8vl8rF+/nq+//pp69erx2muv0aFDB69jiVSJLvUkUReuoNX0gwQqkpWVxYsvvsiuXbtYsmQJ//qv/8rw4cMZMGBArXw9RGLp5MmTLFiwgDNnztCzZ0/GjBlDRkaG17FEqkyXepKo0ybOB5kZTz75JO3atWPRokWsWLGCwsJCnn/+ee2bJhIF9+7dY926dWzYsIGsrCxeeuklunbt6nUskYg9tKCZmVXiaE1d6klK1dajOCujfv36TJ8+nYKCApYtW8a7777L4MGDefrpp0lJicqFPURqnSNHjrBw4UIuXbpE7969GTVqlNaaScKrzBJhrZnNAfKdc8eCA80sDRgMzADWArrckwDhz4OmgvZ7ZsYTTzxBx44dWb58OevXr2f37t1MmDCB1q1bex1PJGHcvn2bFStWsG3bNho2bMjPfvYz2rdv73UskaioTEEbA7wBfG5mHYBLQB1KzqG2AvjfzrltsYsoiUYHCVROZmYmL7zwAo8//jiLFi3igw8+IC8vj2eeeYY6dep4HU8kbjnnKCwsZPny5dy4cYOnnnqKYcOGkZqa6nU0kaipTEF7BpjvnPu/ZpYKNAFuOecuxzSZJCwdJFA1nTt35he/+AVr1qzh+++/Z/fu3YwcOZKePXtScuC0iASdP3+epUuXcvjwYXJycpg+fTotW7b0OpZI1FWmoL0A/K2ZNafkqM0dwHYz2w7scc7pNOlyHx0kUHXp6emMHTuWXr16sWTJEvLz89m2bRvPPfecDiIQAe7evcv69evZsGEDqampPPfcc/Tt21d/U6TGemhBc879HMDM/gpoRcm+ZsOBd4GLgE7JLPdJTk6muLj4vmEqaJXTokUL3njjDbZt28aqVav49a9/Tf/+/Rk+fLguvi61knOOvXv3snz5cq5cuULPnj0ZOXIkWVlZXkcTiamqHDb2knOu9FqcZvZ/gf8c/UiS6LQG7dGYGX369KFr166ll6gpLCxkxIgR2uwptcq5c+dYsWIFBw8epFmzZsycOZO2bdt6HUukWlSloF01s77OuR8AnHM/mNljMcolCayiozh1kEDlZWZm8vzzz9OnTx+WLl1Kfn4+mzdvZtSoUbRr187reCIxc+PGDdatW8cPP/xAWloao0aNon///vr7IbVKVQram8BcM/se+AF4ArgXk1SS0HSQQHS1atWKN998k4KCAlatWsXHH39M165dGTlypC4ZJTVKcXExmzdvZv369dy9e5e8vDyGDh2qzZlSK1XlYun7zawPMImScrYH+KsY5ZIEpk2c0Rc8d1rXrl3ZsGED33zzDfv376d///4MHTpUJ+WUhOacY8+ePaxatYpLly7RuXNnRo4cSdOmTb2OJuKZKp263Dl3F5gV+BIJSwUtdlJTUxkyZAi9e/dm7dq1bNy4ke3btzN48GD69++v80BJwjly5Ahr1qyhqKiIZs2a8eqrr9KxY0evY4l4TteWkair6FJP2ockOurVq8eECRPo378/a9asYdWqVWzcuJEhQ4bQp08fvc4S906cOMGaNWs4fPgw9evX5/nnn6dXr176J04kQAVNos7MtAatmuTk5PDKK69w7NgxVq9ezZIlS/juu+8YNmwYTzzxhF5viTtnz55l7dq17N27l8zMTEaPHk1eXp6uRStShj4REnXhjuLUQQKx1aZNG2bOnMmhQ4dYvXo18+fP59tvv2Xo0KF069ZNr7t47vz583z99dfs3LmT9PR0hg0bxsCBA3V+P5FyxEVBM7MGwG+AxwFHybU/9wFfAu2Ao8A059wlbxJKVVS0iVNFIXbMjE6dOtGxY0f27NnD2rVrmT17No0bN+bpp5/m8ccf16ZPqXZnzpzh66+/prCwkJSUFJ566ikGDRpEZmam19FE4lpcFDTgn4BlzrmpZpYGZFJyhOhq59zfmdkvgV8Cf+FlSKkcHSTgLTOje/fudO3alT179vD1118zf/581q1bx6BBg+jVq5c2J0nMnThxgq+//pp9+/aRlpbG4MGDGThwoE6ZIVJJnv+VNrNsYAgwE0qPFL1rZhOBYYHRPgbWoYKWEMoraGams+BXo6SkJHr06EH37t05cOAA69evZ/Hixaxfv56nnnqK3r17a/OSRJVzjiNHjvDdd99x6NAhMjIyGDZsGP3796dOnTpexxNJKJ4XNKA9cA740Mx6UnIS3D8FmjvnTgXGOQ2EvWK0mb0NvA0l++GI98o7Ua3WnnnDzHjsscfo3LkzR44cYf369Sxfvpx169bRt29f+vfvT3Z2ttcxJYH5fD4KCgrYsGEDZ86cISsrixEjRtCvXz/9EyASoXgoaClAH+BPnHObzOyfKNmcWco558zMhXuwc+5dSi7cTl5eXthxpHoFC5pzrnSNmd/vV0HzmJnRoUMHOnToQFFRERs3bmTDhg1s2LCBHj16MHDgQFq1auV1TEkgt27dYsuWLWzevJnr16/TtGlTJkyYwBNPPKHN6CKPKB4+QUVAkXNuU+Dn2ZQUtDNm1sI5d8rMWgBnPUsoVRIsYmULmnZQjx+5ublMnTqVK1eusGnTJrZu3UpBQQGtW7emX79+dOvWTQtYKdepU6fYsmULu3bt4t69e3To0IGJEyfSsWNH7cYgEiWe/wV2zp02s+Nm1sU5tw8YAewOfM0A/i7wPd/DmFIFwSIWutZMa9DiU3Z2NqNGjWLo0KFs27aNzZs3M3fuXDIzM+nduzd9+/alYcOGXseUOHDv3j0KCwvZsmULJ06cICUlhccff5yBAwfSvHnYPVBE5BF4XtAC/gT4LHAE52HgdSAJmGVmbwI/AtM8zCdVECxiPp+vdC2MClp8S09PZ+DAgQwYMIDDhw+zZcsWvvvuO7799ls6duxIXl4enTt31lrQWujcuXNs3bqVHTt2cOvWLRo3bszo0aPp2bOndvwXiaG4KGjOue1AXpi7RlRzFImC0LVmQSpoicHM6NixIx07duTq1ats3bqVrVu38uWXX5KVlcXjjz9Or169yMnJ8TqqxNCtW7coKChg+/btnDx5kqSkJLp27UpeXh7t2rXTZkyRahAXBU1qFhW0mqF+/foMGzaMIUOGcODAAXbs2MGWLVvYtGkTzZs358knn+TJJ5+kbt26XkeVKPD5fBw6dIgdO3awb98+fD4fzZs3Z9SoUTzxxBOazyLVTAVNoq68gqbNY4kpKSmJLl260KVLl9I1Kzt27GDlypWsWrWK9u3bl54YVychTSx+v58jR45QWFjI3r17uXXrFpmZmeTl5WlNqYjHVNAk6kIPEgjSedBqhjp16tCvXz/69evH+fPn2bFjB7t372bRokUsXrxYZS0B+P1+fvzxRwoLC9mzZw83b94kLS2NLl260KNHDzp16qR/pkTigAqaRJ02cdYOTZo0YcSIETzzzDOcOXOGwsLC+8pamzZt6Ny5M4899hhNmjTRfkseun37NgcPHmT//v0cOHCA27dvk5qaSpcuXejevTudOnUiNTXV65giEkIFTaIu9CjOIBW0msvMyMnJIScnp7Ss7d69m/3797Nq1SpWrVpFw4YNS8ta27ZtdY61GHPOcf78+dJS9uOPP+KcIzMzky5dupReWUKlTCR+6a+kRJ3WoNVeZcvalStXOHDgAAcOHGDr1q1s3ryZ5ORk2rRpQ7t27Wjfvj2tWrXSeyMKrly5wuHDhzly5AhHjhzh+vXrADRr1oxBgwbx2GOP6bUWSSAqaBJ1OkhAgrKzs8nLyyMvL4979+5x9OhRDh8+zNGjR1m7di1r164lLS2Ntm3b0qZNG1q3bk3Lli21ZuchnHNcuHCB48ePc/z4cX788UcuXrwIQFZWFu3bt6d9+/Z06NCBBg0aeBtWRCKigiZRF66g6SABSU1NpXPnznTu3BmAmzdvcvTo0dI1PgcOHAB+vxYuNzeX3NxcWrVqRcOGDWv1++fGjRucPn2aEydOUFRURFFREbdu3QIgIyODNm3a0K9fP9q3b0+zZs20v59IDaCCJlEX7ihOv9+v/Y7kPpmZmXTv3p3u3bsDJYWtqKiI48ePU1RUxPbt2/n++++BknLXrFkzcnJyaN68OTk5OTRr1oz09HQvJyHqfD4fly5d4uzZs5w+fbr069q1a6XjNG3alK5du9K6dWtyc3N1AIZIDaUlpkSdDhKQSGRmZvLYY4/x2GOPASXvmbNnz3Lq1ClOnz5deqToDz/8UPqYrKwsGjduTOPGjWnUqFHp9/r165ORkRGXxeXevXtcvXqVq1evcvHiRc6fP1/6/dKlSzjngJI1iU2bNqV9+/al+/Xl5OTo8koitYQKmkSd9kGTaEhKSiotJUHOOa5evcrp06c5d+4cFy5c4OLFi+zfv58bN27c9/jU1FTq169f+lW3bl0yMzOpU6cOderUKb2dkZFBamoqqampJCUlVanU+f1+iouLuXfvHnfv3uXWrVvcvHmz9Hvw69q1a1y5coWrV69y8+bN+54jJSWFRo0akZOTQ/fu3WnSpAlNmzalWbNmWussUovp0y9Rp33QJFbMjOzsbLKzs+nSpct9992+fZuLFy9y6dKl0jVU165d4+rVqxw9epRr167d954s7/lTUlJITU0lOTm5tKwF12oFbwdLWeha4vLUqVOHevXqUb9+fVq2bEl2djb169cnOzubhg0bkp2dHZdr+kTEWypoEnU6zYZ4ISMjg5YtW9KyZcuw9zvnStdyha7pun37Nvfu3SstXcHbxcXF9z0+tEQF17iV/QpdO5eZmUlGRobe9yISERU0iToVNIlHZkZ6ejrp6ek69YSIxD0tMSXqyjuKUwVNRESkcrTElKjTUZwiIiKPRktMiTodJCAiIvJotMSUqNM+aCIiIo9GS0yJOp0HTURE5NGooEnU6SABERGRR6MlpkSdNnGKiIg8Gi0xJerKHsXpnFNBExERqQKdqFaiLikpCQoLufKb37AsMKwPcOeLL7i7YwdpaWlexhMREYl7WqUhUZeUlESfDRvuG5YCcP06O954w5NMIiIiiUQFTaIuKSmJrT/5yX3DigHq1qXnBx94kklERCSRqKBJ1JkZ9OhB+iefMOb4cYbu38/Wt96iwYcfavOmiIhIJaigSdSZGUlJSaVHcQa/6yABERGRytESU2IiXEHTiWpFREQqRwVNYkJr0ERERCKnJabERGhBC54PTQVNRESkcuJmiWlmyWa2zcwWBX5ub2abzOygmX1pZtq7PIFoDZqIiEjk4mmJ+afAnpCf/x74R+dcJ+AS8KYnqSQiKmgiIiKRi4slppnlAuOA3wR+NuAZYHZglI+BSZ6Ek4joIAEREZHIxUVBA/438OdA8OrajYHLzrniwM9FQKtwDzSzt81si5ltOXfuXMyDSuVoHzQREZHIeb7ENLPxwFnn3A+RPN45965zLs85l9e0adMop5NIaROniIhI5OLhYumDgAlm9hyQAdQH/gloYGYpgbVoucAJDzNKFamgiYiIRM7zJaZz7i+dc7nOuXbAy8Aa59xPgbXA1MBoM4B8jyJKBFTQREREIhfPS8y/AP6jmR2kZJ+09z3OI1WggwREREQiFw+bOEs559YB6wK3DwP9vcwjkdNBAiIiIpHTElNiQps4RUREIqclpsSECpqIiEjktMSUmFBBExERiZyWmBITOkhAREQkcipoEhM6SEBERCRyWmJKTGgTp4iISOS0xJSYUEETERGJnJaYEhMqaCIiIpHTElNiQgcJiIiIRE4FTWJCBwmIiIhETktMiQlt4hQREYmclpgSEypoIiIikdMSU2KibEEzM8zM41QiIiKJQQVNYqJsQdPaMxERkcrTUlNiouxBAipoIiIilaelpsRE2TVoOsWGiIhI5amgSUxoE6eIiEjktNSUmAgWNOecCpqIiEgVaakpMREsZCpoIiIiVaelpsREsJD5/X4VNBERkSrSUlNiomxB00ECIiIilaeCJjERWtB0mg0REZGq0VJTYkKbOEVERCKnpabEhAqaiIhI5LTUlJhQQRMREYmclpoSEzpIQEREJHIqaBITwUKmgwRERESqTktNiQlt4hQREYmclpoSEypoIiIikdNSU2JCBU1ERCRyni81zay1ma01s91mVmhmfxoY3sjMVprZgcD3hl5nlcrTQQIiIiKR87ygAcXAf3LOdQcGAn9kZt2BXwKrnXOdgdWBnyVB6EoCIiIikfN8qemcO+Wc2xq4fQ3YA7QCJgIfB0b7GJjkSUCJiDZxioiIRC6ulppm1g7oDWwCmjvnTgXuOg009yqXVJ0KmoiISOTiZqlpZnWBOcC/d85dDb3POecAV87j3jazLWa25dy5c9WQVCpDBU1ERCRycbHUNLNUSsrZZ865uYHBZ8ysReD+FsDZcI91zr3rnMtzzuU1bdq0egLLQ6mgiYiIRM7zpaaZGfA+sMc5979C7loAzAjcngHkV3c2iZwOEhAREYlcitcBgEHAa8AuM9seGPZXwN8Bs8zsTeBHYJo38SQSOs2GiIhI5DwvaM65bwAr5+4R1ZlFoidY0Hw+nzZxioiIVJGWmhIT2gdNREQkclpqSkyooImIiEROS02JiWAhKy4uvu9nEREReTgtNSUmgoXs3r17AKSkeL67o4iISMJQQZOYKFvQdBSniIhI5amgSUyULWjaxCkiIlJ5WmpKTGgNmoiISORU0CQmVNBEREQip4ImMREsZCpoIiIiVaeCJjERXIN29+5dQAVNRESkKlTQJCbMjOTkZBU0ERGRCKigScyooImIiERGBU1iRgVNREQkMipoEjOhBU3nQRMREak8LTUlZlJSUrQGTUREJAIqaBIz2sQpIiISGRU0iZnk5GSKi4tLb4uIiEjlqKBJzISWMhU0ERGRylNBk5hJSUkpva2CJiIiUnkqaBIzWoMmIiISGRU0iRkVNBERkciooEnMqKCJiIhERgVNYiZ0HzSdqFZERKTytNSUmNEaNBERkciooEnMBEuZmWkNmoiISBVoqSkxEyxoaWlpHicRERFJLCpoEjPBgpaenu5xEhERkcSigiYxo4ImIiISGRU0iZlgMQs9mlNEREQeTgVNYiYrKwsAn8/ncRIREZHEooImMRMsaMXFxR4nERERSSxxX9DMbIyZ7TOzg2b2S6/zSOWpoImIiEQmrguamSUD/wKMBboD082su7eppLJU0ERERCIT1wUN6A8cdM4dds7dBb4AJnqcSSopMzMTKDlRrYiIiFRevB9e1wo4HvJzETAgdAQzext4G6BNmzbVl0weKiMjg8GDB9OjRw+vo4iIiCSUeF+D9lDOuXedc3nOubymTZt6HUdCmBkjRowgJyfH6ygiIiIJJd4L2gmgdcjPuYFhIiIiIjVWvBe074HOZtbezNKAl4EFHmcSERERiam43gfNOVdsZn8MLAeSgQ+cc4UexxIRERGJqbguaADOuSXAEq9ziIiIiFSXeN/EKSIiIlLrqKCJiIiIxBkVNBEREZE4o4ImIiIiEmdU0ERERETijAqaiIiISJxRQRMRERGJMypoIiIiInFGBU1EREQkzphzzusMUWNm54Afq+FXNQHOV8PviUea9tqrNk9/bZ52qN3Tr2mvvapj+s8758aEu6NGFbTqYmZbnHN5Xufwgqa9dk471O7pr83TDrV7+jXttXPawfvp1yZOERERkTijgiYiIiISZ1TQIvOu1wE8pGmvvWrz9NfmaYfaPf2a9trL0+nXPmgiIiIicUZr0ERERETijApaOcxsjJntM7ODZvbLMPenm9mXgfs3mVk7D2LGhJm1NrO1ZrbbzArN7E/DjDPMzK6Y2fbA1197kTUWzOyome0KTNeWMPebmf1zYN7vNLM+XuSMBTPrEjJPt5vZVTP792XGqTHz3sw+MLOzZlYQMqyRma00swOB7w3LeeyMwDgHzGxG9aWOnnKm/x/MbG/gvT3PzBqU89gKPyfxrpxp/xszOxHy3n6unMdWuHyId+VM+5ch033UzLaX89iEnu9Q/jIu7j77zjl9lfkCkoFDQAcgDdgBdC8zzi+Afw3cfhn40uvcUZz+FkCfwO16wP4w0z8MWOR11hhN/1GgSQX3PwcsBQwYCGzyOnOMXodk4DTQtqbOe2AI0AcoCBn2P4BfBm7/Evj7MI9rBBwOfG8YuN3Q6+mJ0vSPAlICt/8+3PQH7qvwcxLvX+VM+98Af/aQxz10+RDvX+Gmvcz9/x/w1zVxvgemIewyLt4++1qDFl5/4KBz7rBz7i7wBTCxzDgTgY8Dt2cDI8zMqjFjzDjnTjnntgZuXwP2AK28TRVXJgKfuBIbgQZm1sLrUDEwAjjknKuOkz97wjm3HrhYZnDoZ/tjYFKYh44GVjrnLjrnLgErgbAnm4xn4abfObfCOVcc+HEjkFvtwapBOfO+MiqzfIhrFU17YDk2Dfi8WkNVowqWcXH12VdBC68VcDzk5yIeLCil4wT+mF0BGldLumoU2HTbG9gU5u6fmNkOM1tqZj2qN1lMOWCFmf1gZm+Hub8y74+a4GXK/yNdU+c9QHPn3KnA7dNA8zDj1Jb3wBuUrC0O52Gfk0T1x4HNux+Us4mrps/7p4EzzrkD5dxfo+Z7mWVcXH32VdCkXGZWF5gD/Hvn3NUyd2+lZNNXT+D/APOrOV4sDXbO9QHGAn9kZkO8DlTdzCwNmAD8LszdNXne38eVbNOolYe6m9l/AYqBz8oZpSZ+Tn4FdAR6Aaco2dRX20yn4rVnNWa+V7SMi4fPvgpaeCeA1iE/5waGhR3HzFKAbOBCtaSrBmaWSskb9zPn3Nyy9zvnrjrnrgduLwFSzaxJNceMCefcicD3s8A8SjZphKrM+yPRjQW2OufOlL2jJs/7gDPBTdaB72fDjFOj3wNmNhMYD/w0sKB6QCU+JwnHOXfGOedzzvmB9wg/TTV23geWZZOBL8sbp6bM93KWcXH12VdBC+97oLOZtQ+sSXgZWFBmnAVA8OiNqcCa8v6QJZrAPgjvA3ucc/+rnHFygvvcmVl/St5LCV9QzSzLzOoFb1Oyw3RBmdEWAD+zEgOBKyGrxWuKcv+LrqnzPkToZ3sGkB9mnOXAKDNrGNgMNiowLOGZ2Rjgz4EJzrmb5YxTmc9JwimzL+kLhJ+myiwfEtWzwF7nXFG4O2vKfK9gGRdfn30vj6SI5y9KjtTbT8nROv8lMOxvKfmjBZBByeafg8BmoIPXmaM47YMpWbW7E9ge+HoO+EPgDwPj/DFQSMkRTBuBp7zOHaVp7xCYph2B6QvO+9BpN+BfAu+NXUCe17mj/BpkUVK4skOG1ch5T0kJPQXco2Rfkjcp2Zd0NXAAWAU0CoybB/wm5LFvBD7/B4HXvZ6WKE7/QUr2sQl+9oNHq7cElgRuh/2cJNJXOdP+aeAzvZOShXWLstMe+PmB5UMifYWb9sDwj4Kf85Bxa9R8D0xHecu4uPrs60oCIiIiInFGmzhFRERE4owKmoiIiEicUUETERERiTMqaCIiIiJxRgVNREREJM6ooImIiIjEGRU0ERERkTijgiYiUg4zSzazfzKzQjPbZWYdvM4kIrWDCpqISPn+EjjsnOsB/DPwC4/ziEgtkeJ1ABGReBS41uALzrm+gUFHgHEeRhKRWkQFTUQkvGeB1ma2PfBzI0quzyciEnPaxCkiEl4v4K+dc72cc72AFZRcVFlEJOZU0EREwmsI3AQwsxRgFLDQ00QiUmuooImIhLcfGBi4/R+Axc65Ix7mEZFaxJxzXmcQEYk7ZtYQWAo0ATYAbzvnbnmbSkRqCxU0ERERkTijTZwiIiIicUYFTURERCTOqKCJiIiIxBkVNBEREZE4o4ImIiIiEmdU0ERERETijAqaiIiISJxRQRMRERGJM/8/CZBKdApXA/QAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "abc = pyabc.ABCSMC(\n", " model,\n", " prior,\n", " pyabc.PNormDistance(p=2),\n", " population_size=pop_size,\n", " eps=pyabc.SilkOptimalEpsilon(k=10),\n", ")\n", "\n", "abc.new(db_path, y_obs)\n", "\n", "h = abc.run(max_total_nr_simulations=n_samples)\n", "\n", "plot_posterior(h)\n", "plot_pars_over_data(h);" ] }, { "cell_type": "markdown", "id": "dc829f6b-2750-4c56-853d-b6c0b5e7fa12", "metadata": {}, "source": [ "This approach more or less reliably converges to the global minimum.\n", "\n", "Note that this threshold method may suffer from deteriorating acceptance rates and may thus perform inferior to quantile based thresholds on problems where the latter are applicable. The `SilkOptimalEpsilon` can be also be combined with adaptive distances.\n", "\n", "So, when to use such advanced threshold strategies? For most low-dimensional problems, a simple quantile-based strategy may be sufficient. However, as seen above, especially in the presence of local optima, approaches such as the above one may be necessary. At the least, carefully checking the analysis, e.g. examining low-distance particles, may generally be a good idea." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 5 }