Kernel Density Estimation Bandwith Slider

kde_bandwidth.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.append(np.random.normal(100, 100, 1000), np.random.normal(300, 40, 1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def K(x, mu=0, std=1):\n",
    "    return 1 / (np.sqrt(2*np.pi*std)*std) * np.exp(-((x-mu)*(x-mu)) / (2*std*std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def silverman():\n",
    "    return 1.06 * np.sqrt(X.var()) * np.power(len(X), -1/5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
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    {
     "data": {
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       "model_id": "8032aefaff784bd7a73edac730856b61",
       "version_major": 2,
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      "text/plain": [
       "interactive(children=(FloatSlider(value=29.36836731473305, description='h', max=88.10510194419915, min=-29.368…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact\n",
    "def plot_edens(h=silverman()):\n",
    "        # estimated density\n",
    "    def f_n(x):\n",
    "        s = 0\n",
    "        for xi in X:\n",
    "            s += K((x-xi)/h)\n",
    "        return s / (len(X)*h)\n",
    "    xvals = np.arange(np.floor(X.min()), np.ceil(X.max()))\n",
    "    b = plt.hist(X, bins=100, density=True)\n",
    "    a = plt.plot(xvals, f_n(xvals))"
   ]
  }
 ],
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