examples/Time-Space KDE.ipynb

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    "# Time / Space KDE algorithms\n",
    "\n",
    "These are a general class of prediction algorithms which are motivated by the \"pro-hotspot\" algorithm, but which work in continuous space and time and so remove the annoying problem of choosing how to compute distances in a grid etc.  In principle, this algorithm, with well-chosen kernels, should out perform all the \"classical\" algorithms.  Unfortunently, the extensive use of KDEs means that this algorithm can be a little slow.\n",
    "\n",
    "## References\n",
    "\n",
    "1. Bowers, Johnson, Pease, \"Prospective hot-spotting: The future of crime mapping?\", Brit. J. Criminol. (2004) 44 641--658.  doi:10.1093/bjc/azh036\n",
    "2. Rosser et al. \"Predictive Crime Mapping: Arbitrary Grids or Street Networks?\" Journal of Quantitative Criminology 33 (2017) 569--594 [10.1007/s10940-016-9321-x](https://link.springer.com/article/10.1007/s10940-016-9321-x)\n",
    "\n",
    "(1) is motivation, and (2) contains an example of this class of algorithm (see page 11, equation (2) of that paper, for example)."
   ]
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   "source": [
    "## Algorithm\n",
    "\n",
    "A grid is only used right at the end to produce the final prediction.\n",
    "\n",
    "### Aim of the algorithm\n",
    "\n",
    "We estimate a relative \"risk\" at the current time, and at location $x$ (a two dimensional vector) by\n",
    "$$ r(x) = \\sum_i f(t_i) g(x-x_i) $$\n",
    "where we have events which occurred $t_i$ time units in the past, and at location $x_i$.  This is hence a combined time and space KDE method.\n",
    "\n",
    "We then compute the average of $r$ in each grid cell to obtain the prediction (in practise we use a monte-carlo approach, and sample $r$ at random locations in each grid cell).\n",
    "\n",
    "Our code allows complete freedom in choosing $f$ and $g$; we provide some common choices.  For the time component $f$:\n",
    "\n",
    "- $f(t)=1$ for all $t$.  So take no account of time.\n",
    "- $f(t) = e^{-\\beta t}$ exponential decay.\n",
    "- $f(t) = ( 1 + (x/\\beta)^2 )^{-1}$ quadratic decay.\n",
    "\n",
    "For space we use a classical KDE method:\n",
    "\n",
    "- Either a general Gaussian KDE method, as implemented by our class `GaussianBase` (which with default parameters replicates the behaviour of the `scipy` KDE method.\n",
    "- A variable bandwidth nearest neighbour estimator.  This tends to produce \"clusters\" which look more realistic."
   ]
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   "execution_count": 1,
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    "collapsed": true
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   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import open_cp\n",
    "import open_cp.kde as kde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "# Generate some random data\n",
    "import datetime\n",
    "times = [datetime.datetime(2017,3,10) + datetime.timedelta(days=np.random.randint(0,10)) for _ in range(20)]\n",
    "times.sort()\n",
    "xc = np.random.random(size=20) * 500\n",
    "yc = np.random.random(size=20) * 500\n",
    "points = open_cp.TimedPoints.from_coords(times, xc, yc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "region = open_cp.RectangularRegion(0,500, 0,500)\n",
    "predictor = kde.KDE(region=region, grid_size=50)\n",
    "predictor.time_kernel = kde.ExponentialTimeKernel(1)\n",
    "predictor.space_kernel = kde.GaussianBaseProvider()\n",
    "predictor.data = points\n",
    "gridpred = predictor.predict(samples=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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   "outputs": [
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CnYiGiZgkSZqki4GdVfVIVe0HbgPWzNhnDXBrDWwDzkyyfJa+a4BNzfIm4Iqh9tuqal9V\nPQrsBC5ujndGVW2rqgJuHeozMZ1IxKaWnsDTrzqt7WGMbP9LD7Q9hLF9/6lPtD2Esd3x3Iq2hzCW\nv3p2VdtDGNv/88AFbQ9hbEue6sS/tkZ2wr72E4hx5WDbIxjfCc+3PYLFoQuJGHAu8PjQ+i4Gqdds\n+5w7S99lVbWnWd4LLBs61rbDHOv5Znlm+7R/lOTHgB3AP6uq4e+dNyZikiRpvp2T5N6hz0SfgNwk\nXDWHQ/zfwCuq6tXAXXwnaZt3i+v/WkqSpGMy4Sfrf6WqLjrCtt3AeUPrK5q2UfY58Sh9n0iyvKr2\nNJcdn5zlWLub5e86VlU9NdT+AeC3j/C7zJmJmCRJmqR7gFVJViY5icFE+i0z9tkCXNXcPXkJ8Exz\n2fFofbcA65rldcDtQ+1rk5ycZCWDGwDubo73bJJLmrslr5ru0xRy094OfGHefvsZTMQkSeqJ6sAc\nsao6kOS9wJ3AEuCDVbU9ybXN9lsY3MH4NgYT678JvOtofZtD3wBsTnI18BhwZdNne5LNwIPAAWB9\nc8ckwHuADwFLGdwtOX3H5D9N8vZm/68CP7cApwKwEJMkSRNWVXcwKLaG224ZWi7gsM89OVzfpv0p\n4NIj9LkeuP4w7fcCrzpM+3XAdUf9JeaJlyYlSZJaYiImSVJP+NLv7jERkyRJaomJmCRJPVC+9LuT\nTMQkSZJaYiImSVJPdOHxFTqUiZgkSVJLTMQkSeqFib7iSCMyEZMkSWqJiZgkST3hHLHuMRGTJElq\niYmYJEk9UPgcsS4yEZMkSWqJiZgkSX1Qg6frq1tMxCRJklpiIiZJUk8cxDliXWMiJkka25c/dBNf\n/tBNbQ9DWvQsxCRJklripUlJ0simU7BvPfbwIesv/7n1rY1Joyl8oGsXmYhJkiS1xERMkjSy6eTL\nJGwx8qXfXWQiJkmS1BITMUnS2EzCFicf6No9JmKSJEktMRGTJKknvGuye0zEJEmSWmIiJklSD1SZ\niHWRiZgkSVJLTMQkSeoJnyPWPSZikiRJLTERkySpJ3yOWPeYiEmSJLXEREySpJ7wrsnuMRGTJElq\niYWYJElSS7w0KUlSDxTx0mQHmYhJkiS1xERMkqSe8OkV3WMiJkmS1BITMUmS+sCXfneSiZgkSVJL\nTMQkSeoLJ4l1jomYJElSS0zEJEnqCeeIdc+siViSU5LcneRvkmxP8ptN+9lJ7kryUPPzrKE+1yXZ\nmWRHkssW8heQJElarEa5NLkPeEtVvQa4EFid5BJgA7C1qlYBW5t1kpwPrAUuAFYDNydZshCDlyRJ\no6uazEejm7UQq4FvNKsnNp8C1gCbmvZNwBXN8hrgtqraV1WPAjuBi+d11JIkSceBkSbrJ1mS5D7g\nSeCuqvo0sKyq9jS77AWWNcvnAo8Pdd/VtEmSpJYUgzlik/hodCNN1q+qKeDCJGcCH03yqhnbK8lY\nYWSSa4BrAE469SwW1d/t5INtj2Bsf/GV/6btIYxtz7Ova3sIY/nmF89sewhjO/PLi+l/eAMnPre4\nrnscOKXtERyDxfePBS/++wNtD0E6JmM9vqKqvgZ8isHcryeSLAdofj7Z7LYbOG+o24qmbeaxNlbV\nRVV10YtOOfVYxi5JkkZVQGUyH41slLsmv6dJwkiyFHgr8EVgC7Cu2W0dcHuzvAVYm+TkJCuBVcDd\n8z1wSZKkxW6US5PLgU3NnY8nAJur6mNJ/hrYnORq4DHgSoCq2p5kM/AgcABY31zalCRJ0pBZC7Gq\nuh947WHanwIuPUKf64Hr5zw6SZI0b3y0RPf4iiNJkqSW+IojSZL6wkSsc0zEJEmSWmIiJklSL/iw\n1S4yEZOk48BDt9/EQ7ff1PYwJI3JREySpL5wjljnWIhJ0iI2nYI993cPH7K+as361sYkaXQWYpIk\n9UHhHLEOshCTpEVsOvkyCZMWJwsxSZL6wjlinWMhprHc874/AeCH//efbXkkkoaZhEmLk4WYJEm9\n4RyxrrEQ00imk7Cn/2b3IesmY5IkHTsLMUmS+sI5Yp1jIaaRTCdfJmGSJM0fX3EkSZLUEhMxjcUk\nTJIWMS9Ndo6JmCRJUktMxCRJ6oMCfMVR55iISZIkzUGSyw/Tdu0ofS3EJEnqiarJfHroXyZ5y/RK\nkl8G1ozS0UuTkiRJc/N24GNJ/jmwGvhBLMQkSdIh+plWLbiq+kqStwOfBD4D/GzVaNmghZgkSdIx\nSPJ1BuVtmp8nAd8H/GySqqozZjuGhZgkSX3hXZPzqqpOn+sxnKwvSZI0B0nemOTUZvmdSX4nyctH\n6WshJklST6Qm85l1HMnqJDuS7Eyy4TDbk+TGZvv9SV43W98kZye5K8lDzc+zhrZd1+y/I8llQ+2v\nT/JAs+3GJIdEhkn+UZJKctEsv9L7gW8meQ3wS8DDwH+e/UxYiEmSpAlKsgS4CbgcOB94R5LzZ+x2\nObCq+VzDoNCZre8GYGtVrQK2Nus029cCFzC4o/Hm5jg0x3330HetHhrn6cD7gE+P8GsdaCbnrwF+\nt6puAka6bGkhJklSH9QEP0d3MbCzqh6pqv3AbXz3ox7WALfWwDbgzCTLZ+m7BtjULG8Crhhqv62q\n9lXVo8BO4OLmeGdU1bamiLp1qA/A/wr8W+Dbs/5G8PUk1wHvBP5rkhOAE0foZyEmSZIm6lzg8aH1\nXU3bKPscre+yqtrTLO8Flo1wrF2HO1ZzKfS8qvqvI/5O/wOwD7i6qvYCK4B/N0rHRXPX5I47bgbg\nB972npZHIknSYpRJ3jV5TpJ7h9Y3VtXGSX15VVUyymy179akWb8D/NwY37e36TO9/mUGCdusFk0h\nJkmSFo2vVNWRJrjvBs4bWl/RtI2yz4lH6ftEkuVVtae57PjkLMfa3SzPbD8deBXwZ83c/ZcBW5K8\nvaqGi0uS/GVV/ejQ88Re2MSgHpz1OWKdvzS5446b2XHHzXxj78N8Y+/DL6xLkqRF6R5gVZKVSU5i\nMJF+y4x9tgBXNXdPXgI801x2PFrfLcC6ZnkdcPtQ+9okJydZyWBS/t3N8Z5Ncklzt+RVwO1V9UxV\nnVNVr6iqVwDbgO8qwgCq6kebn6dX1RlDn9NHKcLAREySpP7owCuOqupAkvcCdwJLgA9W1fYk1zbb\nbwHuAN7GYGL9N4F3Ha1vc+gbgM1JrgYeA65s+mxPshl4EDgArK+qqabPe4APAUuBjzefsTR3YG6v\nqh8cty8sgkJsek6Yc8QkSTo+VNUdDIqt4bZbhpYLWD9q36b9KeDSI/S5Hrj+MO33MrgMebSxvmmW\n7VPN88le3swNG0vnCzFJkjRPOpCIHafOArYnuRt4brqxqt4+W8dFU4iZhEmSpI76l8facdEUYpIk\naY5MxBZEVf35sfbt/F2T88k7LiVJUpeYiEmS1AfFJB/oqhH1ohCbTsG+sffhQ9addyZJkuZDkqXA\ny6tqxzj9enVpUpKkPktN5tM3SX4auA/4RLN+YZKZD6k9rF4kYj6LTJIkLaDfAC4G/gygqu5rnuI/\nq14UYpIkCe+aXDjPV9Uzzbspp410tntViJmESZKkBbA9yf8ILEmyCvinwP83SkfniEmSJM3N/wxc\nAOwDPgw8A/zCKB17lYhJkiQtgB+sql8Dfm3cjhZikiT1RB/vaJyQf5/kZcCfAH9cVZ8ftaOXJiVJ\nkuagqt4MvBn4e+D3kjyQ5F+M0rcTiVim4JSvHWx7GCM75ZGT2h7C2HZ8Y0XbQxjb0r1L2h7CWM55\nePH8MzzttF3fbnsIY6sli+vJ4PtfcmLbQxjbYnz4+slf3d/2EBaHxfjHXSSqai9wY5JPAb8M/Cvg\nX8/Wz0RM0nHts5/7fT77ud9vexiSjmNJ/tskv5HkAeD/YHDH5EgJSCcSMUmSpEXsg8AfA5dV1d+N\n09FCTNJxaToF+9rXHj1k/XWvfXdrY5JaVfhA1wVSVT9yrH0txCRJko5Bks1VdWVzSXK4zA1QVfVD\nsx3DQkzScWk6+TIJk4aYiM239zU/f+pYD+BkfUmSpGNQVXuaxfdU1WPDH2Ck9yqaiEk6rpmESd/h\nA10XzFuBX5nRdvlh2r6LhZgkSdIxSPI/MUi+vi/J/UObTgf+apRjWIhJktQXJmLz7cPAx4F/A2wY\nav96VX11lANYiEmSJB2DqnoGeAZ4B0CSlwKnAKclOa2qvjzbMZysL0lSX9SEPj2T5KeTPAQ8Cvw5\n8CUGSdmsLMQkSZLm5l8DlwB/W1UrgUuBbaN0tBCTJKkHUpP79NDzVfUUcEKSE6rqU8BFo3R0jpgk\nSdLcfC3JacBfAH+Y5EnguVE6WohJktQXlbZHcLxaA3wb+GfAPwZeAvwvo3S0EJMkSZqDqhpOvzaN\n09dCTJKkvujn/K0Fk+TrHOZl39M/q+qM2Y5hISZJknQMqur0uR7DuyYlSZLmKMmPJnlXs3xOkpWj\n9DMRkySpJ3r6aIkFl+TXGTyu4geA/wScBPwB8MbZ+pqISZIkzc1/D7yd5pEVVfV3DF78PSsTMUmS\n+sJEbKHsr6pKBpljklNH7WgiJkmSNDebk/wecGaSdwOfBD4wSkcTMUmS+qC/rx9acFX1vyV5K/As\ng3li/6qq7hqlr4WYJEnSHDWF110ASU5I8o+r6g9n6+elSUmS+qIm9OmJJGckuS7J7yb5iQy8F3gE\nuHKUY5iISZIkHZv/DDwN/DXw88CvMniq/hVVdd8oB7AQkySpL3qUVk3I91XVqwGSfADYA7y8qr49\n6gG8NClJknRsnp9eqKopYNc4RRiYiEmS1BveNTnvXpPk2WY5wNJm3Zd+S5IkLaSqWjLXY3hpUpIk\nqSUWYpIkSS3x0qQkSX3hHLHOMRGTJElqiYWYJElSS7w0KUlSH/jS704yEZMkSWqJiZgkSX1hItY5\nJmKSJEktMRGTJKkvTMQ6x0RMkiSpJSZikiT1QPCuyS4yEZMkSWqJiZgkSX1hItY5JmKSJEktMRGT\nJKkPfLJ+J5mISZIktcRETJKkvjAR65xZE7Ek5yX5VJIHk2xP8r6m/ewkdyV5qPl51lCf65LsTLIj\nyWUL+QtIkiQtVqNcmjwA/FJVnQ9cAqxPcj6wAdhaVauArc06zba1wAXAauDmJEsWYvCSJGkMNaGP\nRjZrIVZVe6rqs83y14EvAOcCa4BNzW6bgCua5TXAbVW1r6oeBXYCF8/3wCVJkha7sSbrJ3kF8Frg\n08CyqtrTbNoLLGuWzwUeH+q2q2mTJEnSkJEn6yc5DfgvwC9U1bNJXthWVZWMd1NskmuAawBOXnrm\nOF0lSdIx8PEV3TNSIZbkRAZF2B9W1Uea5ieSLK+qPUmWA0827buB84a6r2jaDlFVG4GNAC859Xvr\n1C8/d4y/QhtObXsAYzuwdPE9qeTkrz7f9hDG8uJHn257COP79r62RzC2g2ef3vYQxvL8aYvv5vSp\nRfjvC2mxGuWuyQD/EfhCVf3O0KYtwLpmeR1w+1D72iQnJ1kJrALunr8hS5KkY+Jk/c4Z5f+qvRH4\nJ8ADSe5r2n4VuAHYnORq4DHgSoCq2p5kM/Aggzsu11fV1LyPXJIkaZGbtRCrqr8EcoTNlx6hz/XA\n9XMYlyRJmk+mVZ3kRABJkqSWLL5ZpJIk6Zh412T3mIhJkiS1xERMkqS+MBHrHBMxSZKklliISZLU\nE6nJfGYdR7I6yY4kO5NsOMz2JLmx2X5/ktfN1jfJ2UnuSvJQ8/OsoW3XNfvvSHLZUPvrkzzQbLux\neXYqSa5t2u9L8pdJzj/2s350FmKSJGlikiwBbgIuB84H3nGYQudyBg+EX8XgdYjvH6HvBmBrVa0C\ntjbrNNvXAhcAq4Gbm+PQHPfdQ9+1umn/cFW9uqouBH4bGH6g/byyEJMkqS+68WT9i4GdVfVIVe0H\nbgPWzNhnDXBrDWwDzmxep3i0vmuATc3yJuCKofbbqmpfVT0K7AQubo53RlVtq6oCbp3uU1XPDo3l\n1JF+q2PkZH1JkjRJ5wKPD63vAt4wwj7nztJ3WVXtaZb3AsuGjrXtMMd6vlme2Q5AkvXALwInAW8Z\n4fc6JiZikiT1waTSsEF2dE6Se4c+10zkd2w0CdecUqyquqmqXgn8CvAv5mVgh2EiJkmS5ttXquqi\nI2zbDZwc/yiaAAARm0lEQVQ3tL6iaRtlnxOP0veJJMurak9z2fHJWY61u1k+2jhgcPnz/Uf4XebM\nREySJE3SPcCqJCuTnMRgIv2WGftsAa5q7p68BHimuex4tL5bgHXN8jrg9qH2tUlOTrKSwaT8u5vj\nPZvkkuZuyaum+yRZNTSWnwQemrfffgYTMUmSeiDNp21VdSDJe4E7gSXAB6tqe5Jrm+23AHcAb2Mw\nsf6bwLuO1rc59A3A5iRXA48BVzZ9tifZDDwIHADWV9VU0+c9wIeApcDHmw/Ae5P8OIN5ZE/znQJv\n3lmISZKkiaqqOxgUW8NttwwtF7B+1L5N+1PApUfocz1w/WHa7wVedZj29x39N5g/FmKSJPWFrzjq\nHOeISZIktcRETJKknhjl9UOaLBMxSZKklpiISZLUFyZinWMiJkmS1BITMUmS+sJErHNMxCRJklpi\nIiZJUh+Ud012kYmYJElSS0zEJEnqCxOxzjERkyRJaomJmCRJPeEcse4xEZMkSWqJhZgkSVJLvDQp\nSVJfeGmyc0zEJEmSWmIiJklSTzhZv3tMxCRJklpiIiZJUh8UzhHrIBMxSZKklpiISZLUFyZinWMi\nJkmS1BITMUmSeiB412QXmYhJkiS1xERMkqS+MBHrHBMxSZKklpiISZLUEykjsa4xEZMkSWqJiZgk\nSX3gk/U7yURMkiSpJRZikiRJLfHSpCRJPeEDXbvHREySJKklJmKSJPWFiVjnmIhJkiS1pBuJ2PNT\nnLD3q22PYmSnfXt/20MYX9L2CMaWp55pewhjOfjMs20PYWwnnH5a20MY2/5/sKztIYzlmVd041+z\n4ziwtO0RjG/fS17c9hDG9/9O/iudI9Y9JmKSJEktWXz/V02SJB0bE7HOMRGTJElqiYmYJEl9UM4R\n6yITMUmSpJaYiEmS1BcmYp1jIiZJktQSEzFpAdzzrTsB+OGll7U8EkkaCM4R6yITMUmSpJaYiEnz\naDoJe/rgE4esm4xJ6oQyEusaEzFJ0gse/shNfOmPbmp7GFJvmIhJ82g6+TIJkySNwkJMksTDHxmk\nYM/tfhjghVTsFe9Y39qYNP+crN89FmLSAjAJkySNwkJMksQrf2aQfD38kZuoE0zCjkuFD3TtICfr\nS5IktcRETJL0glf+zHoOLG17FFooOdj2CDSTiZgkSVJLTMQkSeoL54h1jomYJElSS0zEJEnqCZ8j\n1j0mYpIkSS0xEZMkqQ8KX/rdQSZikiRJLTERkySpJ5wj1j0mYpIkSS0xEZMkqS9MxDrHREySJKkl\nFmKSJEkt8dKkJEk9EJys30UmYpIkSS0xEZMkqQ+qfKBrB5mISZIktcRETJKknnCOWPeYiEmSJLXE\nREySpL4wEescEzFJkqSWmIhJktQTzhHrHhMxSZKklpiISZLUBwUcNBLrGhMxSZKklpiISZLUFwZi\nnWMiJkmSJirJ6iQ7kuxMsuEw25Pkxmb7/UleN1vfJGcnuSvJQ83Ps4a2XdfsvyPJZUPtr0/yQLPt\nxiRp2n8xyYPNd29N8g8X6lxYiEmS1BOpyXyOOoZkCXATcDlwPvCOJOfP2O1yYFXzuQZ4/wh9NwBb\nq2oVsLVZp9m+FrgAWA3c3ByH5rjvHvqu1U3754CLquqHgD8Bfnuc8zwOCzFJkjRJFwM7q+qRqtoP\n3AasmbHPGuDWGtgGnJlk+Sx91wCbmuVNwBVD7bdV1b6qehTYCVzcHO+MqtpWVQXcOt2nqj5VVd9s\n+m8DVszrGRhiISZJkibpXODxofVdTdso+xyt77Kq2tMs7wWWjXCsXbOMA+Bq4ONH/nXmxsn6kiT1\nRU1stv45Se4dWt9YVRsn9eVVVcncH1+b5J3ARcCPzX1Uh2chJkmS5ttXquqiI2zbDZw3tL6iaRtl\nnxOP0veJJMurak9z2fHJWY61m0MvOR4yjiQ/Dvwa8GNVte8Iv8uceWlSkqSe6MJkfeAeYFWSlUlO\nYjCRfsuMfbYAVzV3T14CPNNcdjxa3y3AumZ5HXD7UPvaJCcnWclgUv7dzfGeTXJJc7fkVdN9krwW\n+D3g7VU1XdAtiFkLsSQfTPJkks8PtY19i6gkSVJVHQDeC9wJfAHYXFXbk1yb5NpmtzuARxhMrP99\n4D1H69v0uQF4a5KHgB9v1mm2bwYeBD4BrK+qqabPe4APNN/zMN+ZC/bvgNOA/zPJfUlmForzZpRL\nkx8CfpfB3QTTpm8RvaF5hscG4Fdm3CL6vcAnk3z/0C8sSZLaUHTmga5VdQeDYmu47Zah5QLWj9q3\naX8KuPQIfa4Hrj9M+73Aqw7T/uNH/w3mz6yJWFX9BfDVGc1j3SI6T2OVJEk6rhzrZP2j3SK6bWi/\nI90KKkmSJihAJnfXpEY058n6TXw49l82yTVJ7k1y7/6D35rrMCRJkhadY03Exr1F9Ls0zxPZCPCS\nU15WnHLyMQ6lBQfbHsD48txzbQ9hbAe/9kzbQxhL7d/f9hDG9z3/oO0RjO2by05sewhj+dbL2h7B\n+Pafvfim9R48ecnsO2lR/vfreHesidhYt4jObYiSJEnHp1kTsSR/BLyJwVNydwG/zuCW0M1JrgYe\nA66EwS2iSaZvET3AobeISpKkFjlHrHtmLcSq6h1H2DTWLaKSJEk6lK84kiSpDzr0HDF9h684kiRJ\naomJmCRJvVDgHLHOMRGTJElqiYmYJEk9EQOxzjERkyRJaomFmCRJUku8NClJUl84Wb9zTMQkSZJa\nYiImSVIfFMSXfneOiZgkSVJLTMQkSeoL54h1jomYJElSS0zEJEnqCwOxzjERkyRJaomJmCRJPRHn\niHWOiZgkSVJLTMQkSeoLE7HOMRGTJElqiYmYJEl9UIBP1u8cEzFJkqSWmIhJktQDobxrsoNMxCRJ\nklpiISZJktQSL01KktQXXprsHBMxSZKklpiISZLUFyZinWMiJkmS1BITMUmS+sAHunaSiZgkSVJL\nTMQkSeoJH+jaPSZikiRJLTERkySpL0zEOsdETJIkqSUmYpIk9UKZiHWQiZgkSVJLTMQkSeqDwkSs\ng0zEJEmSWmIiJklSX/hk/c4xEZMkSWqJhZgkSVJLvDQpSVJP+Iqj7jERkyRJaomJmCRJfWEi1jkm\nYpIkSS0xEZMkqQ8KOGgi1jUmYpIkSS0xEZMkqRd86XcXmYhJkiS1xERMkqS+MBHrnG4UYgmc2I2h\njORFBomTUPv3tz2EsdTUVNtDGN+SJW2PYGzxvyML74TFd5LjOxS1SC2i6keSJM2JiVjnGO1IkiS1\nxERMkjSv9v77WwB42S9d2/JIdAifI9ZJJmKSJEktMRGTJM2L6SRs398+csi6yVhXFJR3NXSNiZgk\nSVJLTMQkSfNiOvkyCZNGZyEmSVJf+PiKzrEQkyTNK5MwaXQWYpIk9YGPr+gkJ+tLkiS1xERMkqS+\ncI5Y55iISZIktcRETJKkvjAR6xwTMUmSpJaYiEmS1AtlItZBJmKSJEktMRGTJKkPCjjoS7+7xkRM\nkiSpJSZikiT1hXPEOsdETJIkqSUWYpIk9UXVZD6zSLI6yY4kO5NsOMz2JLmx2X5/ktfN1jfJ2Unu\nSvJQ8/OsoW3XNfvvSHLZUPvrkzzQbLsxSZr2/y7JZ5McSPKzczjjs7IQkyRJE5NkCXATcDlwPvCO\nJOfP2O1yYFXzuQZ4/wh9NwBbq2oVsLVZp9m+FrgAWA3c3ByH5rjvHvqu1U37l4GfAz48X7/3kViI\nSZKkSboY2FlVj1TVfuA2YM2MfdYAt9bANuDMJMtn6bsG2NQsbwKuGGq/rar2VdWjwE7g4uZ4Z1TV\ntqoq4NbpPlX1paq6H1jw20ydrC9JUi8UHOzEZP1zgceH1ncBbxhhn3Nn6busqvY0y3uBZUPH2naY\nYz3fLM9snygLMUmSNN/OSXLv0PrGqto4qS+vqkrSiapzNhZikiT1QUHVxB7o+pWquugI23YD5w2t\nr2jaRtnnxKP0fSLJ8qra01x2fHKWY+1ulo82jgXnHDFJkjRJ9wCrkqxMchKDifRbZuyzBbiquXvy\nEuCZ5rLj0fpuAdY1y+uA24fa1yY5OclKBpPy726O92ySS5q7Ja8a6jMxJmKSJPVFB+aIVdWBJO8F\n7gSWAB+squ1Jrm223wLcAbyNwcT6bwLvOlrf5tA3AJuTXA08BlzZ9NmeZDPwIHAAWF9VU02f9wAf\nApYCH28+JPlh4KPAWcBPJ/nNqrpgIc6HhZgkSZqoqrqDQbE13HbL0HIB60ft27Q/BVx6hD7XA9cf\npv1e4FWHab+HQy9bLhgLMUmS+sJXHHWOc8QkSZJaYiImSVIfVMHBid01qRGZiEkay6d338and9/W\n9jAk6bhgIiZJUl84R6xzLMQkjWQ6BXv627sOWX/DuWtbG5MkLXYWYpIk9UQ5R6xzLMQkjWQ6+TIJ\nk6T5YyEmSVIvlHPEOshCTNJYTMIkaf74+ApJkqSWmIhJktQHRSde+q1DmYjNo7sfvpW7H7617WFI\nkqRFwkRMkqS+KB9f0TUWYvNgOgV7+rkvH7J+8Suvam1MkiSp+yzEJEnqgQLKOWKdYyE2D6aTL5Mw\nSZI0DgsxSZL6oMo5Yh1kITaPTMIkSdI4FuzxFUlWJ9mRZGeSDQv1PZIkaTR1sCby0egWpBBLsgS4\nCbgcOB94R5LzF+K7JEmSFquFujR5MbCzqh4BSHIbsAZ4cIG+T5IkzcY5Yp2zUJcmzwUeH1rf1bRJ\nkiSp0dpk/STXANc0q/s+8YV/8/m2xtIj5wBfaXsQx7nFdY4fbnsAx+DhRXaOFyfP8WT8wCS/7Os8\nfecn60/OmdDX+c/PiBaqENsNnDe0vqJpe0FVbQQ2AiS5t6ouWqCxqOF5Xnie44XnOV54nuPJSHLv\nJL+vqlZP8vs0moW6NHkPsCrJyiQnAWuBLQv0XZIkSYvSgiRiVXUgyXuBO4ElwAeravtCfJckSdJi\ntWBzxKrqDuCOEXffuFDj0CE8zwvPc7zwPMcLz3M8GZ5nkSofvCZJktSGBXuyviRJko6u9ULMVyHN\njyQfTPJkks8PtZ2d5K4kDzU/zxradl1zznckuaydUS8uSc5L8qkkDybZnuR9TbvneZ4kOSXJ3Un+\npjnHv9m0e47nWZIlST6X5GPNuud4niX5UpIHktw3fYek51kztVqI+SqkefUhYOatyRuArVW1Ctja\nrNOc47XABU2fm5u/hY7uAPBLVXU+cAmwvjmXnuf5sw94S1W9BrgQWJ3kEjzHC+F9wBeG1j3HC+PN\nVXXh0ONAPM86RNuJ2AuvQqqq/cD0q5A0pqr6C+CrM5rXAJua5U3AFUPtt1XVvqp6FNjJ4G+ho6iq\nPVX12Wb56wz+I3Yunud5UwPfaFZPbD6F53heJVkB/CTwgaFmz/FkeJ51iLYLMV+FtLCWVdWeZnkv\nsKxZ9rzPUZJXAK8FPo3neV41l8zuA54E7qoqz/H8+w/ALwPDLx70HM+/Aj6Z5DPN22TA86wZWnvF\nkSarqiqJt8jOgySnAf8F+IWqejbJC9s8z3NXVVPAhUnOBD6a5FUztnuO5yDJTwFPVtVnkrzpcPt4\njufNj1bV7iQvBe5K8sXhjZ5nQfuJ2KyvQtKcPJFkOUDz88mm3fN+jJKcyKAI+8Oq+kjT7HleAFX1\nNeBTDObLeI7nzxuBtyf5EoPpIG9J8gd4juddVe1ufj4JfJTBpUbPsw7RdiHmq5AW1hZgXbO8Drh9\nqH1tkpOTrARWAXe3ML5FJYPo6z8CX6iq3xna5HmeJ0m+p0nCSLIUeCvwRTzH86aqrquqFVX1Cgb/\nzv3TqnonnuN5leTUJKdPLwM/AXwez7NmaPXSpK9Cmj9J/gh4E3BOkl3ArwM3AJuTXA08BlwJUFXb\nk2wGHmRwJ+D65nKQju6NwD8BHmjmMAH8Kp7n+bQc2NTcLXYCsLmqPpbkr/EcLzT/OZ5fyxhcWofB\nf2s/XFWfSHIPnmcN8cn6kiRJLWn70qQkSVJvWYhJkiS1xEJMkiSpJRZikiRJLbEQkyRJaomFmCRJ\nUkssxCRJklpiISZJktSS/x/IE3jNe9DYwgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff26b57e668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,10))\n",
    "\n",
    "m = ax.pcolor(*gridpred.mesh_data(), gridpred.intensity_matrix)\n",
    "ax.scatter(points.xcoords, points.ycoords, marker=\"+\", color=\"black\")\n",
    "cb = plt.colorbar(m, ax=ax)\n",
    "cb.set_label(\"Relative risk\")\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['2017-03-10T00:00:00.000', '2017-03-10T00:00:00.000',\n",
       "       '2017-03-11T00:00:00.000', '2017-03-13T00:00:00.000',\n",
       "       '2017-03-13T00:00:00.000', '2017-03-13T00:00:00.000',\n",
       "       '2017-03-14T00:00:00.000', '2017-03-14T00:00:00.000',\n",
       "       '2017-03-14T00:00:00.000', '2017-03-16T00:00:00.000',\n",
       "       '2017-03-16T00:00:00.000', '2017-03-17T00:00:00.000',\n",
       "       '2017-03-17T00:00:00.000', '2017-03-18T00:00:00.000',\n",
       "       '2017-03-18T00:00:00.000', '2017-03-18T00:00:00.000',\n",
       "       '2017-03-18T00:00:00.000', '2017-03-19T00:00:00.000',\n",
       "       '2017-03-19T00:00:00.000', '2017-03-19T00:00:00.000'], dtype='datetime64[ms]')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points.timestamps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  10.80687601,  203.91685156,  370.45133436,  264.94532001,\n",
       "         338.92134828,  314.17419851,   53.99550215,  422.97038893,\n",
       "         313.82997602,  399.52179916,   29.52651396,  212.27188   ,\n",
       "         378.85486229,   56.75241036,  410.8388701 ,  462.25832124,\n",
       "         210.65487633,  224.4827453 ,  418.81953078,  121.01936992]),\n",
       " array([ 265.17580815,  139.20982958,  474.06359622,   15.23132019,\n",
       "         359.40735878,  246.54587443,  493.97658973,  353.63379925,\n",
       "         383.49718973,  137.2806373 ,  257.1771003 ,  421.78195639,\n",
       "         288.49195233,    6.96268501,  326.20905873,  382.40320547,\n",
       "         419.20469557,  433.21287992,   44.15961916,  283.50612546]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points.xcoords, points.ycoords"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see the dependence on time: the most recent event gives much more total risk than an event far in the past."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}