Mindlab_Course_PartII.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from notebook.services.config import ConfigManager\n",
    "cm = ConfigManager()\n",
    "cm.update('livereveal', {\n",
    "        'width': 1024,\n",
    "        'height': 768,\n",
    "        'scroll': True,\n",
    "})\n",
    "import pandas as pd\n",
    "import pylab as plt\n",
    "import pystan\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from matplotlib.transforms import Transform\n",
    "from matplotlib.ticker import (\n",
    "    AutoLocator, AutoMinorLocator)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](./assets/DJlogo_alpha.png?raw=true)<!-- .element height=\"80%\" width=\"80%\" -->\n",
    "\n",
    "<http://www.DataJavelin.com>\n",
    "## Dr Peter Hurley & Dr Phil Rooney"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Bayesian Data Analysis Workflow with Stan\n",
    "\n",
    "A good workflow for developing and testing models is essential!\n",
    "\n",
    "1. Model Building\n",
    "2. Model Inference\n",
    "3. Model Checking\n",
    "4. Model Improvment\n",
    "\n",
    "For more detailed information see [Bayesian Data Analysis](http://www.stat.columbia.edu/~gelman/book/) book by Andrew Gelman and co-authors and [Michael Betancourt's case study](https://betanalpha.github.io/assets/case_studies/principled_bayesian_workflow.html#1_bayesian_modeling_and_inference)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lets go through steps with an example problem\n",
    "\n",
    "## Golf putting\n",
    "An example from [Andrew Gelman's blog](https://statmodeling.stat.columbia.edu/2019/03/21/new-golf-putting-data-and-a-new-golf-putting-model/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>n</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>1443</td>\n",
       "      <td>1346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>694</td>\n",
       "      <td>577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>455</td>\n",
       "      <td>337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>353</td>\n",
       "      <td>208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>272</td>\n",
       "      <td>149</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   x     n     y\n",
       "0  2  1443  1346\n",
       "1  3   694   577\n",
       "2  4   455   337\n",
       "3  5   353   208\n",
       "4  6   272   149"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=pd.read_csv('orig_golf_data.txt',sep='\\s+')\n",
    "data[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p=data['y']/data['n']\n",
    "error=np.sqrt(p*(1-p)/data['n'])\n",
    "plt.errorbar(data['x'],data['y']/data['n'],yerr=error,fmt='o')\n",
    "plt.xlabel('Distance to hole (feet)');\n",
    "plt.ylabel('Probability of Success' );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "With error bars taken as simple classical standard deviations $\\sqrt{\\hat{p}_j(1-\\hat{p}_j)/n_j}$ where $\\hat{p}_j=y_j/n_j$ success rate for putts taken at distance $x_j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model Building\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Build generative model\n",
    "1. construct a probabilistic generative model of the observation process. \n",
    "2. generative observation model can be a crude approximation to the complexity of the true measurement process\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "An ideal generative model will use mathematical functions to describe how an observation is produced based on a given model configuration. It is described as generative as it models how the data was generated (i.e. joint distribution)\n",
    "\n",
    "Simple approximations are often good enough to answer even sophisticated questions. We describe the model as generative as we are trying to build a model that replicates how the data was generated. \n",
    "\n",
    "Often it is helpful to visualise the model via a probabilistic graphical model. These visualisations are a good way of understanding and showing how different variables relate and depend on each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 590.551x354.331 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import daft\n",
    "pgm = daft.PGM(shape=(5,3),observed_style=\"inner\",dpi=150)\n",
    "\n",
    "# Hierarchical parameters.\n",
    "pgm.add_node(\"a\", r\"$a$\", 0.5, 2)\n",
    "pgm.add_node(\"b\", r\"$b$\", 1.5, 2)\n",
    "\n",
    "# Latent variable.\n",
    "pgm.add_node(\"x\", r\"$x_j$\", 1, 1)\n",
    "\n",
    "# Data.\n",
    "pgm.add_node(\"y\", r\"$y_j$\", 2, 1, observed=True)\n",
    "pgm.add_node(\"n\", r\"$n_j$\", 3, 1)\n",
    "\n",
    "pgm.add_edge('a','y')\n",
    "pgm.add_edge('b','y')\n",
    "pgm.add_edge('x','y')\n",
    "pgm.add_edge('n','y')\n",
    "\n",
    "pgm.add_plate([0.5, 0.5, 3, 1], label=r\"$j = 1, \\ldots, J$\", shift=-0.1)\n",
    "\n",
    "# Render and save.\n",
    "pgm.render()\n",
    "pgm.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Our first model, Logistic regression \n",
    "We want to model the probability of success in golf putting as a function of distance from the hole? the natural starting point would be logistic regression:\n",
    "\n",
    "$$y_j\\sim\\mbox{binomial}(n_j, \\mbox{logit}^{-1}(a + bx_j)),\\mbox{ for } j=1,\\dots, J.$$\n",
    "\n",
    "*\"the binomial distribution with parameters $n$ and $p$ is the discrete probability distribution of the number of successes in a sequence of n independent experiments.\"*\n",
    "\n",
    "This is exactly what we want"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Logistic regression overview\n",
    "\n",
    "The Binomial distribution gives us the number of successfull trials from N independent trials, with probability of success $P$. We know:\n",
    "\n",
    "* $y_j$ the number of successfull putts at distance $x_j$\n",
    "* $n_j$ the number of putting attempts at distance $x_j$\n",
    "\n",
    "We don't know $P$. But we know it will change with distance.\n",
    "\n",
    "*The aim of logistic regression is to predict some unknown probability P for a successful event, for any given linear combination of independent variables (features).*\n",
    "\n",
    "i.e. $$P=f(x)$$\n",
    "\n",
    "**Problem**\n",
    "$$0\\le P\\le1$$\n",
    "But in Linear regression, where $y=a+bx$:\n",
    "$$-\\infty \\le y \\le \\infty$$\n",
    "$$-\\infty \\le x \\le \\infty$$\n",
    "\n",
    "Our function is going to have to do some sort of transformation to map from $[-\\infty,\\infty]$ to $[0,1]$.\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could try taking the odds ratio, i.e.:\n",
    "    $$\\frac{P}{1-P}$$\n",
    "but that only gives us:\n",
    "$$0\\le \\frac{P}{1-P}\\le\\infty$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But if we take the logarithm,i.e.:\n",
    "    $$\\log\\frac{P}{1-P}$$\n",
    "We get:\n",
    "$$-\\infty\\le\\log\\frac{P}{1-P}\\le\\infty$$\n",
    "\n",
    "This works. Because the transformation has many uses its been given the name of:\n",
    "\n",
    "$$\\mbox{logit(P)}=\\log\\frac{P}{1-P}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logit(P):\n",
    "    return np.log(P/(1-P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(0,1,0.01),logit(np.arange(0,1,0.01)))\n",
    "plt.xlabel('P');\n",
    "plt.ylabel(r'logit(P)');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### logit and inverse logit\n",
    "logit is a link function that can map continuous variables to a range of 0-1. useful when we need a probability output.\n",
    "\n",
    "combining the $\\mbox{logit(P)}$ with the linear regression equations gives us **logisitic regression**\n",
    "\n",
    "$$\\mbox{logit(P)}=y=a+bx$$\n",
    "\n",
    "we need P, rearrange to get inverse logit function:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inv_logit(a,b,x):\n",
    "    return 1/(1+np.exp(-1*(a+b*x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in log\n",
      "  \n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in log\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.ticker as ticker\n",
    "\n",
    "def inv_logit_plot(x):\n",
    "    return 1/(1+np.exp(-1*(x)))\n",
    "def logit_plot(x):\n",
    "    return np.log(x/(1-x))\n",
    "\n",
    "cmap=sns.color_palette(\"colorblind\")\n",
    "fig=plt.figure(figsize=(10,4))\n",
    "x=np.arange(-5,5,0.5)\n",
    "ax1=fig.add_subplot(1,2,1)\n",
    "a=0\n",
    "for i,b in enumerate([-2,-1,1,2]):\n",
    "    ax1.plot(x,a+b*x,label=r'$a$ = {}, $b$ = {}'.format(a,b),c=cmap[i])\n",
    "\n",
    "ax1.legend()\n",
    "ax1.set_xlabel('x')\n",
    "ax1.set_ylabel('y')\n",
    "ax1.set_ylim(-3,3)\n",
    "secax = ax1.secondary_yaxis('right', functions=(inv_logit_plot, logit_plot))\n",
    "secax.yaxis.set_minor_locator(AutoMinorLocator())\n",
    "secax.set_ylabel('$P$')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "ax3=fig.add_subplot(1,2,2)\n",
    "b=-1\n",
    "for i,a in enumerate([-1,1,2]):\n",
    "    ax3.plot(x,a+b*x,label=r'$a$ = {}, $b$ = {}'.format(a,b),c=cmap[i])\n",
    "ax3.set_xlabel('x')\n",
    "ax3.set_ylabel('y')\n",
    "ax3.set_ylim(-3,3)\n",
    "\n",
    "secax = ax3.secondary_yaxis('right', functions=(inv_logit_plot, logit_plot))\n",
    "secax.yaxis.set_minor_locator(AutoMinorLocator())\n",
    "secax.set_ylabel('$P$')\n",
    "\n",
    "ax3.legend()\n",
    "\n",
    "plt.subplots_adjust(wspace=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig=plt.figure(figsize=(10,4))\n",
    "x=np.arange(-5,5,0.5)\n",
    "ax1=fig.add_subplot(1,2,1)\n",
    "a=0\n",
    "for i,b in enumerate([-2,-1,1,2]):\n",
    "    plt.plot(x,inv_logit(a,b,x),label=r'$a$ = {}, $b$ = {}'.format(a,b),c=cmap[i])\n",
    "plt.legend()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('p')\n",
    "\n",
    "ax1.set_ylim(0.001,0.9999)\n",
    "secax = ax1.secondary_yaxis('right', functions=(logit_plot,inv_logit_plot))\n",
    "secax.yaxis.set_minor_locator(AutoMinorLocator())\n",
    "secax.set_ylabel('$y$')\n",
    "\n",
    "ax3=fig.add_subplot(1,2,2)\n",
    "b=-1\n",
    "for i,a in enumerate([-1,1,2]):\n",
    "    ax3.plot(x,inv_logit(a,b,x),label=r'$\\alpha$ = {}, $\\beta$ = {}'.format(a,b),c=cmap[i])\n",
    "ax3.set_xlabel('x')\n",
    "ax3.set_ylabel('p')\n",
    "ax3.set_ylim(0.001,0.9999)\n",
    "\n",
    "secax = ax3.secondary_yaxis('right', functions=(logit_plot,inv_logit_plot ))\n",
    "secax.yaxis.set_minor_locator(AutoMinorLocator())\n",
    "secax.set_ylabel('$y$')\n",
    "\n",
    "ax3.legend()\n",
    "\n",
    "plt.subplots_adjust(wspace=0.5)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Always good to think about problem and put informative priors if possible.\n",
    "\n",
    "Thinking about our model,\n",
    "Priors:\n",
    "* $a$ going to be larger than 0 since we know more than half the putts are made when distance is zero, so put something sensible e.g. 0 to 10\n",
    "* $b$ has to be negative (probability is not going to increase with distance) it is also going to be larger than -1 since we know the longer distance plots are not impossible"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Writing the model in Stan\n",
    "* A Stan program is organized into a sequence of named blocks\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "example_model=\"\"\"functions {\n",
    "// ... function declarations and definitions ...\n",
    "}\n",
    "data {\n",
    "// ... declarations ...\n",
    "}\n",
    "transformed data {\n",
    "// ... declarations ... statements ...\n",
    "}\n",
    "parameters {\n",
    "// ... declarations ...\n",
    "} \n",
    "transformed parameters {\n",
    "// ... declarations ... statements ...}\n",
    "model {\n",
    "// ... declarations ... statements ...\n",
    "}\n",
    "generated quantities {\n",
    "// ... declarations ... statements ...\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Other things to note:\n",
    "* Add comments with `\\\\`\n",
    "* Sampling statements with `~`\n",
    "* Can print output with `print()`\n",
    "* `;` at end of each line\n",
    "\n",
    "\n",
    "Documentation for Stan: https://mc-stan.org/docs/2_19/stan-users-guide/index.html\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "golf_model_1=\"\"\"\n",
    "data {\n",
    "  int J;\n",
    "  int n[J];\n",
    "  vector[J] x;\n",
    "  int y[J];\n",
    "  int fit;           //boolean for fitting\n",
    "}\n",
    "parameters {\n",
    "  real<lower=0,upper=10> a;\n",
    "  real<lower=-1,upper=0> b;\n",
    "}\n",
    "model {\n",
    "  if (fit>0){\n",
    "  y ~ binomial_logit(n, a + b*x);\n",
    "}\n",
    "}\n",
    "generated quantities {\n",
    "int y_pred[J];\n",
    "for (i in 1:J){\n",
    "y_pred[i]=binomial_rng(n[i], inv_logit(a + b*x[i]));\n",
    "}\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_9d53bd31a44b027fe0ac8c6c89a16c2f NOW.\n"
     ]
    }
   ],
   "source": [
    "sm=pystan.StanModel(model_code=golf_model_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Analyse the Generative Ensemble\n",
    "* Analyse a range of samples from generative model\n",
    "* Check outputs are realistic\n",
    "* Good way of checking model (especially priors) is behaving appropriately and how you expect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Before drawing inferences from a real observation, we first want to analyse a range of samples from our generative model to check that the resulting putting success relation is realistic. This is a good way of checking that the prior distribution is sensible and the model is behaving approriately.\n",
    "\n",
    "To do that we first simulate parameters and observations from the complete generative model. We do this with the Python interface to Stan, PyStan.\n",
    "\n",
    "Simulating from the generative model allows us to see how our model and the prior choices we have made, affect the trend and whether they are realistic or whether we need to go back and rethink the priors. Simulating from the generative model also gives us simulated data for which we know the true parameter values. We can then use this simulated data to carry out the same inference procedures we would run on real data to test whether we can accurately recover the true parameter values. This gives us confidence that when we run it on real data we can trust the parameter values we get."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "model_data={\n",
    "        'J':len(data),\n",
    "        'n':data['n'],\n",
    "        'x':data['x'],\n",
    "        'y':data['y'],\n",
    "        'fit':0}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "fit=sm.sampling(data=model_data,chains=4,iter=1000,seed=194838)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_9d53bd31a44b027fe0ac8c6c89a16c2f.\n",
       "4 chains, each with iter=1000; warmup=500; thin=1; \n",
       "post-warmup draws per chain=500, total post-warmup draws=2000.\n",
       "\n",
       "             mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a            4.99    0.07    2.9   0.26   2.38    5.0   7.51   9.83   1639    1.0\n",
       "b            -0.5  7.4e-3   0.29  -0.98  -0.76   -0.5  -0.25  -0.03   1519    1.0\n",
       "y_pred[1]  1244.0   10.21 309.53  373.4 1161.8 1417.0 1441.0 1443.0    920    1.0\n",
       "y_pred[2]  569.23    5.84 182.06   95.0 501.45  674.0  692.0  694.0    972    1.0\n",
       "y_pred[3]  352.48    4.26  137.8   30.0  278.0  432.5  453.0  455.0   1045    1.0\n",
       "y_pred[4]  257.44    3.52 118.02   9.41  171.0  325.0  351.0  353.0   1122    1.0\n",
       "y_pred[5]  185.31    2.77  98.43    3.0   94.0  240.0 269.55  272.0   1265    1.0\n",
       "y_pred[6]  162.49    2.66  97.42    1.0   61.0  210.5  252.0  256.0   1340    1.0\n",
       "y_pred[7]  141.42     2.5  94.85    0.0   34.0  176.5  235.0  240.0   1440    1.0\n",
       "y_pred[8]  118.35    2.34  87.59    0.0   18.0  135.5  211.0  217.0   1397    1.0\n",
       "y_pred[9]  100.61    2.28  81.84    0.0    9.0  100.0  191.0  200.0   1284    1.0\n",
       "y_pred[10] 109.97    2.79  97.67    0.0    5.0   94.0  223.0  237.0   1226    1.0\n",
       "y_pred[11]  86.67    2.35  83.36    0.0    2.0   59.0  186.0  202.0   1257    1.0\n",
       "y_pred[12]  76.58    2.21   79.0    0.0    1.0   40.5  171.0  192.0   1274    1.0\n",
       "y_pred[13]  64.67    1.96  71.22    0.0    0.0   24.0  150.0  174.0   1314    1.0\n",
       "y_pred[14]  57.98    1.77  67.77    0.0    0.0   15.0  134.0  167.0   1461    1.0\n",
       "y_pred[15]  65.49    2.03  80.65    0.0    0.0   11.0 151.55  201.0   1576    1.0\n",
       "y_pred[16]  59.71    1.91  77.19    0.0    0.0    7.0  136.0  195.0   1636    1.0\n",
       "y_pred[17]  55.18    1.85  74.61    0.0    0.0    4.0 122.55  191.0   1625    1.0\n",
       "y_pred[18]  40.39    1.41  56.79    0.0    0.0    2.0   86.0  147.0   1612    1.0\n",
       "y_pred[19]  39.65    1.45  57.92    0.0    0.0    1.0   76.0  152.0   1598    1.0\n",
       "lp__        -1.71    0.04   1.16   -4.8   -2.2  -1.38  -0.86   -0.5    702   1.01\n",
       "\n",
       "Samples were drawn using NUTS at Tue Feb 25 14:08:19 2020.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "* $\\hat{R}$ compares variation within and between chains. You want $\\hat{R} < 1.1$\n",
    "* The amount by which autocorrelation within the chains increases uncertainty in estimates can be measured by effective sample size, $n_{eff}$. Typical MCMC has a low $n_{eff}$ and requires thinning (as to keep all samples would be too memory intensive). Since Stan is efficient, no need to chuck samples away. If $n_{eff} / N < 0.001$, then there is a problem with model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:n_eff / iter looks reasonable for all parameters\n",
      "INFO:pystan:Rhat looks reasonable for all parameters\n",
      "INFO:pystan:No divergent transitions found.\n",
      "INFO:pystan:No transitions that ended prematurely due to maximum tree depth limit\n",
      "INFO:pystan:Chain 1: E-BFMI (= 0.942) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:Chain 2: E-BFMI (= 1.04) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:Chain 3: E-BFMI (= 0.949) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:Chain 4: E-BFMI (= 1.02) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:E-BFMI indicated no pathological behavior\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'n_eff': True,\n",
       " 'Rhat': True,\n",
       " 'divergence': True,\n",
       " 'treedepth': True,\n",
       " 'energy': True}"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pystan.diagnostics.check_hmc_diagnostics(fit,verbose=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "*Divergent transitions*:Critical warning. Step size is too large. Try fixing by increasing `adapt_delta` e.g. `fit=sm.sampling(data=data,control=dict(adapt_delta=0.9)`\n",
    "\n",
    "*Maximum Tree depth*: Not as critical. A detail specific to NUTS algorithm. Fix by increasing tree depth e.g. `fit=sm.sampling(data=data,control=dict(max_treedepth=15)`\n",
    "\n",
    "*BFMI low*: Bayesian Fraction of Missing Information. Adaptation phase of the Markov Chains did not turn out well and those chains likely did not explore the posterior distribution efficiently. Can try running for more iterations, but probably need to re-parameterise model.\n",
    "\n",
    "\n",
    "Details on diagnostics are [here](https://mc-stan.org/misc/warnings.html). Good explanation for divergences can also be found [here](https://dev.to/martinmodrak/taming-divergences-in-stan-models-5762)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Prior distribution on parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/matplotlib/contour.py:1000: UserWarning: The following kwargs were not used by contour: 'normed'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x7fbcc879d630>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tri=sns.PairGrid(pd.DataFrame(np.vstack((fit['a'],fit['b'])).T,columns=[r'$a$',r'$b$']))\n",
    "tri.map_diag(plt.hist)\n",
    "tri.map_lower(sns.kdeplot,shade=True,shade_lowest=False,cmap=\"Blues_d\",alpha=0.3,n_levels=10,normed=True)\n",
    "tri.map_upper(plt.scatter,alpha=0.5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lets look at Prior predicitive distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "for i in range(0,1000,100):\n",
    "    plt.plot(data['x'],fit['y_pred'][i,:]/data['n'],'b',alpha=0.2)\n",
    "plt.plot(data['x'],data['y']/data['n'],'r')\n",
    "plt.xlabel('Distance to hole (feet)');\n",
    "plt.ylabel('Probability of Success' );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Fit the Simulated Observations and Evaluate\n",
    "* Test ability to fit model (testing fitting algorithms)\n",
    "* Fit samples from the prior predicitive distribution\n",
    "* Compare Posterior probabillity distribution with truth\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "We have generated a sample of simulated observations from our generative model. To test our ability to draw inferences with the model when using real data, we can attempt to fit each of these simulated observations and construct a posterior distribution on the parameters of interest. The advantage of fitting simulated results is we know the truth and so we can compare the posterior probability distributions coming from the inference with the true values. Lets start with fitting one sample from our simulated observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s=800\n",
    "plt.plot(data['x'],fit['y_pred'][s,:]/data['n'],'bo',alpha=0.2,label='Predicted data')\n",
    "plt.plot(data['x'],inv_logit(fit['a'][s],fit['b'][s],data['x']),'r',label='Model')\n",
    "plt.xlabel('Distance to hole (feet)');\n",
    "plt.ylabel('Probability of Success' );\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "data_samp={\n",
    "        'J':len(data),\n",
    "        'n':data['n'],\n",
    "        'x':data['x'],\n",
    "        'y':fit['y_pred'][s,:].astype('int'),\n",
    "        'fit':1}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "fit_samp=sm.sampling(data=data_samp,chains=4,iter=1000,seed=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_9d53bd31a44b027fe0ac8c6c89a16c2f.\n",
       "4 chains, each with iter=1000; warmup=500; thin=1; \n",
       "post-warmup draws per chain=500, total post-warmup draws=2000.\n",
       "\n",
       "             mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a             4.1  4.4e-3    0.1   3.91   4.03   4.09   4.15   4.29    483   1.01\n",
       "b           -0.39  4.4e-4 9.8e-3  -0.41   -0.4  -0.39  -0.39  -0.37    491   1.01\n",
       "y_pred[1]  1391.8    0.25   8.28 1375.0 1386.0 1392.0 1398.0 1407.6   1086    1.0\n",
       "y_pred[2]  658.16    0.17   6.27  645.0  654.0  658.0  662.0  670.0   1410    1.0\n",
       "y_pred[3]  421.17    0.16   5.93  409.0  417.0  421.0  425.0  432.0   1397    1.0\n",
       "y_pred[4]  315.72    0.14    5.9  304.0  312.0  316.0  320.0  327.0   1674   1.01\n",
       "y_pred[5]  231.17    0.15   6.27  219.0  227.0  231.0  235.0  243.0   1640    1.0\n",
       "y_pred[6]  202.92    0.15   6.64  190.0  199.0  203.0  208.0  215.0   1931    1.0\n",
       "y_pred[7]  172.94    0.17   7.14  159.0  168.0  173.0  178.0  187.0   1766    1.0\n",
       "y_pred[8]  137.88    0.16   7.34  124.0  133.0  138.0  143.0  153.0   1982    1.0\n",
       "y_pred[9]  108.53    0.17   7.52   94.0  103.0  109.0 113.55  123.0   2017    1.0\n",
       "y_pred[10] 104.83    0.19    8.2   89.0   99.0  105.0  110.0  121.0   1798    1.0\n",
       "y_pred[11]  70.54    0.16   7.07   57.0   66.0   70.0   75.0   84.0   1973    1.0\n",
       "y_pred[12]  51.12    0.15   6.45   39.0   47.0   51.0   55.0   64.0   1860    1.0\n",
       "y_pred[13]  34.29    0.13   5.57   24.0   31.0   34.0   38.0   45.0   1732    1.0\n",
       "y_pred[14]  23.62    0.11   4.81   14.4   20.0   23.0   27.0   33.0   1754    1.0\n",
       "y_pred[15]  20.24    0.11   4.56   12.0   17.0   20.0   23.0   29.0   1770    1.0\n",
       "y_pred[16]  13.86    0.09   3.78    7.0   11.0   14.0   16.0   21.0   1967    1.0\n",
       "y_pred[17]   9.35    0.08   3.07    4.0    7.0    9.0   11.0   16.0   1507    1.0\n",
       "y_pred[18]   4.98    0.05   2.23    1.0    3.0    5.0    6.0   10.0   2020    1.0\n",
       "y_pred[19]   3.49    0.05   1.88    0.0    2.0    3.0    5.0    8.0   1598    1.0\n",
       "lp__        -2019    0.05   1.15  -2022  -2019  -2019  -2018  -2018    525    1.0\n",
       "\n",
       "Samples were drawn using NUTS at Tue Feb 25 14:24:20 2020.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_samp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n_eff': True,\n",
       " 'Rhat': True,\n",
       " 'divergence': True,\n",
       " 'treedepth': True,\n",
       " 'energy': True}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pystan.diagnostics.check_hmc_diagnostics(fit_samp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/seaborn/distributions.py:423: UserWarning: The following kwargs were not used by contour: 'normed'\n",
      "  cset = contour_func(xx, yy, z, n_levels, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(2.9783182618673516, 4.978318261867352)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tri=sns.PairGrid(pd.DataFrame(np.vstack((fit_samp['a'],fit_samp['b'])).T,columns=[r'$a$',r'$b$']))\n",
    "tri.map_diag(plt.hist,alpha=0.3,color='red')\n",
    "tri.map_lower(sns.kdeplot,shade=True,shade_lowest=False,cmap=\"Reds_d\",alpha=0.3,n_levels=10,normed=True)\n",
    "tri.map_upper(plt.scatter,alpha=0.5,color='red')\n",
    "\n",
    "#g.axes[0,1].set_axis_off()\n",
    "tri.axes[0,0].axvline(x=fit['a'][s],color='g')\n",
    "tri.axes[1,0].axvline(x=fit['a'][s],color='g')\n",
    "tri.axes[1,0].axhline(y=fit['b'][s],color='g')\n",
    "tri.axes[1,1].axvline(x=fit['b'][s],color='g')\n",
    "tri.axes[0,1].axvline(x=fit['b'][s],color='g')\n",
    "tri.axes[0,1].axhline(y=fit['a'][s],color='g')\n",
    "\n",
    "#tri.data=(pd.DataFrame(np.vstack((fit['a'],fit['b'])).T,columns=[r'$\\alpha$',r'$\\beta$']))\n",
    "#tri.map_diag(plt.hist,color='blue',alpha=0.1)\n",
    "#tri.map_lower(sns.kdeplot,shade=True,shade_lowest=False,cmap=\"Blues_d\",alpha=0.3,n_levels=10,normed=True)\n",
    "#tri.map_upper(plt.scatter,alpha=0.5,color='blue')\n",
    "\n",
    "tri.axes[1,0].set_xlim(fit['a'][s]-1,fit['a'][s]+1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "When analysing posterior probability distributions for model parameters, it is good practise to do so alongside the prior distribution. This allows us to visualise whether we are gaining much information from the data, beyond our prior knowledge."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lets plot replicated data from our model fit, and compare to fitted data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7.5))\n",
    "plt.violinplot(fit_samp['y_pred']/data['n'].values,positions=data['x'],showextrema=False);\n",
    "plt.plot(data['x'],fit['y_pred'][s,:]/data['n'],'o')\n",
    "plt.xlabel('Distance to hole (feet)');\n",
    "plt.ylabel('Probability of Success' );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Evaluate Prior-Posterior Consistency\n",
    "\n",
    "We have fitted one sample. To be confident our chosen fitting algorithm works for all possible values (i.e. within Prior) we should fit *many* samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    " To check the model and our inference technique (i.e. the algorithm used to fit the data) is perfoming appropriately, you can carry out simulated-based calibration. This involved fitting each prior sample as if it were data. The posterior distributions on the fits should look like the prior. This approach checks this is correct. If everything is working, the plots below for each parameter should be uniform.\n",
    " \n",
    "For details, see [Talts et al. 2018](https://arxiv.org/pdf/1804.06788) and [Michael Betancourt's case study](https://betanalpha.github.io/assets/case_studies/principled_bayesian_workflow.html#22_computational_faithfulness)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pystan:18 of 2000 iterations ended with a divergence (0.9 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:1 of 2000 iterations ended with a divergence (0.05 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:1 of 2000 iterations ended with a divergence (0.05 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:23 of 2000 iterations ended with a divergence (1.15 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:17 of 2000 iterations ended with a divergence (0.85 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:25 of 2000 iterations ended with a divergence (1.25 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:1 of 2000 iterations ended with a divergence (0.05 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:2 of 2000 iterations ended with a divergence (0.1 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:8 of 2000 iterations ended with a divergence (0.4 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:1 of 2000 iterations ended with a divergence (0.05 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:2 of 2000 iterations ended with a divergence (0.1 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:4 of 2000 iterations ended with a divergence (0.2 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:4 of 2000 iterations ended with a divergence (0.2 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:1 of 2000 iterations ended with a divergence (0.05 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:2 of 2000 iterations ended with a divergence (0.1 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:1 of 2000 iterations ended with a divergence (0.05 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:13 of 2000 iterations ended with a divergence (0.65 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n"
     ]
    }
   ],
   "source": [
    "samples=[]\n",
    "n_samp=100\n",
    "a_cal=np.empty(n_samp)\n",
    "b_cal=np.empty(n_samp)\n",
    "for s in range(0,n_samp):\n",
    "    #set data to one of the samples\n",
    "    data_samp={\n",
    "        'J':len(data),\n",
    "        'n':data['n'],\n",
    "        'x':data['x'],\n",
    "        'y':fit['y_pred'][s,:].astype('int'),\n",
    "        'fit':1}\n",
    "    #fit the data\n",
    "    fit_tmp=sm.sampling(data=data_samp,chains=4,iter=1000,seed=10,verbose=False)\n",
    "    #append samples to list\n",
    "    samples.append(pd.DataFrame(np.vstack((fit_tmp['a'],fit_tmp['b'])).T,columns=['a','b']))\n",
    "    #carry out calibration statistic\n",
    "    a_cal[s]=np.sum(fit_tmp['a']<fit['a'][s])\n",
    "    b_cal[s]=np.sum(fit_tmp['b']<fit['b'][s])\n",
    "    \n",
    "samples=pd.concat(samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "plt.subplot(2,2,1)\n",
    "plt.hist(samples['a'],density=True,alpha=0.5,label='Posterior');\n",
    "plt.hist(fit['a'],density=True,alpha=0.5,label='Prior');\n",
    "plt.xlabel(r'$a$');\n",
    "plt.subplot(2,2,2)\n",
    "plt.hist(samples['b'],density=True,alpha=0.5,label='Posterior');\n",
    "plt.hist(fit['b'],density=True,alpha=0.5,label='Prior');\n",
    "plt.xlabel(r'$b$');\n",
    "plt.subplot(2,2,3)\n",
    "plt.hist(a_cal)\n",
    "plt.xlabel('Rank Statistic')\n",
    "plt.subplot(2,2,4)\n",
    "plt.hist(b_cal)\n",
    "plt.xlabel('Rank Statistic')\n",
    "plt.subplots_adjust(hspace=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Analyse Posterior Behaviours\n",
    "\n",
    "**Z score**\n",
    "$$z=|(\\mu_{post}-\\theta_{true})/\\sigma_{post}|$$\n",
    "\n",
    "how accurately the posterior recovers ground truth and whether there is any bias. Close to zero indicate more accurate, less biased posteriors.\n",
    "\n",
    "**Posterior Shrinkage**\n",
    "$$s=1-\\sigma^2_{post}/\\sigma^2_{prior}$$\n",
    "\n",
    "quantifies how much the posterior learns from a given observation. Close to zero indicates dominated by prior, close to one indicates dominated by data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Assuming that we are accurately recovering posteriors across all of the simulated observations then we can proceed to analyse the range of behaviors in these posteriors. For example, the posterior z-score of a given parameter,\n",
    "\n",
    "$$z=|(\\mu_{post}-\\theta_{true})/\\sigma_{post}|$$\n",
    "\n",
    "quantifies how accurately the posterior recovers the ground truth and whether there is any bias. Values close to zero indicate more accurate, less biased posteriors.\n",
    "\n",
    "At the same time the posterior shrinkage,\n",
    "\n",
    "$$s=1-\\sigma^2_{post}/\\sigma^2_{prior}$$\n",
    "\n",
    "quantifies how much the posterior learns from a given observation. Our visualisation of the posterior and prior for $\\alpha$ and $\\beta$ had already indicated that the inference had given us information on both parameters. Shrinkage allows us to quantify this. A value near zero indicates that the data provide little information beyond that encoded in the prior distribution while shrinkage near one indicates highly informative observations.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src=\"./assets/sensitivity.png\" alt=\"Drawing\" style=\"width: 600px;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def zscore(posterior, truth):\n",
    "    return np.abs((np.mean(posterior)-truth)/np.std(posterior))\n",
    "def shrinkage(posterior,prior):\n",
    "    return 1-(np.var(posterior)/np.var(prior))\n",
    "n_post_samps=int(len(samples)/n_samp)\n",
    "\n",
    "z_score_array=np.empty((2,n_samp))\n",
    "shrinkage_array=np.empty((2,n_samp))\n",
    "for i in range(0,n_samp):\n",
    "    z_score_array[0,i]=zscore(samples['a'][i*n_post_samps:(i+1)*n_post_samps],fit['a'][i])\n",
    "    z_score_array[1,i]=zscore(samples['b'][i*n_post_samps:(i+1)*n_post_samps],fit['b'][i])\n",
    "    shrinkage_array[0,i]=shrinkage(samples['a'][i*n_post_samps:(i+1)*n_post_samps],fit['a'])\n",
    "    shrinkage_array[1,i]=shrinkage(samples['b'][i*n_post_samps:(i+1)*n_post_samps],fit['b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g=sns.PairGrid(pd.DataFrame(np.vstack((shrinkage_array[0,:],z_score_array[0,:])).T,columns=['Shrinkage','Zscore']))\n",
    "g.map_diag(plt.hist,color='blue',alpha=0.5,bins=np.arange(0,5,0.1))\n",
    "g.map_lower(plt.scatter,color='blue',alpha=0.5)\n",
    "g.data=pd.DataFrame(np.vstack((shrinkage_array[1,:],z_score_array[1,:])).T,columns=['Shrinkage','Zscore'])\n",
    "g.map_diag(plt.hist,color='red',alpha=0.5,bins=np.arange(0,5,0.1))\n",
    "g.map_lower(plt.scatter,color='red',alpha=0.5)\n",
    "g.axes[1,0].set_xlim(0,1.2)\n",
    "g.axes[0,1].set_axis_off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model Inference\n",
    "Having satisfied ourselves that model is behaving as we expect, lets fit our model to observational data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "model_data={\n",
    "        'J':len(data),\n",
    "        'n':data['n'],\n",
    "        'x':data['x'],\n",
    "        'y':data['y'],\n",
    "        'fit':1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "fit_obs=sm.sampling(data=model_data,chains=4,iter=1000,seed=194838)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference for Stan model: anon_model_9d53bd31a44b027fe0ac8c6c89a16c2f.\n",
       "4 chains, each with iter=1000; warmup=500; thin=1; \n",
       "post-warmup draws per chain=500, total post-warmup draws=2000.\n",
       "\n",
       "             mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
       "a            2.23  2.9e-3   0.06   2.12   2.19   2.23   2.27   2.36    422   1.01\n",
       "b           -0.26  3.4e-4 6.8e-3  -0.27  -0.26  -0.26  -0.25  -0.24    409   1.01\n",
       "y_pred[1]  1224.0     0.5  16.06 1192.0 1213.0 1224.0 1235.0 1255.0   1050    1.0\n",
       "y_pred[2]  563.54     0.3  11.35  541.0  556.0  563.0  571.0  585.6   1422    1.0\n",
       "y_pred[3]   350.3    0.22   9.53  331.0  344.0  350.0  357.0  368.0   1955    1.0\n",
       "y_pred[4]  255.06    0.21   8.69  237.0  249.0  255.0  261.0  272.0   1707    1.0\n",
       "y_pred[5]  181.64    0.19    8.2  166.0  176.0  182.0  187.0  197.0   1824    1.0\n",
       "y_pred[6]  156.01    0.18   7.99  140.0  150.0  156.0  162.0  172.0   1880    1.0\n",
       "y_pred[7]  131.12    0.17   7.78  116.0  126.0  131.0  137.0  146.0   2012    1.0\n",
       "y_pred[8]  104.66    0.17   7.57   90.0  100.0  105.0  110.0  119.0   2066    1.0\n",
       "y_pred[9]   83.79    0.16   7.17   69.0   79.0   84.0   89.0   98.0   2116    1.0\n",
       "y_pred[10]  85.03    0.18   7.72   70.0   80.0   85.0   90.0  100.0   1917    1.0\n",
       "y_pred[11]  60.92    0.15   6.69   48.0   57.0   61.0   66.0   74.0   2009    1.0\n",
       "y_pred[12]  48.08    0.15   6.22   36.0   44.0   48.0   52.0   60.0   1813    1.0\n",
       "y_pred[13]  35.76    0.12   5.48   25.0   32.0   36.0   39.0   47.0   2009    1.0\n",
       "y_pred[14]  27.99    0.11   4.95   19.0   24.0   28.0   31.0   38.0   2104    1.0\n",
       "y_pred[15]   27.0    0.12   5.16   17.0   23.0   27.0   30.0   37.6   1721    1.0\n",
       "y_pred[16]   21.0    0.11   4.57   13.0   18.0   21.0   24.0   30.0   1669    1.0\n",
       "y_pred[17]  16.37    0.09   4.09    9.0   13.0   16.0   19.0   25.0   2004    1.0\n",
       "y_pred[18]   9.82    0.07   3.08    4.0    8.0   10.0   12.0   16.0   1828    1.0\n",
       "y_pred[19]   8.04    0.07   2.94    3.0    6.0    8.0   10.0   14.0   1892    1.0\n",
       "lp__        -3022    0.04   0.99  -3024  -3022  -3022  -3021  -3021    531    1.0\n",
       "\n",
       "Samples were drawn using NUTS at Tue Feb 25 14:56:12 2020.\n",
       "For each parameter, n_eff is a crude measure of effective sample size,\n",
       "and Rhat is the potential scale reduction factor on split chains (at \n",
       "convergence, Rhat=1)."
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Diagnostic tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:n_eff / iter looks reasonable for all parameters\n",
      "INFO:pystan:Rhat looks reasonable for all parameters\n",
      "INFO:pystan:No divergent transitions found.\n",
      "INFO:pystan:No transitions that ended prematurely due to maximum tree depth limit\n",
      "INFO:pystan:Chain 1: E-BFMI (= 1.19) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:Chain 2: E-BFMI (= 0.929) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:Chain 3: E-BFMI (= 1.12) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:Chain 4: E-BFMI (= 1.19) equals or exceeds threshold of 0.2.\n",
      "INFO:pystan:E-BFMI indicated no pathological behavior\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{'n_eff': True,\n",
       " 'Rhat': True,\n",
       " 'divergence': True,\n",
       " 'treedepth': True,\n",
       " 'energy': True}"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pystan.diagnostics.check_hmc_diagnostics(fit_obs,verbose=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model Checking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/matplotlib/contour.py:1000: UserWarning: The following kwargs were not used by contour: 'normed'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x7fbcc9f684a8>"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tri=sns.PairGrid(pd.DataFrame(np.vstack((fit_obs['a'],fit_obs['b'])).T,columns=[r'$a$',r'$b$']))\n",
    "tri.map_diag(plt.hist,alpha=0.3,color='red')\n",
    "tri.map_lower(sns.kdeplot,shade=True,shade_lowest=False,cmap=\"Reds_d\",alpha=0.3,n_levels=10,normed=True)\n",
    "tri.map_upper(plt.scatter,alpha=0.5,color='red')\n",
    "\n",
    "#g.axes[0,1].set_axis_off()\n",
    "\n",
    "#tri.data=(pd.DataFrame(np.vstack((fit['alpha'],fit['beta'])).T,columns=[r'$\\alpha$',r'$\\beta$']))\n",
    "#tri.map_diag(plt.hist,color='blue',alpha=0.1)\n",
    "#tri.map_lower(sns.kdeplot,shade=True,shade_lowest=False,cmap=\"Blues_d\",alpha=0.3,n_levels=10,normed=True)\n",
    "#tri.map_upper(plt.scatter,alpha=0.5,color='blue')\n",
    "\n",
    "#tri.axes[1,0].set_xlim(fit['alpha'][s]-0.3,fit['alpha'][s]+0.3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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P56s3ZGLsItpse7q1NnxQu7JcTbQ7Z8OlGycAAMCoIuzh0Lj/+Lga5VNdP2amzsZay83VhsJoYtl0fS0O0NwlbA3XUzNAF1EAAAAcPoQ9HBrFnKOlb/ygPGfn/D2bLUmPfDjWWm6t9R6ePqjbId5rULWWp7rrJX52EAAAAOEj7OFQmf6mH9DzD39U9fJpWRk1x87IPPakdPHx2GpwPV8bjXZo91upJbOy12r7arV9WSvVWN0DAAAYOYxewKEyXsiq+obv0X/aHLXwptOTOjNdirWGIMPTB9F0ffm+VSYT35lDSdpo3g2sG422xgv8dQAAADBKWNnDoTM7lr/7fjnf58poeBFsefQSaNKyVnfvvt9w+1wJAACAw4iwh0NnstgZRJ7LZmIdoL4lilyWREPO7dtHV6rJNYkBAABANAh7OHQmS53thhPFZLYd+hEksyju2ffz+VartbureeuNtpptzu0BAACMEsIeDp1SzpHjGE0mFPbaEWzjdL14Z90tVpt7tqMurDdjrQEAAADRIuzh0DHGaCyf1VhCDUWiWIWLexfnzdW94x5uVpIbAQEAAIDwEfZwKJXzjkq5+M/rSVIhG/7nLWTj+1+x1mprcWPvKl6l5mo1oTEQAAAACB9hD4dSPpuJJHQFMV3KKeuENyZhopiN9Wt5aaHasyHMiwvV2OoAAABAtAh7OJTyTkb5GFfDtstkjC7MjYV2v3vnw7vXflZrLd3qs11zpdrSnXW2cwIAAIwCwh4OpWLOkRPzEPLtLsyWQzkzeGyioOMTxRAq2p/vW71wc33f675yaz32hjEAAAAIH2EPh1K5kMwWzi2ZjNGbz0zKDJE3c9mM3nRqIryi9vHiwoaqzfa+1zVdX1+5tX8ojJMfQQdUAACAUUfYw6G0NVg96Rrumx8/8OvfdGoitrN6K9WWrizVAl9/q9LQnbX0bOdcoXEMAADAwAh7wBDumStrujx48Dw9XYpt+6bnWz1/c23g171waz0Vg9attWqxrRQAAGBghD1gCMYYvfn0lJwBunOW845ef+LgK4KDenFhQ/XW4KHNbfv62u2NCCoasA7Pym2zjRMAAGBQhD1gSKW8ozeeDHb2zhjpzaenlHXi+V9vveHq6nLw7Zu73ao0tNRlJl+cXM9nZQ8AAOAACHtACE5NlXRsorDvdRfmypo6wLbPg/rq7fWeM/WC32NDdtibDKHV9ukOCgAAcACEPSAkbzgxoUyf/6MKuYzuPRbf9s3laksrVXfo+1Sbbd1eS251r+X5arUJewAAAIMi7AEhKeUdnZ4u9fz4PXNjsc4GvLZy8O2bUd5rUE3XV5OwBwAAMDDCHhCi87Plrs9nHdM3CIbNWqulanjjClZrbmJbKZttTw03+a6gAAAAhw1hDwhROZ/VzNjeM3knJouxrurVXU+eF+45uyAD2aNQdz212r48BqsDAAAMhLAHhOzk1N4VvFNT8czU2xLFqIKkOmLWNsdG1FrJhE0AAIDDirAHhGx+vCCzbRGvkMtoqhRfB05Jsgo/7CXRkNP37Wshr9pkKycAAMAgCHtAyPLZjCa3hbvZsbyMiW8LZ1SS+Aqqrbb8zQXF9cbwnUUBAACOEsIeEIHJ4t2wF/eqniSZKKJZAmlvtXY34FXqhD0AAIBBEPaACIwXs6+9P1GIP+z1m/d3UE4Cq5MrtbsdRSt1V22GqwMAAARG2AMiMJ6/G/bGCk7sn7+QDf9z5rPx/nXh+zvHR1irUMdJAAAAjDrCHhCB8WJWxkjlvKOsE///ZvlsRrkQw5kx0ti2ABuHxY3mnvERt9casdYAAABwmBH2gAg4GaNyPquJYvxbOLeEeVZwophTJsY5gZJ0fbW+57nFjaaabbpyAgAABEHYAyIyUczuOLsXt5lyeGEvzHsFUW22tbSxd8um70vXV/aGwDTwGfoOAABShrAHRKScd1TOx39eb8vsWD6V9wrilaVqz4+9ulxLZaMW109fTQAA4Ggj7AERKeQcFWJuarLdRDGnUghh03GMZsrxhb1qs61bld5n89qe1ZXlWmz1BJXE0HkAAIB+CHtARHKOib2D5W6npopD3+PkZDHW83qX72zsG5xeXaql7uyexzZOAACQMoQ9ICK5TEbZKAbeDeDMTGnomXvnZsvhFBPAaq2lhfXmvtd5vtXLi723eiahTdgDAAApQ9gDIuI4RtmYO1juVsg6Oj1dOvDr5ycKGi/E12TmxYWNwNdeX6mr3krP6l4azxECAICjjbAHRMQxJvZxBd2cH2Jl7sJcfKt6K9WWVqpu4OutVapW91jZAwAAaUPYAyLipCDoSVI5n9Xs+OANVsaLWU3H2JilXwfOXm6t1dVw07G6R9gDAABpQ9gDImLSkfUkSScmB2/UcpDXHNRGj7l6+/F96VpK5u55HmEPAACkC2EPiIhRetLesQOs7M1PFCKopLurQ4xSuL5aT8VA8zZz9gAAQMoQ9oCI5Jz0hL1C1tF0ORf4+nLeia0xS9vzdWut91y9/bhtX3cCdPCMGts4AQBA2hD2gIiYNO3jlHRygJl7J0KYzxfU7fXm0Fsgr68mu5XTWiuXbpwAACBlCHvAEXFysignwGqjMdKZIcY1DOpWZfigtlJtJdqoxfWsXM7sAQCAlCHsAUdE1sno3Mz+Ie7kVFHFnBNDRVKz7Q00bqGfO2vJbeVstj01U9IVFAAAYAthDzhCzs2Wldnn//p75sbiKUbS4gE6cPaysJFc2Ku3PNUIewAAIGUIe8ARUsg6OjXVe3Xv2ERBYzE1ZpE62y/DUqm35CXUJGW92Zbn2dTM/AMAAJAIe8CRc6bPVs6zAbZ5hqlSD2cLp9SZubfRaId2v0Gsb37etRC/HgAAgGER9oAjZrKY67p6l8tmNDc2+Dy+g/J9q3or3JWwaiuZsLcVWsMMrwAAAMMi7AFH0PHJvQPTj08UYh0X4UYwhLydQEfMarMtt935WlYJewAAIEUIe8ARdGJy7xy94xN7A2CUbAS5zCr+sLdSu3vucK3uqs28PQAAkBKRhj1jzHcaY75ijLlsjPlgj2u+zRjzRWPMl40xn4uyHgAd44Xsjq2cuWxGszFu4ZQkJxP+KmImgUH220dHWMtWTgAAkB6RhT1jjCPpVyS9U9KDkt5tjHlw1zXTkn5V0mPW2jdL+r6o6gGw04ltWznj3sIpSdmMUdifMufEv1lh+8pet8cAAABJifIno3dIumytfcla25L0KUnfveua75f0aWvtq5Jkrb0TYT0Atpmf2Bn24maMUSEb7vD2Yi7esLfRbKvV3rltczmkIfFRYIspAABHS5Q/GZ2RdHXb42ubz233ekkzxpj/aIz5vDHmByOsB8A2E8Wc8tmMMhlpuhzvFs4tpXy4YS/s++1nuctQ+PWGKzeloSqhMYQAACAh+4Y9Y8z3GWMmNt//kDHm08aYtwW4d7cNWrt/1MhK+gZJ3yXpOyT9tDHm9V1q+DFjzLPGmGcXFhYCfGoAQUyVcpoo5iI5PxfERDG8Ae75bCb0lcL9LGw09zxnrbTUJQSmQRINbAAAQHKCrOz9tLV23RjzX6sTyD4h6dcCvO6apHPbHp+VdKPLNb9vra1aaxcl/bGkt+6+kbX249bah621D8/Pzwf41EDCLj0lfewt0s9Od95eeirpiroaK2Q1lg8vcA1qupwL7V4zMa9ONtueVnucz7u11oi1FgAAgG6ChL2tqcffJenXrLW/JynIT1V/KekBY8y9xpi8pHdJenrXNb8n6b8xxmSNMWVJ3yjphWClAyl16SnpmfdJlauSbOftM+9LZeAr5x2VY976uN1sOa9MSJvJj03EG/ZurDZ6jo9Y2miq4YY7MB4AAGBQQX7Mum6M+Q1Jj0v6jDGmEOR11tq2pB+X9AfqBLinrLVfNsa8xxjzns1rXpD0+5IuSfoLSb9prf3Swb4UICU++xHJre98zq13nk+ZQjajQsxNTbbLOhnNj++d+TeoTEY6Nh5fkxnPt7q6XOv5cWulV/t8PClRzDYEAADpFWT/1uOSvlPSv7DWrhpjTkn6h0Fubq39jKTP7Hru13c9/gVJvxCsXOAQqFwb7PkEZZ1M4k07Tk4VdXvIbY/HJ4qxjl24vlLf04Wz2zXnZ8sq5pJbOd2NsAcAwNES5KejU5L+nbX2a8aYb1NnFt5fRFoVcJhNnR3s+QRlMyax5ixbjo3nh15dPD1dCqma/bU9Xy8vVfe9zvOtXl7c/7o4tf10dgkFAADRCPIT1u9K8owx90v6LUn3SvrXkVYFHGaPfFjK7QofuVLn+ZQxpnvb3HhrMDo1dfCwVso7mgmx0ct+rizX5O6zqrflxmpdtVY74oqCcz2W9gAAOEqChD1/8/zd90j6JWvtT6qz2gegm4uPS48+KU2dk2Q6bx99svN8Cpmk056kszOlA9fReW08X0Tb8/ue1dvNWumVxfSc3aNpDAAAR0uQM3uuMebdkn5Q0qObz8X3a3TgMLr4eGrD3W5pOMdVzDk6MVnUrcpgZ/ccx8S6hfP2elPtAVfHbq819PoT48rGeKawlzStMgIAgOgF+enjhyX9V5L+qbX2ZWPMvZJ+O9qyABw1F+bKA7/m3Ewp1sYsB2kk4/lWS9V0DFlfaxD2AAA4SoKMUHhe0gckfWHz8cvW2p+PujAA8UjDNk5JmijmdGwi+PiETEY6Nzt4QDwo37eq1NwDvXY5BWHP962qTcIeAABHyb5hzxjzqKQvqjMPT8aYrzPG7B6ODuAQyhgT23m3IO49Nhb42jPTZRWy8Y01WG+25R1wTsXqAUNimJptX03Xl5/0rA0AABCbIPufflbSOyStSpK19ovqdOQEcMgZIyU8eWGHqVJOs+P5fa/LZA627XMYB13Vk6Rqs73vXL6obTVnaXmMXwAA4KgIEvba1trKruf41TAwAjLGKJOilT1JuhBga+aJyWLsw8oXNppDvX6pOtzrh9XcDJtNl7AHAMBRESTsfckY8/2SHGPMA8aYfynpzyKuC0AM0hj25sYLGiv0bxR8PsazelJnVWxlyHN3NwfsNBq2Ztvb8RYAAIy+IGHvvZLeLKmpzjD1iqR/EGVRAOJhlJ4GLdudm+09TmG6nNNEMd7pL9dX60PfY3mjpXoruaC1tY20mfB2UgAAEJ8g3Thr1tqfsta+ffPPh6y1yf6KGkAoMhmjfArmv+12crIop8dhwjMz8c3VkzpdLK+vDB/2JOnaSnID1puEPQAAjpwg3Tj/0Bgzve3xjDHmD6ItC0BcMmnq0LIp62Q032UMg+MYHZ8oxlrLUrUVWnOVm5WGbEJT7O+GPbZxAgBwVAT5lf4xa+3q1gNr7Yqk49GVBCAWl56SPvYW6WenO28vPZV0RTucmNwb6ubHCz1X/KKysB5eY5VW21elnswYhq1unFtvAQDA6AsS9nxjzPmtB8aYC6IbJ3C4XXpKeuZ9UuWqJNt5+8z7UhX45sbye4LdsfHgQ9fDEnY4W6vHP9jc8+1rIa+W4LlBAAAQryBh76ck/akx5pPGmE9K+mNJ/yjasgBE6rMfkdxd59Dceuf5lMhkjGbG7s7cM0aaCzCDL2yNkLc91hNYWdtotrW1e7Tp+mzlBADgiOjf31yStfb3jTFvk/RN6jTv+0lr7WLklQGITuXaYM8nZG4sr8XNbZQTxZxyCTSTCfuMnU1gY8TugfCVmqvjk/HOKQQAAPEL0qDl70pyrbX/1lr7jKS2Mea/i740AJGZOjvY8wmZ3bayt/39OIUdMJMIrIu7Brovbgw3MxAAABwOQX7q+BlrbWXrwWazlp+JriQAkXvkw1Ju1wiDXKnzfIqMFbIq5Dp/Tc0lFPbK+XBXwMK+335abX/PQPiFjaZ8n6PXAACMuiBhr9s1+27/BJBiFx+XHn1SmjonyXTePvpk5/k0ufSUvvH3vlWPPPUGTX/8bYk0kAl7gHvcA+FvVuravRPVbfta2AivyygAAEinIKHtWWPME5J+RZ0unO+V9PlIqwIQvYuPpy/cbbfZMTS/1Uhmq2OoFGvd06WcXg3pXlnHaCzGlT3ft7q63H0g/KvLta7jLZLW9nxlE9jqCgDAKAryHfW9klqSfkfS/y2pIenvR1kUAKSlY+hkKbyVuKlSTsbENyfw5loXNrnZAAAgAElEQVSj51y9Ss3VcjV9Z/eS6FYKAMCoCtKNsyrpgzHUAgB3paRjaDHnqJx3QplPN12O79yh71u9vFDte82LCxuaHZuNqaJgfD/pCgAAGB37hj1jzB+pyxB1a+3fiqQiAJA6nUErV7s/H7PZ8bxqPbZDDnSfGJvMXFup91zV21Kpubqz3tDxifRs52yT9gAACE2QM3v/+7b3i5K+V1I7mnIAYNMjH+6c0du+lTOhjqHHJ4q6NmTYK+YcTYW4JbQfz7d6ean/qt6WF+9UNT9eiHV7aT9eyHMNAQA4yoJs49zdjOU/GWM+F1E9ANCx2YTFfvafSJXrMlNnO0EvgaYyM+WcSnlH9SG2cp6ejm/17PpKXW472ApZtdnWwnpTx1PSrKXtEfYAAAhLkG2c2w90ZCR9g6STkVUEAFsuPi499H26WWno9HRp/+sjYozRuZmyvnp7/UCvz2SkMzPx1G+t1avLtYFe8+pyLTVhz/XYxgkAQFiCbOP8vDpn9ow62zdflvQjURYFAFuMMco6yW8xPD1d1EuLGwdaeTo1VVIhG8/IheVqa9+zerut1lzVWm2V88mPUG0GXJEEAAD7C7KN8944CgGAXvIpmLuWdTI6O1PWK4vBzsJtd2GuHEFF3d1aaxzodTcrDb1ufjzkagY3aFAFAAC99fwJyhjzdmPMyW2Pf9AY83vGmCd3be0EgEg5meRX9iTp3GxJmQFz5/xEIbYVM8+3urPePNBrb1cOFhLDVm0S9gAACEu/H1t+Q51h6jLGfIukn5f0ryRVJH08+tIAoCOXgpU9SSpkHZ0Y8Gzb+dn4VvXurDfkHbDBSa3labWW/JD1Ztvj3B4AACHp9xOUY61d3nz/v5f0cWvt71prf1rS/dGXBgAdKZkKIEk6N0B4Gy9mNRPjbL3rK8ONh7g25OuH5flWbc9ybg8AgJD0DXvGmK29R49I+g/bPpb8KX4AR0YmRWlvspjTdDnYvLxBguGw1hquVmvuUPe4s95I9Mxcs9353JzbAwAgHP3C3v8l6XPGmN+TVJf0J5JkjLlfna2cAHAkBQlxuWxGJ2McZzDs0HdJ8n3pxmpyq3tbcwyHmWcIAADu6rlCZ639p8aYz0o6Jen/s9ZuHQTJSHpvHMUBgJSulT1JOj5RUDHn9F2BOjtTiq2xjOdb3T5gF87dblYaui+hrpy1Fit7AACEqe92TGvtn3d57qvRlQMAe6WlG+cWY4wuzJX1lVvdh6xnMtK5mfi2cC5Vm/L8gzVm2a3e8rTecDVRDLZVNUz1zZBXZWUPAIBQpKPFHQAcMqenSz2HvZ+eLimfje+v18qQZ/V2G/bs30FVm21JUm3zLQAAGE6/OXuFOAsBgMPEyRid7bF6F+e4BUnaCDkchX2/QT9vreWFtlIJAMBR1u9Xz/9Zkowxn4ypFgA4VM7OlPaMhZgbz8c2RH1L2KMKWgmMPmi2PTXdu593o8HqHgAAw+r3E0neGPM/SfpmY8z37P6gtfbT0ZUFAOlXzDmaGctreePuMPJTU6XY6/BtuKtgXsj3C2KtvjPcVequpgKOuAAAAN31C3vvkfQDkqYlPbrrY1YSYQ/AkXdsrLAj7M2NxzdEfUvY3UqT6H5aqbd2PU7m3CAAAKOk3+iFP5X0p8aYZ621vxVjTQBwaEyV7q4+jRWyyjnx973KhtytNOz7BbGyqynMSq3V40oAABBUkIMlnzTGvE/St2w+/pykX7fW8mtXAEfeePHuX6PjhXjP6m3Jhhwwe3UZjYrr+VrbtZLXavuJjYAAAGBUBPkJ4VclfcPm21+V9DZJvxZlUQBwWDgZo0Ku81dpueAkUkMu5HAW9+rkcrWlbscElzZY3QMAYBhBfg39dmvtW7c9/g/GmL+OqiAAOGzKeUdN11c5n0zYK4Q80y/s++1nYb3Z9fk7603dc2ws1loAABglQb6je8aY1209MMbcJ8mLriQAOFy2Ri2Uc8ls4yzmwg2ZYd+vn7bn9wx7a3VXtRYjGAAAOKggP5n8Q0l/ZIx5SZKRdEHSD0daFQAcFpee0gN/+LN64/oNaeqM9MjPSBcfj7WEsZDn+sV59vD2erPvAPUbq3Xdf3witnoAABgl+35Ht9Z+1hjzgKQ3qBP2/sZa2/3XsABwlFx6Snrmfcq69c7jyjXpmfd13o8x8E0UszJGXc+9DSqXzcS6svfqUq3vx6+t1HXvsXE5CXQIBQDgsAt0MMNa27TWXrLW/jVBDwA2ffYj0lbQ2+LWO8/HKOtkNFkKp2vlbDm+OYGLG01Vm/23abY9qxur9b7XxM3vsxIJAECaxD8QCgBGReXaYM9HaH68EM59JsK5TxCvLFYDXXdlqZaqgLW+T0AFACAtCHsAcFBTZwd7PkInp4oyQ+50zDomtrC3WmtptRZsXGvD9XRrrRFxRcG1PT/pEgAACGTfsGeM+V1jzHcZYwiGALDdIx+WcqWdz+VKnedjVsw5OjlVHOoe52fLsZ2Nu7LPWb3dXl0e7PootQh7AIBDIkiA+zVJ3y/pa8aYnzfGvDHimgDgcLj4uPTok9LUOVkZaepc53HM3Ti3vG5+XJkD/loul83o/Gw53IJ6aLieFjcGO/690WhrpZqOIetNl7AHADgcgnTj/PeS/r0xZkrSuyX9oTHmqqT/U9JvW2uD7cMBgFF08XHp4uNKQ6/IYs7R+dmyXlkcfBXsdfNjyjrxbOC4sVo/UOfQ66t1zYzF10Cml2absAcAOBwCfWc3xsxJ+iFJPyrpryT9H5LeJukPI6sMADCwe+bGlMsOFtrKBUdnpkv7XxiSW5WDnb9b2GcmX1xcz09FHQAA7CfImb1PS/oTSWVJj1prH7PW/o619r2SxqMuEAAQXNbJ6MKA2zHvOzYuM2x3l4DWGq5qLe9Ar/V8O/D2zyh4viXsAQAOhSC//v1Na+2D1tp/Zq29KUnGmIIkWWsfjrQ6AMDAzsyUAp/dK+QyOjEZ37iFO2vDhbVhXx8GzxL2AACHQ5AfBz7a5bn/HHYhAIBw5JyMjgWcu3dyshjbqp7U2Yo5jMVqM/GZe75v5R3k0CEAADHr2aDFGHNS0hlJJWPM10uv9R+YVGdLJwAgpeYnCoFWwYKGwjA0XE/VIQeSe55Vpe4m2qilzTZOAMAh0a8b53eo05TlrKQntj2/LukfR1gTAGBIM+X9w5CTMZoq5WKopmOlFs7ohOVaK9Gw53q+XGbtAQAOgZ5hz1r7CUmfMMZ8r7X2d2OsCQAwpGLO0Vgh23clbbqcUyamIeqSVKmHM6knrPschO9btdq+Gu7BmswAABCnfts4/wdr7W9LuscY8/7dH7fWPtHlZQCAlDg2nu8b9uLcwilJa/XhtnDevU9yYa/uerJWB+4oCgBAnPo1aBnbfDsuaaLLHwBAis1P9A9z+308TNZabTTDCWltzya2srbW6HwNSQZOAACC6reN8zc23/6T+MoBAIRlqpRTIZdR0917vmyylFMx58RWS63lyQ/xmNt6ox1r/VtWa5thr+HK922s22ABABhUv22cT/Z7obX2feGXAwAIizFGxyeKurpc2/OxOGfrSRq6C2e3+8W5Mrllq8mM7yvxrqAAAOynXzfOz8dWBQAgEvMTha5hL+6gVA35jFu1FW54DKLheqo1734dKwl3BQUAYD/7deMEABxi06WcHMfI8+7OhSsXHJXz/X7XF756yGEviTN7u7uArtTSe27P9XzlnH7H8gEAR0G/bZy/ZK39B8aYZyTtmR5rrX0s0soAAEPLZIxmynktrt8dsD43Fv/2x7Dn0rXa8Q81X67unBNYqbdSe27PMvMdAKD+2zg/ufn2X8RRCAAgGjPl3I6wN1OOb5D6Fj/k9GETSDNLGzvDnu93tnLOxTzCAgCAoPpt4/z85tvPGWPykt6ozgrfV6y1rV6vAwCky1RpZ7ibLMUf9jIm3NUvE/L99lOpu123jt5ea6Yy7Nm9G3IAAEfQvhv6jTHfJelFSU9K+mVJl40x74y6MABAOCaKOW1lo0Iuk8jIAifkrY45J96wd7NS7/r87fWGPJ9gBQBIpyCnt39R0rdba7/NWvutkr5d0seC3NwY853GmK8YYy4bYz7Y57q3G2M8Y8zfC1Y2ACAoJ2NUyncC3ngh3sYsWwrZcJuFxNl8xPV83aw0un7M86xurHYPgknizB4AQAoW9u5Yay9ve/ySpDv7vcgY40j6FUnvlPSgpHcbYx7scd0/l/QHgSoGAAxsbLP75lhiYS/c1cQ4Vyevr9R3dDPd7epyLZEzhP2krBwAQEL6deP8ns13v2yM+Yykp9Q5s/d9kv4ywL3fIemytfalzft9StJ3S3p+13XvlfS7kt4+WOkAgKDKmyt7pQS2cEqdcQ+h3i8fz9fh+1avdplTuF2t5enOelMnJoux1BSER9oDAKh/N85Ht71/W9K3br6/IGkmwL3PSLq67fE1Sd+4/QJjzBlJf1fS31KfsGeM+TFJPyZJ58+fD/CpAQDbba2EJXFeTwp/++hEMZ4VyhuVulrt/cdGvLJYTVXYa4c86gIAcDj168b5w0Peu9vp+d2/avwlSR+w1nr9OqtZaz8u6eOS9PDDD/PrSgAYUCHX2bVfzCUzaLuYczRWyKrabA99L8cxmixG31HUWqtXl/qv6m1Zb7S1tJGezpytti9rbexdSwEA6bLvr0aNMUVJPyLpzZJe+7WltfZ/3uel1ySd2/b4rKQbu655WNKnNr8ZHZP0d4wxbWvtv9m/dABAUFsremGfnRvEyamiXryzMfR9jk8UYhlkfnutqVpr77iFXl5ZqqYm7Lm+ledbZWPuWgoASJcgv+L9pKSTkr5D0ufUCW3rAV73l5IeMMbcuzmn712Snt5+gbX2XmvtPdbaeyT9P5L+V4IeAISvkM0ok5HyIXfFHMSZ6VIoIxjOz5ZDqKY/a61eXqwO9JqVqqvVWjrG0LY9X21GQgDAkRfku/791tqfllS11n5C0ndJemi/F1lr25J+XJ0umy9Iespa+2VjzHuMMe8ZpmgAwGDyTkbFBFf1pE7QPDtTGuoe8xMFTcSwhfPOevNAW05fXBgsIEbF9Xy1OLcHAEdekBPu7ubbVWPMWyTdknRPkJtbaz8j6TO7nvv1Htf+UJB7AgAGZ4xJbOzCdhfmxnR9ta52n1EGvRgj3X98PIKqdrLW6qUDhraVakurtZamy/mQqxpMs+0HaiwDABhtQVb2Pm6MmZH00+psw3xenbl4AIBDZCzk8QcHkc9mdM/c2IFee2qqFEtgXaq2hmokcyVgU5coNdu+moQ9ADjy9v2uaa39zc13PyfpvmjLAQBEJamxC7udmy3r1eXaQCtPmYx03/zBQuKgrq/Uh3r94kZTzbaXaDOchuup6QZvLgMAGE37ruwZY+aMMf/SGPMFY8znjTG/ZIyZi6M4AEB4kgwf2zkZo3uPDRbczkyXYwmrvm+1XB2uyYq10uJGco1arLVquJ7qhD0AOPKCbOP8lKQ7kr5X0t+TtCjpd6IsCgAQvrmxZM+RbXd6uhS4M2gmI12Yi74DpyRV6q68ELpYrgwZGIfRbPvyfak+wNgIAMBoCvKddtZa+3PW2pc3/3xU0nTUhQEAwhXHbLqgnIwJHOBOTZVi24Jaqbv7XxTAWkj3OYitkDfIjEAAwGgKEvb+yBjzLmNMZvPP45L+XdSFAQBG25np0r5Dv43RgRu6HERYYa/W8hLrhrmx2Vym1fblMn4BAI60nmHPGLNujFmT9L9I+teSWpt/PiXpJ+MpDwAwqrJORmdn+q/unZgsqpSP76xhWGFPklbryWzl3NjWSXS9cfCuogCAw69n2LPWTlhrJzffZqy12c0/GWvtZJxFAgBG07nZkjJ99picm43nrJ4k1VrtUFfjKrVktnJu30Ka5HZSAEDyAg0sMsY8JulbNh/+R2vtv42uJADAUVHIOpofL+r2WmPPxyaKWU2VcrHVslYPdxVsLYFVNdfzd6zsraY47LXavrIZk6qzpAAwaoKMXvh5ST+hzjD15yX9xOZzAAAM7dR0sevzp6dLsdZRa4UbzsK+XxArtZas3fnYD6G7aBQ838q36awNAEZFkJW9vyPp66y1viQZYz4h6a8kfTDKwgAAR8NsOS/HMfK8nT/4z08UYq3D9cINHkk0R9k9I9DzrCp1VzMpGruxxcrKilU9AIhSsCFHO0ctTEVRCADgaMpkzJ4ZgOPFbGzjFkbJ4vrepjCLG80EKgEApEGQlb1/JumvjDF/JMmoc3bvH0VaFQDgSJku5XVn7W4omSnHvxLlBP31Z0AZE++qVaXuquHuna23sN7UAycmYq0lCGsldnECQLT6hj1jjJH0p5K+SdLb1Ql7H7DW3oqhNgDAETFZyvZ9HIe8E+5KYj4bcnrcR7cmN1Jn5l+l7sba7CYIch4ARK/vd1NrrTXG/Btr7TdIejqmmgAAR8xYIdv3cRwKuXDDWZzbUD3f6male9iTpOsr9fSFPds5tQcAiE6Q72x/box5e+SVAACOrJyT2RG2xvLxh71yyMPb4/wabqzW5faZEXhrrd51i2fS2MYJANEKEva+XZ3A96Ix5pIx5jljzKWoCwMAHC1bYauQy8hJYPbaWD4b6uedKMYT9jzf6pWlat9rfF96ebH/NXHzObMHAJEL8p3onZFXAQA48k688owe/C8/r2LtpjR1Vnrkw9LFx2P7/JmM0VQ5p+WNvR0tDyKuJjNXlqpquvuPebixWte52bLGE9gi2w3bOAEgej3/xjfGFCW9R9L9kp6T9FvW2vgnxAIARt+lp3T6Tz6gTLveeVy5Kj3zvs77MQa++fFCKGFvvJhVKeRtod00XE9XlmqBrrVW+urtdb3t/EzEVQVjbWd1DwAQnX7bOD8h6WF1gt47Jf1iLBUBAI6ez37kbtDb4talz34k1jKOTxYUxsSEk5PF4W8SwOU7G/IGSEzLGy3dWe/dyCVOnrXy2ccJAJHqt5fjQWvtQ5JkjPktSX8RT0kAgCOncm2w5yNSyDqanyjsmPk3KGOkk1PRh71K3dWtPh04e7l8e0Pz4wWZmOcA7ub5Vm0v/WHPWpv4PysAOKh+K3vu1jts3wQARGrq7GDPR+jsTHmo1x+fKMYyduHFhY0Dva7W8vqOaYhLq+3L9fY/a5i0QVZOASBt+oW9txpj1jb/rEu6uPW+MWYtrgIBAEfAIx+WzZV2PpcrdZq0xGx2LK/xITppnp8dLiwGUam7Q50tfGWxKpvwFspm2wvUWCZprOoBOMx6hj1rrWOtndz8M2GtzW57fzLOIgEAI+7i4zKPPqlG+bSsjDR1Tnr0yVibs2x337GxA71udjyvqXL0w8uvLgdrytJLreVpYePgW1XDUG16qrbYOAQAUUpH/2UAQHQuPdVpdFK5lshIg8AuPq7nJv+23n7PbNKVaH6ioIliVuuNwcLI6+bHI6rormbb0+214bdhXlup6/hEPI1kutlotpVrBxn3myzW9QAcZoQ9ABhll57qjDBwkx1pEFQphrNuQRhj9MCJCX3hysqO509ceVr3P/eEirWbapRP6fJD79ftC49J6jRlmSpFv6p3u9IMZRj58kZLDdeL5Xzhbq22r3rLUzPjyfetMiEOsw8buzgBHGbp/5UaAODgPvuRu0FvSwIjDYKKYzZdULNjec1PFF57fOLK03rw2Q+pVLshI6tS7YYefPZDOnHlaWUy0v3Ho1/VkxTq9svFhLZyrtY65w19X1pruPtcnSymQwA4zAh7ADDKUjLSIKgkVpn6eeDE+GsrO/c/94Qcb+f2Scdr6P7nntD52XIstfu+VaU+/ND3Lau1ZILWyrbPu1wN7+sJ1aWnpI+9ReYjM9LH3tJ5DACHDGEPAEZZikYaBJF30vVtqZzP6vR0p0tosXaz6zXF2k1dmDtYQ5dB1VxPfogNLAc9kxiW7QFvpZbCsLe1/blyVUb27vZnAh+AQyZd31UBAOF65MOdEQbbJTTSIIick74DUvceG5MxUqN8quvH2+OnlYsppNZbXqj3a7TDvV+gz+l6qjbvhsxK3VU7bfP2Dtn2ZwDohbAHAKPs4uOdEQZT56QUjDTYj5PCRh3FnKPjE0Vdfuj98pyd3Ss9pyj97fiCc9hDyD3Pxj40fGnXtk3fl5bTtrp3yLY/A0AvdOMEgFF38fHUhrvd0hj2JOn0dFF/tdl1c3s3zoV3fEDnv+5dsdURRTBr+76cTHxnJRfX9zaFWVxvJToGYo+ps52tm92eB4BDhLAHAEgNk9KpZrNjeeWyGd2+8NhroxYk6eLZqVjr8CNoDRlnt8m252upujfsLWw00zWC4ZEP7xxZIqV6+zMA9MI2TgAA9mGM0dxYftdznRAYax0pDcNB3Vlvdm0w47b9Pds7E7W5/dmfPCt7CLY/A0AvrOwBAFIjzQOsZ8fyulW5O3phspRTNubuoZkIPl02xtW0G6v1nh+7WanvmGuYuIuPq/aG79FGo62TUynaYgoAA2BlDwCAAKbLuZ2PS7keV0Yn7NEUxsR3TrLabPed67ew3lQzge6g/XieVTvMWRcAEDPCHgAgNQrZ9H5bKuezym4bDTGZQNgrZMNtpFLIOjIxLaf2W9WTOmcHb642+l4TN9f3Y+9WCgBhSu93VQDAkRNX8Dio7QFvshh/2Cvmw/22XQr5fr34vtWNyv5B7sZqXTbOjjH78Hwr10tPPQAwKMIeAAABTRY7R92zjlEpH9+4gi2FrLNjdXFY5Xw8R/fvrDfltvffDllreVrps9Uzbq7ns40TwKFG2AMAIKDxQmc1byKBVb0tUyFuHw3zXv1cW6lFcm3UXM+qzcoegEOMsAcAQEDjmyt7E8XkmlkfGw+nY6Ux0tx49KMj1htu38Ysuy2sN9Vw09Gope35anms7AE4vAh7AAAEVM45MkYqJ7CFc8vJqWIoHTTnJwqhN3zp5srSYCt11kqvLqdjda/l+YG2nwJAWhH2AAAIKJMxKuWc2M66dZNzMjo7Uxr6PvccGwuhmv4arqfba4N32Ly+WpebghW1tkeDFgCHG2EPAIABFHKOSrnkVvakTlAbplHLicliLN1Er63UdJDmmp5n9x3VEIdm21fLS8eW0n7S1MEUQLoQ9gAAGEAhm1E+4XmAOSej+46NH+i1mYx0//GDvXYQnm91beXgge3qcvJjGOquJ99Xas4Q9sLqI4BeCHsAAAygkM2EcmZuWGdnSioeYIXxzHQ5lrERd9YbQ3WybLielqqtECsaTLPtvXZer9psJ1ZHEFaEPQDdEfYAABhA0qt6WzIZowtz5YFeY4wGfs1B3QwwRH0/t0K4x0Ft7yC6Wk/P7L9u2MUJoJd0fMcCAOCQyDnp+dZ5aqooZ4Cze8cnigdaDRyU6/laCWFVbmGjKd9PJsksbjTvvr/e7HNl8gh7AHpJrp0YAACH0DCNUcKWdTI6MVHc0czkxJWndf9zT6hYu6lG+ZQuP/R+3b7wmCTp9HQxlrpWqq1QAojnWVXqrmbGop8HuJ3vWy1sC3jrjbbqLS+W7a8H4ZP2APSQnl9PAgBwCGQz6frWeWrqboA7ceVpPfjsh1Sq3ZCRVal2Qw8++yGduPK0CrmMZmMKTSsDDFHf/17xn9tbrrX2nDc8yAiJuBD2APSSru9YAACkXBqas2w3Xc69tjXz/ueekOPtDCWO19D9zz2hk5NFGRNP7ashBrQkzst1Oyt4K81hL/mRhABSirAHAMAA0hb2jDE6OVWQJBVrN7teU6zd1MmpeLZw+r7VRojdK9diDnu+b7WwsfeM3kajrVornV05XdIegB4IewAADMCJaXVsECenSpKkRvlU1483x05pIoYh6pJUbbVDbRjS9mysc+4Wq015PUZGJNkdtJ9mm7AHoDvCHgAAA0hh1tN4IauJYlaXH3q/PGfnCp7nFLX+zf84tlqiCB5xhpk7a707b97u87GktD1fzZQPfQeQHMIeAAADyKdo9MJ2J6eKun3hMT3/8EdVL5+WlVG9fFrPP/xRTbzj+2OrI4pmITamBiRejy2cW6rNdqhbVMPQbPus7AHoidELAAAMIJOyM3tbTkwW9bXbG7p94bHXRi1I0tS2Bi5xKDj7f65+4yG6iWuQ/VKfLZxbFtabGi+k58enuuupzsoegB7S+etJAAAwkGLO0XhxbwiZHy/EWsd4Mdt3q2u/8RDdZB2jUkxhdXF9/y6iCykbsF5veaq3CHsAuiPsAQAwIo6N752jN9fluSg5GdN3CHq/8RDdHBsvxDIywlqrxT5bOLes1d1YG8bsp9by1HA9+T6z9gDsRdgDAGBEzJR3hqxcNpPIlsMTk73HPPQbD9HN8cl4ViZXaq5aAc++9WviErfaZvfTRjs9ARRAehD2AAAYEdPl/I4tlNOlXGyD1Lc7PlFQpsdPGL3GQ3R7PusYHRuLJ+xdW6kFv3a1FlvTmP003E5AZSsngG4IewAAjAgnY3bM09u90heXnJPRdI/P3Ws8xOWH3r/n2mPjhVga4qw13IFW62pNTzdTMnOvubmiR0dOAN0Q9gAAGCHT5bthb6oczyD1bmZ7hL1e4yG6dePsd/YvLL5v9cKNtYFf97U7G4G3fUbF963am91Dk64FQDqlp3cwAAAY2nQpp1clZTLSRIIjAiZLvYPm7vEQPe/Rpbto2F5eqmq9MfjsPLft64Wba3rruekIqgqm5d0NeK5H2AOwFyt7AACMkK2QNVHMJToTcHKfEQz7cTIm8uYyaw1XryxWD/z6hfWmblbqIVY0mO1bN9nGCaAbwh4AACOkmHOUdaIPSvvJOpkd5wcHNV2OvrnMV2+ta9g+K1+7vSEvobEH1ebdFcmN5uCrk3Fi5RFIBmEPAIARM1bIaiyf/EmNk31GMOz72qmDvzaISs3Vas0d+j6ttq9ba8k0a9lef7XZTnWgSioQA0cdYQ8AgBFTzDoq5pP/Fn9quijHGXx1rpDL6MREtH5XsSAAACAASURBVGFvIcAA9aDuJBD2fN/u+Bqsle6sp2f+326EPSAZyX8nAAAAocpnM8o7yX+LzzkZXZgtD/y6e4+NRX7ecK0x/KreloM0eBnW7fWG3F3n9K4tB58VGLc0rzoCoyz57wQAACBUWccol4KwJ0kX5sZUyAWvpVxwdGa6FGFFHY0Qh5C32n6sK1fWWr3cpbHMeqOtxRBXLMO0NfwdQLzS8Z0AAACEJpsxchLsxLmdkzG6b3488PX3Hx+PvDGLFH73yq3h5nG4vdZUrdn98720cPDuolGqtdLdQAYYVZGGPWPMdxpjvmKMuWyM+WCXj/+AMebS5p8/M8a8Ncp6AAA4CpwUhT1JOj1VVCnv7HvdRDGr4xGf1ZM6WwrDXomLa6i571u9uLDR8+NrdTeRM4T9WGtT3y0UGFWRhT1jjCPpVyS9U9KDkt5tjHlw12UvS/pWa+1FST8n6eNR1QMAwFHhZIycGFbHgjLG6NzM/mf3LsyNxVBNNOfH4gp7Nyp11ffZgvriQlV22JkSIWp5PnMAgYREubL3DkmXrbUvWWtbkj4l6bu3X2Ct/TNr7crmwz+XdDbCegAAOBKcjEl0oHo3p6aLyvT5qSOXzej4RCGWWqI4X+fFEK6stbqytH8TlmqzrYUUdeZstX01ObMHJCLKsHdG0tVtj69tPtfLj0j6fyOsBwCAIyHXL1UlJOdk+m7RPDVVjC2gRnEm0Cj62hc2mvuu6m25upKezpyttq+WF9+ZRgB3RfndoNvfel1/7WWM+XZ1wt4Henz8x4wxzxpjnl1YWAixRAAARk+Q83FJ6Ndl83QMHTi3RDGWIneAeYKDulUJfhZvpeqq4aYjYLU8X77P+AUgCVGGvWuSzm17fFbSjd0XGWMuSvpNSd9trV3qdiNr7cettQ9bax+en5+PpFgAAEZFMZfOsDczlle5SxCdKuc0XsjGVkc+m1EuG+6PQGMR1+/7VksbrYFek5atnFtbODm3B8QvyrD3l5IeMMbca4zJS3qXpKe3X2CMOS/p05L+R2vtVyOsBQAApMCpLit4ca7qbZku5UK7VynvRB6w1xruwGcNV2qDhcOo1Da3njJ+AYhfZGHPWtuW9OOS/kDSC5KestZ+2RjzHmPMezYv+7CkOUm/aoz5ojHm2ajqAQAAyTs1tfPcXiaj2BqzbDc7lk/lvXpZqbkHek0aunKuN9zNt+kOe2n4ZwWELdI9B9baz0j6zK7nfn3b+z8q6UejrAEAAKRHMedoupzT6mZ4mRsrKBfBGbr9zE8U9JVb66Hc69h49GF1aWPwLZlu29dao62pEFcxB9Vq+6+FvOVqS69L8Wmchuun9rwrcFDpa9cFAABG2vZwdCyBVT3pbugcVtYxmot4Za/heq+F40EtrCc7YH1hW0it1NLTNKYbn5U9jCDCHgAAiNVM+W44mi1HvwWylzDOCp6eLkU+MuL22sED281KI9Htibs7iN5ZS0fTmG7imJUIxI2wBwDA/9/evQfHdV/3Af+ee/eFxS4WAPEmKFISRYmkSMm25EdVp3TleGxNJCepLNtNbcdJazu148iaNHZajevxJDNK1cixnDSqk2hiZxzbchM1jCpVdl3XybhRLUqRRb1FUaQJEQQIEm/sAvs4/WMvqMVyd7G7uI/f7n4/MxyCd++9+GEv7+4enN/vHPJVMhaCSDErFuS0uZGeGKLh5j8KWRZwSX/cxRFdTFUxMZtu+vjVbGFDds1PmWwes8sbi8Sc2ULg6rV8nsEetR8Ge0REROQryxJ0hW3P2xXUM47LBxNNHz/eF/e8CufUQv2N1Ks5MRNMg/VKrR8W0uZO5TS+NcTTDwBfuhr4Qm/x76cfCHpE1AIY7BEREZHvomEbsVDwxTBGUzGkmli7FwlZuHSg24MRvU5Vcfzs0pbPs5DOYjqAtXvVMoqm9P8rlzY0CAVQDOz+9tPA/CkAWvz7bz/NgI82xWCPiIiIfBcNWVuaQukWEcFVI0lIg8vu9gwnPa8iemYhc6FHXSXDJw/jhocO4cYHrsQNDx3C8MnDVfd99eyyF0Osai1XuGgK57ogAs96LK8a3Bri+18EsmXTebPp4naiGoJ/lSUiIqKOEwlZgbRcqCQZC2PntvrX3m1LRDBS1i/QC6/VWKs3fPIw9h25E10rpyFQdK2cxr4jd1YN+BYzOcynm6vo2Ywz8xlUq3cyu5w1ssF6rcA6cPMTjW0ncpjxKktEREQdJWxbCNveVrFsxKUDiboyjZYFXDmS9Hw8hYLWDM52H70Hdn5jhszOZ7D76D1Vj5lbqZxpc1uhoDh5vnYmMah1hNUUCmp2Zi813th2IgeDPSIiIvJdyBJjMnsAYNdZrGW8L454xPvCMgXVqpkxAIitTDa0HQDyBX+qTU7MprGarV3sZHI+bU5w9fQDwB9cjUPf2oPCPfvNXAd34+eBcFmrkHBXcTtRDea8yhIREVHHCNsWQh73p2vUaCpWsxWEZaGh6Z5bEbKtmmPJxEcb2g4AiZj3QWo2X8Dxmc2LyqgCL09vvfjMljmFT6yFCQgU1sKEmYVPDt4G3HwvNLUDgACpHcDN9xa3G8avXyo0rcOqmjLYIyIiIt+FbUE4ZNbHEBHB9hqN1oeSMUR9rCA6lIxWfezYgTuQtzeuG8zbMRw7cEfF/W1bsK27+vnccmJmGbk6+9XNLK5WLeLim1YqfHLwNix8/B+BL8wBn3nGyEAPKGaljdWBVU3NepUlIiKijhCyzMvsAahZeMWPoiyltvdVDzyndt6C5677HaTjY1AI0vExPHfd72Bq5y0V9x9NxWB7/Hxnsnmcmm1sLd4rLrSW2JIWK3yymje4iEwraKXg3iXBdjMlIiKijmRZgNVovwMfxMI2krEQFjMb15PZlqA/HvF1LPFICP2JCM4vVc5+Te28pWpwV65WxtItJ84to9BgX/K5lSxmllYxkPA+61hRatzJ8lTYbqA10xu/m67Fgns3MLNHREREvrMt8TzT1KxtiYuDur7uCKwAxjvSs/VsYiIWQjLWeOP4RqTX8jg9V71VRC2vTC9Bg5r6d+PnUQhtDIQLIXMLn2TrnCIbJBN/iXNBB1Y1ZbBHREREvrNEjP1Q2F9hbZvfWb11g8loww3fy9Va++eWV84uNZzVW7eYyWFqYdXdAdUpt/9WPH/9xumwL1z/u8hf/b5AxrOZXN78zJ6Zd7WjA6uachonERERBcLUD4WprjAsCxuCl75ubzNj1YRtC73xMGaXm2+IPuBxsDe/ksWZ+czmO9ZwbHoJg8mo79neyfkMJnfcjMkdN2/Y3ruQwZgPU18btdoC0zgN/R1OkVPURr//Rcj8RDGjd+PnjS124wYGe0REROS7iG0Z+6HQtgSprsiFSpHhkIVENLiPTIOJWNPBXixso8fjKZzHXCiyksnm8dpsGpf41Npi3WSVIHVyPm1ksJfO5lEoaCBTiuulan7Ap1e/D2Lwc+gmTuMkIiIi31mWQAz+RNgXfz1A6o9HAh3rUE/zmbnhLRxbj6XVnGvtExqt5LlVK2s5LKQrB9Gzy1lksuZVvkyv5c3O7j39AOTLB4zvYWfwS4/rGOwRERERlekrWaPXGw9mCue6WNhuehrpsMftIs4t1V5rN3zyMG546BBufOBK3PDQIQyfPFx13/RaHitruaqPu+212doFZV5rsuCMVwoFxVqugNWceUEogAs97KQFetiZ/IsmtzHYIyIiIirT0/V6cOX1NMh6jKQan1KYiIU8H/vKWvXAY/jkYew7cie6Vk5DoOhaOY19R+6sGfAtr/oTyKzm8pjYJJg7dX7FqFYHa05xFmMzex3Yw64VMNgjIiIiKmNbgnjUBlAMmoI2nIzCthvLRvjRWy9fqN4KYPfRe2DnN66Js/MZ7D56T1Pnc9PLU0vIb9LGIJdXHJsOuOl7ifVppSZOLwXQkT3sWgGDPSIiIqIKuiMhdEVsI/oBhmyroeDNtgWjHk/hBGoHZ7GVyYa2A0Deh35755fX6q4eenoujbkVd9YkblXaCfJqZVMD1YE97FoBgz0iIiKiCuIRG10RO+hhXHBJf7zuwHNnfxwh2/uPebkazfUy8dGGtgP+9JFrNFv3igvVRt2wkC6uZ1zM+LeusSEd2MOuFTDYIyIiIqogFrYRC5kT7MXCNnYNdG+6XzRsYee2zfdzw2q2enB27MAdyNsbs4t5O4ZjB+6oeozXa+Tm09mqFTirmV3OYmk1+ABrximGs5A2s1IoDt4G3HwvcslxAAKkdgA332tkD7uCT9OFTRD8JHQiIiIiA0VCFiIhs34vvrM/jsn5NFZqFDK5ciTp29TTbI0PzVM7bwFQXLsXW5lEJj6KYwfuuLC9kjWPM3vNNn8/M5/G7qGky6Op39zKGtIl0zfPzGfqCvx9d/A2nBi5CZcPdhtd8TKvCgvmjs9NDPaIiIiIKgjbFiI+TIVshGUJ9o704ImTsxUfH0xGMZT0fq3ehfFs8nl5auctNYO7i8/n3QfwfEExOd9cO4XTcxlcNpAIrJn5yXMbexCeml3BJf1xI5urZ7LFXoCxsDlZ8XK5vMLg4bnKrFcwIiIiIkPYliDUYAVMP/R1Ryo2WrcsYM+wv9mnpMutHZIeVj49PZdGbpMKnNWs5QqYXGguK7hVcytrOLu4sZ/harbgexP6eq2s5bFswLTXWrzOIJuEwR4RERFRBSFLjKjEWcmlFabwDSVjvheUGe9zr71DyBYM93iTlcwXFK/OLG/pHK+eXfZ9rVehoHjhzGLFx47PLBu3dq9QUCytZs0tIuPI5QtQHyq/moDBHhEREVEFtsHBXjIWvqj/35gPffXKDSSiGEhenGVsxu6hBMIeTZt1o0F6JpvHa5s0YnfbyfMrWKoSOOXziucnF3wdz2YWMzkUCsBcg0Vw/FbQ4p9OwGCPiIiIqALbEtgGF5kYSEQufG1bgt4ud6dU1mvvaHLLhWwGklGM98VdGtFGhYLip+fdmfJ48tyKbxmhxUwWr87UbvtwbmnN9wC0lvNOT8LZlTWjK16qKgrM7BERERF1LkvEyAIY63pKgruerlBgY42GbFy9PYVm4+JY2Mb+sR53B1ViZmnVtZYOmWwe55a9b7JeKCieeW0BNdoYXvDS1OKGSp1BWl9bmM8rZg1pRl9JXhV5g4NRNzHYIyIiIqrAtmTTapNB6ikpjpIKKKu3rr87gssGEw0fZ1nAgfGUZ9M3AeDs0urmOzVgxuXzVXJ8ZrnuIif5vOI5A6ZzrqzlNvQwPBNQQZt6ZHOKbIcUaWGwR0RERFRFyDL3o1IsbCMaLo6vx+WqmM3YtS2ObSVTS+txxVDS80B1xeWs13KNHoduWFrN4eS5xorJzC6vNd1Wwi2n5zYGd9MLq8gZGlCt5ortITqBua9gRERERAGLGtZUvdx6kNcTcGYPAEQE+8dSFwLQzQz3xLCj35t1eqXczs56ne09Nr2EZpaTHZteCnSd3FRZJi9fUMwsmTmVc3E1Z3x7CLeY/QpGREREFCCT1+wBxb50IVuMaWAdCVk4UMf6va6Ijb2j/vQEdDtz6GUmciGTxcxic9NEV7OFwIq1LGSyFdcNTi+aN5VTVbGQzmLe8IqhbmGwR0RERNSiEtEQElHvGpE3ozcewSWbZOz2jfYg5OE6vVJDLvfu86oXIAD89NzWqoaeOu9ftdBS01XW551bWjNubdzyWh65vGJuhcEeERERERksFrGNyeqVunSgu2o7hpFUDH3dja3t24qeCj0Jm5WKh9HtUXCdXstfNBWyUStr+QsVMf2SzRcwMVs5o5gvaNXHgjLrVFNdyxU6Yiongz0iIiKiFhUNWYjVuUbOTyHbqprd2zXQ7fNogLGUOw3nR1PeZfVOnl9uaq1euVdnGivuslUvTS0il68+8BMzy1hZMyeoOl/SOuOcoWsK3WTeqwMRERER1SVsWZ62LdiK0d7YRWv3euPhQKadjqRi2GphVdsSz6ZwruUKOO3ServFTA7nfGgPAQCn59KYnKudjcwXFE9PzBvR1y5f0A3BntttOUxk5qsDEREREW3KsgTRkHnTOIFis/X+sumaXq53qyUSsjDSs7Xs3lhvl2eB9dRCpq4G6vWanPe+MMpCJosXztTX328pk8PzBvQCPLu4uiHonFtZQyZrRkN6rzDYIyIiImphYdvciqHlxVGGeqIBjQS4bLAbdpPVVUO2YNeAd20i3K4MueBxpclcvoBnJuYbClDPzGcCqxa67rW5jQVwVOFaRtVUDPaIiIiIWljY4F6Ag4nXg7tUPBxoFjIWtrF7KNHUsXuGk8ZmUCvxesLkK2eXm2pW/9LUYmCZtLmVNcwuXxwEn5pNG9v83Q3mvjoQERER0aZCBvcCjISsCw3ft/lYgbOaHf1xjDRYZGWstwtjve4UeKmmK+JuIOn2+UqtrOUwMdtci4h8XnH8rL8FZNYdm16quD2bK+Dk+a21vDAZgz0iIiKiFmZt1sE8YOvr9rZ1BzeFs9S+0R70xutrjN7XHcFVI943f++PuxsIu32+Uq/ObK1q6OR82vfs3vRCpmZfvZ+eW2nbtXsM9oiIiIhamOGxHlJdYVgWkHSp191WWZbg4Hgv4ptkv+JRGwfHU7B8yJz2xsOIuthCw6tCOCtrOZzZYvEXVfia3cvmC3hxarHmPvmC4sUztfdpVQz2iIiIiFqYwOxoLxkLIR4J+RI01SsSsnBwR2/Vgi22Lbh2R69vbS1EBON97hSAGUhGPZvGefysO70AJ+fTvvXee35yAavZzdfknV1cxak2nM7JYI+IiIiohZme2YuFbWOyeqUS0VDVgi17hpOIR/wd846+ri1n90SAywe9aVrvRlZvnSpwYsb7wOr42SVML9TfS++lqcUNffjaAYM9IiIiIvJUT6y+NXJ+297bdVEWLB61MdZgERc3hGwL+0Z7tnSOSwe6kfTouZ5ZdDcIml70thfgmflMw9NFVYGnJ+awvOpP1tEPDPaIiIiIWpjJ1TjXbbY+LiiWJRjv21hpc0dfHBJQunRbItp0P7++7gguHfAmqwcAa3l3C5jk8gp1Y05oBem1fNNN3HN5xdHX5lEoeN3Awh8M9oiIiIhaWFCBSSNCPq19a8ZwT+zCVFjL8q64Sb0uG0ggVWe10HXhkIX9Yz2e/l9wu+qrZXn3f/fY9BLyWwjWljI5nJ5vj2br5t55RERERNQWTE4+xsI2ep1WBf3dUUQCblJvWYL9Yz2w7fqftL2jScTC3mZP3T5/zKMm9Zls3pUpoqfOM9gjIiIiItqU6dnHoWSxB+Bg0oxegPFICHtH6lu/t6M/jqGk99nIni531wJ6tbbw/PKaKxVDl1dzbdF7j8EeEREREXkq3ECWKgh9TuN3L5uRN2okFcN4f1fNfVLxMK6oUlHUbYloyNWAb6zXmwB1dsW9QjJunisoDPaIiIiIyFNRj6bsuaU7YiNki2f96Zq1ZyiJRJW2FbYtOLDdn6bv6/Y1OL20mrHeLmxLeJNFdbN1wrklBntERERERC1NRJByeZqiGyxLsLdKO4bdgwnP1+mVS0RDOLg9BWsLEcRAMoqrRpLuDarEYiZbVwP1ep1bXvOsYqhfGOwRERERUcdLRM1r/A4Aqa4whno2ZsG6Ija299ae4umVbYkort6eQjPLMPu6w55mIxcz7vbHy+YKWM25FzwGgcEeEREREXW8uKHBHoCL+uft3Bb3dfpmuaFkDFc12AA+EQvhmvFe2B6O24uek263nPAbgz0iIiIi6nhdPk+JbEQyFkZ/olg8JhyyMJYKJqtXantvF3b019cAPmQLrhnv9bzf4rZEFGEXW2cMJINvxbFVrT16IiIiIiIXxMJmfyxeD/BGemKBZvVKXTGUQHcdGdG9oz2+FL+xLcGVw+6sB7RtwZ5hfyqdesns/9VERERERD7wcnqhG/qd9hDbEua0h7Aswb5NpnMOJKMY7vG+D+C6kVQMu8qmvTZKBDiwPYV4xNypvfVisEdEREREHc/0tVmRkIV4xEaPR83Im5WKhzFapWeeZSGQ7NjuocSmPQpr2T+WwoBHrSH8xmCPiIiIiDqe2aFeUU9X2Mg1ZJcPJipmRi/pjweWHbtyOImRVOMZxb1jPU0dZyrz/rcQEREREfnM6+IhbjCxFyAAxML2RcVaQrZg57atTafcChHB/rEeDCTrz9BdMZwIrKWFV8z/X01ERERERMZN4Sx1SX98Q7P18b4uhAMOoEUEB7ankIxtnl0c7+8KNDj1CoM9IiIiIqIWkIqbG+xFQtaGdW5jhmTIbEtwzY7emi0Z+rrD2DPkThVP0zDYIyIiIiKiLRtKFte6xaO2UZUsY2Eb+8cqVw0N2YL9Yylj2lm4jcEeERERERFt2Xp7CBMrWQ4kohWzjVeN9CAW9r4HYFAY7BERERER0ZZFQhYSsRB6DZ1uevlQN2z79QxebzzcVpU3K2GwR0REREREruiJhY2tGhoN2djR93rV0MsG/e8B6DcGe0RERERE5IpkLIRoyNxpkeN9XRApritcn3bazsxZOUlERERERC2tK2JuoAcUi7X0xsPoi7d/oAd4nNkTkXeLyIsickxEPlfhcRGRe53HnxaRN3o5HiIiIiIi8k63QVU4q+mLRzoiqwd4GOyJiA3gjwC8B8A+AB8UkX1lu70HwBXOn48B+GOvxkNERERERN4yPbMHAN3RkFGtIbzkZWbvzQCOqepxVV0D8C0A7y3b570Avq5FjwHoFZFRD8dEREREREQdLBayEanRZL2dePlTbgdwquTfE862RveBiHxMRI6IyJGzZ8+6PlAiIiIiIuoMiVhnZPUAb4O9Sm3otYl9oKpfVdXrVPW6wcFBVwZHRERERESdx7YqhSDtyctgbwLAjpJ/jwM43cQ+RERERERE1CAvg73HAVwhIpeKSATABwAcLtvnMIAPO1U53wpgXlUnPRwTERERERFRR/Bswqqq5kTkUwAeBWADuF9VnxWRTziP3wfgYQA3ATgGYAXAR70aDxERERERUSfxdHWiqj6MYkBXuu2+kq8VwCe9HAMREREREVEn6oyao0RERERERB2GwR4REREREVEbYrBHRERERETUhhjsERERERERtSEGe0RERERERG2IwR4REREREVEbYrBHRERERETUhhjsERERERERtSEGe0RERERERG2IwR4REREREVEbYrBHRERERETUhhjsERERERERtSEGe0RERERERG1IVDXoMTRERM4COBn0OAwzAGAm6EFQRbw25uK1MRevjZl4XczFa2MuXhtztfq12amqg5vt1HLBHl1MRI6o6nVBj4MuxmtjLl4bc/HamInXxVy8NubitTFXp1wbTuMkIiIiIiJqQwz2iIiIiIiI2hCDvfbw1aAHQFXx2piL18ZcvDZm4nUxF6+NuXhtzNUR14Zr9oiIiIiIiNoQM3tERERERERtiMFeixCRHSLyAxF5XkSeFZHfqLDPIRGZF5GnnD+fD2KsnUhETojIUed5P1LhcRGRe0XkmIg8LSJvDGKcnUZEriy5H54SkQURub1sH943PhGR+0VkWkSeKdnWLyLfE5GXnb/7qhz7bhF50bmHPuffqNtfletyt4i84LxePSgivVWOrfnaR1tT5dp8QUReK3nNuqnKsbxnPFTl2ny75LqcEJGnqhzL+8Yj1T4vd/J7DadxtggRGQUwqqpPikgSwBMAfl5VnyvZ5xCA31TVnwtomB1LRE4AuE5VK/Zrcd6Mfx3ATQDeAuDLqvoW/0ZIImIDeA3AW1T1ZMn2Q+B94wsR+RkASwC+rqpXO9v+E4DzqnqX88bap6qfLTvOBvASgJ8FMAHgcQAfLH39o+ZVuS7vAvC/VTUnIr8HAOXXxdnvBGq89tHWVLk2XwCwpKr/ucZxvGc8VunalD3++wDmVfWLFR47Ad43nqj2eRnAL6ND32uY2WsRqjqpqk86Xy8CeB7A9mBHRQ14L4pvCKqqjwHodV6QyD83AnilNNAjf6nq3wE4X7b5vQC+5nz9NRTflMu9GcAxVT2uqmsAvuUcRy6odF1U9buqmnP++RiAcd8HRtXumXrwnvFYrWsjIgLgNgDf9HVQVOvzcse+1zDYa0EisgvAGwD8vwoPv01EfiIij4jIfl8H1tkUwHdF5AkR+ViFx7cDOFXy7wkwWPfbB1D9jZf3TXCGVXUSKL5JAxiqsA/vn2D9CoBHqjy22WsfeeNTzhTb+6tMR+M9E6y3A5hS1ZerPM77xgdln5c79r2GwV6LEZEEgL8CcLuqLpQ9/CSAnap6DYCvAPjvfo+vg92gqm8E8B4An3Smd5SSCsdwDrVPRCQC4BYA36nwMO8b8/H+CYiI/AcAOQDfqLLLZq995L4/BnA5gGsBTAL4/Qr78J4J1gdRO6vH+8Zjm3xernpYhW0tf98w2GshIhJG8T/uN1T1r8sfV9UFVV1yvn4YQFhEBnweZkdS1dPO39MAHkRxKkCpCQA7Sv49DuC0P6MjFN9Qn1TVqfIHeN8Ebmp9SrPz93SFfXj/BEBEPgLg5wD8klZZ4F/Hax+5TFWnVDWvqgUAf4LKzznvmYCISAjALwL4drV9eN94q8rn5Y59r2Gw1yKc+d9/BuB5Vb2nyj4jzn4QkTejeH3P+TfKziQi3c4iYIhIN4B3AXimbLfDAD4sRW9FcdH2pM9D7WRVf8vK+yZwhwF8xPn6IwD+psI+jwO4QkQudbK0H3COI4+IyLsBfBbALaq6UmWfel77yGVl671/AZWfc94zwXkngBdUdaLSg7xvvFXj83LHvteEgh4A1e0GAB8CcLSklO+/B3AJAKjqfQBuBfBrIpIDkAbwgWq/jSVXDQN40IkXQgD+UlX/p4h8ArhwbR5GsRLnMQArAD4a0Fg7jojEUays9fGSbaXXhveNT0TkmwAOARgQkQkA/xHAXQAeEJFfBfBTAO9z9h0D8KeqepNTEfJTAB4FYAO4dTTAgwAABfJJREFUX1WfDeJnaEdVrstvA4gC+J7z2vaYqn6i9LqgymtfAD9C26pybQ6JyLUoTi87Aee1jfeMvypdG1X9M1RYH877xlfVPi937HsNWy8QERERERG1IU7jJCIiIiIiakMM9oiIiIiIiNoQgz0iIiIiIqI2xGCPiIiIiIioDTHYIyIiIiIiakMM9oiIiIiIiNoQgz0iIvKEiORF5CkReVZEfiIid4iI5Tx2nYjcW+PYXSLyL/0b7Ybv3Ssi/7bBY3aJSEONkUXkz0Xk1gaPuV1EPux8fZXz/P6jiFzeyHlKzhUv+ff/EpG+Rs9DRETmYrBHREReSavqtaq6H8XG9jeh2BQaqnpEVT9d49hdAAIJ9gD0Amgo2PODiIQA/AqAv3Q2/TyAv1HVN6jqK02c8nYA8ZJ//wUM/LmJiKh5DPaIiMhzqjoN4GMAPiVFh0TkIQAQkX/mZKjWs1RJAHcBeLuz7TNO5uzvReRJ588/cY49JCL/R0T+m4i8ICLfEBFxHrteRP6vk1X8sYgkRcQWkbtF5HEReVpEPl5huHcBuNz53nc7471bRJ4RkaMi8v4qP6YtIn/iZDK/KyJdzjiuFZHHnO/3YKXsmYi8SUR+KCJPiMijIjJa4fz/HMCTqpoTkZtQDNb+tYj8wDnHv3J+zqdE5L+KiO1sf5eI/IPzvH1HRBIi8mkAYwB+sH48gMMAPrjpxSQiopbBYI+IiHyhqsdRfN8ZKnvoNwF8UlWvBfB2AGkAnwPw905m8EsApgH8rKq+EcD7AZROAX0DioHPPgCXAbhBRCIAvg3gN1T1GgDvdM77qwDmVfV6ANcD+DcicmnZeD4H4BXne/87AL8I4FoA6+e5u0owdgWAP3IymXMA/oWz/esAPquqBwEchZPdXCciYQBfAXCrqr4JwP0AfrfC+W8A8ITzXD4M4D4AX1LVd4jIXud5ucF5HvMAfklEBgDcCeCdznN3BMAdqnovgNMA3qGq73DOOQsgKiLbKnxvIiJqQaGgB0BERB1FKmz7EYB7ROQbAP5aVSec5FypMIA/FJH1QGZPyWM/VtUJABCRp1CcAjoPYFJVHwcAVV1wHn8XgIMla+VSKAZpr9YY8z8F8E1VzQOYEpEfohgoHi7b71VVfcr5+gkAu0QkBaBXVX/obP8agO+UHXclgKsBfM/5uW0AkxXGMQrg+SpjvBHAmwA87pyjC8UA+a0oBsE/crZHAPxDjZ91GsWM37ka+xARUYtgsEdERL4QkctQDNSmAexd366qd4nI/0BxTd9jIvLOCod/BsAUitk1C0Cm5LHVkq/zKL63CQCtNAwAv66qjzYy9Dr3Kx9HVwPnf1ZV37bJfmkAsRrn+Jqq/vaGjSI3A/ieqtY7PTPmfB8iImoDnMZJRESeE5FBFKcd/qGqatljl6vqUVX9PRSnGV4FYBFAsmS3FIqZugKAD6GY/arlBQBjInK98z2SToGTRwH8mjN1EiKyR0S6y44t/95/B+D9znq/QQA/A+DH9fzcqjoPYFZE3u5s+hCAH5bt9iKAQRF5mzOmsIjsr3C65wHsrvKtvg/gVhEZcs7RLyI7ATyG4rTW3c72uIisZ0U3/JzOWscRACfq+dmIiMh8zOwREZFXupxplWEAORSrPd5TYb/bReQdKGbDngPwCIACgJyI/ATAnwP4LwD+SkTeB+AHAJZrfWNVXXMKqXzFKZSSRnG93Z+iOM3zSSe4OYtiVcvSY8+JyI+k2ErhEQC/BeBtAH6CYrbwt1T1TAPPw0cA3CfFNgfHAXy0wlhvBXCvM+0zBOAPADxbdp5HUHwOK/28z4nInQC+K8X2FlkU10E+JiK/DOCbIhJ1dr8TwEsAvgrgERGZdNbtvQnAY6qaa+BnIyIig0nZL1iJiIjIUCLyIIrB5ssenPvLAA6r6vfdPjcREQWD0ziJiIhax+dQLNTihWcY6BERtRdm9oiIiIiIiNoQM3tERERERERtiMEeERERERFRG2KwR0RERERE1IYY7BEREREREbUhBntERERERERt6P8DvNVfRN238TgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,7.5))\n",
    "plt.violinplot(fit_obs['y_pred']/data['n'].values,positions=data['x'],showextrema=False);\n",
    "plt.plot(data['x'],data['y']/data['n'],'o')\n",
    "plt.xlabel('Distance to hole (feet)');\n",
    "plt.ylabel('Probability of Success' );"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Posterior Predicitive Checks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "When examining goodness of fits, the typical method is to look at the residuals. i.e. $\\frac{data - model}{\\sigma}$. Because we have distribution of $y^{rep}$, we can do this in a more probabilisitic way using posterior predictive checks. For more information on posterior predictive checks, [Gelman et al. 1996](http://www.stat.columbia.edu/~gelman/research/published/A6n41.pdf) is a good starting point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:12: VisibleDeprecationWarning: Passing `normed=True` on non-uniform bins has always been broken, and computes neither the probability density function nor the probability mass function. The result is only correct if the bins are uniform, when density=True will produce the same result anyway. The argument will be removed in a future version of numpy.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib as mpl\n",
    "sns.set_style(\"white\")\n",
    "\n",
    "fig=plt.figure(figsize=(10,5))\n",
    "\n",
    "\n",
    "# This is  the colormap I'd like to use.\n",
    "cm = sns.diverging_palette(220, 20, as_cmap=True)\n",
    "\n",
    "# Get the histogramp\n",
    "Y,X = np.histogram(fit_obs['y_pred'][:,0]/data['n'].values[0], 25, normed=1)\n",
    "#C = [cm(((x-X.min())/x_span)) for x in X]\n",
    "C = [cm(((((x-np.mean(fit_obs['y_pred'][:,0]/data['n'].values[0]))/np.std(fit_obs['y_pred'][:,0]/data['n'].values[0]))+6)/12.0)) for x in X]\n",
    "\n",
    "\n",
    "plt.bar(X[:-1],Y,color=C,width=X[1]-X[0])\n",
    "plt.xlabel('Prob. of success at distance '+str(data['x'].values[0]))\n",
    "plt.ylabel('p(CO$_2$ in 1980)')\n",
    "plt.axvline(0.82, linestyle='--')\n",
    "plt.axvline(0.87,linestyle=':')\n",
    "plt.annotate('higher success rate than \\n model cannot explain',xy=(0.87, 10),  xycoords='data',\n",
    "            xytext=(0.87, 30), textcoords='data',rotation='vertical',size='large')\n",
    "plt.annotate('success in model to high\\n compared to data',xy=(0.82, 10),  xycoords='data',\n",
    "            xytext=(0.82, 30), textcoords='data',rotation='vertical',size='large')\n",
    "\n",
    "#ax1 = fig.add_axes([0.05, 0.80, 0.9, 0.15])\n",
    "ax1 = fig.add_axes([0.82, 0.15, 0.02, 0.7])\n",
    "\n",
    "norm = mpl.colors.Normalize(vmin=-6, vmax=6)\n",
    "cb1 = mpl.colorbar.ColorbarBase(ax1, cmap=cm,\n",
    "                                norm=norm,\n",
    "                                orientation='vertical')\n",
    "cb1.set_label('$\\sigma$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can calculate fraction of $y^{rep}$ samples above and below real success value. This is often referred to as the Bayesian P-value and is telling us what the probability is of drawing the real success measurement, from our model which has been inferred on the data. This is tells us if the model is inconsistent with the data, given the uncertianties in parameters and data.\n",
    "\n",
    "* $\\sim 0.5$ (i.e. near the middle of the distribution) means our model is consistent with the data \n",
    "* $0.99$ or $0.01$ (i.e. in the tails) means the model is missing something.\n",
    "\n",
    "We can convert this to a typical '$\\sigma$' level, such that  $\\sigma < -3$ or $\\sigma > 3$ indicates a problem with the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "For more information on posterior predictive checks, see:\n",
    "* [Bayesian Data Analysis](http://www.stat.columbia.edu/~gelman/book/)\n",
    "* [http://www.stat.columbia.edu/~gelman/research/published/philosophy.pdf](http://www.stat.columbia.edu/~gelman/research/published/philosophy.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def Bayes_P_value(rep_data,obs_data):\n",
    "    import scipy.stats as st\n",
    "    pval=np.empty_like(obs_data)\n",
    "    for i,d in enumerate(obs_data):\n",
    "        ind=rep_data[:,i]<d\n",
    "        pval[i]=st.norm.ppf(sum(ind)/rep_data.shape[0])\n",
    "    return pval\n",
    "pvalues=Bayes_P_value(fit_obs['y_pred']/data['n'].values,data['y']/data['n'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([        inf,  1.15522085, -1.43250272,        -inf,        -inf,\n",
       "       -2.5758293 , -2.74778139,        -inf, -2.43237906, -1.39837662,\n",
       "       -1.37220381, -0.41246313,  3.29052673, -0.08029831, -0.04889873,\n",
       "        2.03352015,         inf,  2.87816174,         inf])"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior Predictive checks II"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "obs_data_stat=data['y'].values[0]-data['y'].values[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7fc2e19d7d50>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(fit_obs['y_pred'][:,0]-fit_obs['y_pred'][:,-1])\n",
    "plt.axvline(x=obs_data_stat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "ind=(fit_obs['y_pred'][:,0]-fit_obs['y_pred'][:,-1])<obs_data_stat   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as st\n",
    "st.norm.ppf(np.sum(ind)/fit_obs['y_pred'].shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Model Improvement\n",
    "What is wrong with our model?\n",
    "\n",
    "How could we improve it?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}