fixed derivation of posterior of univariate Gaussian

2015-08-01 10:28:06 -07:00
1 parent 912498a843
commit 90cfc4c8bb
@@ -446,7 +446,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e13f28>"
+       "<matplotlib.figure.Figure at 0x6dd6f98>"
      ]
     },
     "metadata": {},
@@ -486,9 +486,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e13da0>"
+       "<matplotlib.figure.Figure at 0x6dcef60>"
      ]
     },
     "metadata": {},
@@ -531,9 +531,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e13390>"
+       "<matplotlib.figure.Figure at 0x6dd6588>"
      ]
     },
     "metadata": {},
@@ -554,9 +554,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA2cAAAE6CAYAAACSxCplAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x75bfb00>"
+       "<matplotlib.figure.Figure at 0x75909b0>"
      ]
     },
     "metadata": {},
@@ -587,7 +587,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x75e98d0>"
+       "<matplotlib.figure.Figure at 0x770bc88>"
      ]
     },
     "metadata": {},
@@ -619,7 +619,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x78bd5c0>"
+       "<matplotlib.figure.Figure at 0x7885be0>"
      ]
     },
     "metadata": {},
@@ -655,7 +655,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x773c0b8>"
+       "<matplotlib.figure.Figure at 0x789aa20>"
      ]
     },
     "metadata": {},
@@ -693,7 +693,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7a35940>"
+       "<matplotlib.figure.Figure at 0x79edbe0>"
      ]
     },
     "metadata": {},
@@ -788,7 +788,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e31e80>"
+       "<matplotlib.figure.Figure at 0x6e1c048>"
      ]
     },
     "metadata": {},
@@ -845,7 +845,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x74a4c88>"
+       "<matplotlib.figure.Figure at 0x6e70240>"
      ]
     },
     "metadata": {},
@@ -898,7 +898,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x741f0f0>"
+       "<matplotlib.figure.Figure at 0x74d6240>"
      ]
     },
     "metadata": {},
@@ -988,7 +988,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7658b00>"
+       "<matplotlib.figure.Figure at 0x7627e10>"
      ]
     },
     "metadata": {},
@@ -1216,7 +1216,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": false
@@ -1246,7 +1246,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x76d76d8>"
+       "<matplotlib.figure.Figure at 0x750b940>"
      ]
     },
     "metadata": {},
@@ -1254,6 +1254,8 @@
    }
   ],
   "source": [
+    "import kf_internal\n",
+    "\n",
    "np.random.seed(13)\n",
    "pos = (0., 400.)   # gaussian N(0, 400)\n",
    "velocity = 1.\n",
@@ -1305,7 +1307,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x753a470>"
+       "<matplotlib.figure.Figure at 0x769fda0>"
      ]
     },
     "metadata": {},
@@ -1424,7 +1426,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
@@ -1443,9 +1445,9 @@
    },
    {
     "data": {
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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5wAAAESCAYAAACRl9pQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e0aa20>"
+       "<matplotlib.figure.Figure at 0x76419b0>"
      ]
     },
     "metadata": {},
@@ -1453,8 +1455,6 @@
    }
   ],
   "source": [
-    "import kf_internal\n",
-    "\n",
    "process_var = 2\n",
    "sensor_var = 4.5\n",
    "pos = (0, 400)   # gaussian N(0, 100)\n",
@@ -1541,7 +1541,7 @@
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAvwAAAEtCAYAAAB00rSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x76d3160>"
+       "<matplotlib.figure.Figure at 0x764a128>"
      ]
     },
     "metadata": {},
@@ -1712,7 +1712,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x77546a0>"
+       "<matplotlib.figure.Figure at 0x742f908>"
      ]
     },
     "metadata": {},
@@ -1742,7 +1742,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x6e0ab00>"
+       "<matplotlib.figure.Figure at 0x73b1400>"
      ]
     },
     "metadata": {},
@@ -1869,18 +1869,11 @@
    "scrolled": false
   },
   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "here\n"
-     ]
-    },
    {
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x74fb5f8>"
+       "<matplotlib.figure.Figure at 0x73f65f8>"
      ]
     },
     "metadata": {},
@@ -1890,7 +1883,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7858c88>"
+       "<matplotlib.figure.Figure at 0x958fc88>"
      ]
     },
     "metadata": {},
@@ -1931,7 +1924,7 @@
    "\n",
    "# plot the filter output and the variance\n",
    "bp.plot_measurements(zs)\n",
-    "bp.plot_filter(estimates, vars=np.array(ps))\n",
+    "bp.plot_filter(estimates, var=np.array(ps))\n",
    "bp.show_legend()\n",
    "plt.show()\n",
    "plt.plot(ps)\n",
@@ -2021,16 +2014,16 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
-      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x99e1978>"
+       "<matplotlib.figure.Figure at 0x74e3048>"
      ]
     },
     "metadata": {},
@@ -2096,7 +2089,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x76c8c18>"
+       "<matplotlib.figure.Figure at 0x7641588>"
      ]
     },
     "metadata": {},
@@ -2154,7 +2147,7 @@
     "data": {
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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b02518>"
+       "<matplotlib.figure.Figure at 0x7ab4ac8>"
      ]
     },
     "metadata": {},
@@ -2217,7 +2210,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b259e8>"
+       "<matplotlib.figure.Figure at 0x7ac3208>"
      ]
     },
     "metadata": {},
@@ -2276,7 +2269,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7b25b00>"
+       "<matplotlib.figure.Figure at 0x790c518>"
      ]
     },
     "metadata": {},
@@ -2322,7 +2315,7 @@
     "data": {
      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x79c55f8>"
+       "<matplotlib.figure.Figure at 0x79a7da0>"
      ]
     },
     "metadata": {},
@@ -2419,9 +2412,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlcVPX+x/HXDPsOsu8isoi4K2pu4Z5tN/OX6bXSm6ml\nt7p1226LZmXLteXeW7Z3s8yuZqVWVlquaIlLLrgvCAiKgCyC7DO/P74yMAIKwjADfJ6PBw9nzpxz\n5juI+J7vfM7nq9Hr9XqEEEIIIYQQzU5r7gEIIYQQQgjRVknYFkIIIYQQwkQkbAshhBBCCGEiEraF\nEEIIIYQwEQnbQgghhBBCmIiEbSGEEEIIIUxEwrYQQgghhBAmcsWw/fLLL9OvXz/c3Nzw8fHhlltu\n4cCBA7X2mzdvHoGBgTg6OhIfH8/BgwdNNmAhhBBCCCFaiyuG7U2bNjFnzhx+++031q9fj7W1NSNH\njiQ3N9ewz6uvvsobb7zB22+/zY4dO/Dx8WHUqFEUFhaafPBCCCGEEEJYMk1jVpAsKirCzc2NVatW\nceONN6LX6wkICODBBx/kqaeeAqCkpAQfHx8WLlzIjBkzTDZwIYQQQgghLF2jarYLCgrQ6XR4eHgA\nkJycTGZmJqNHjzbsY29vz9ChQ9m2bVvzjlQIIYQQQohWplFh+6GHHqJXr14MHDgQgLNnzwLg6+tr\ntJ+Pj4/hMSGEEEIIIdor64bu+Mgjj7Bt2zYSEhLQaDRX3f/yffLz8xs/OiGEEEIIISyEm5tbo49p\n0Mz23/72N5YtW8b69evp2LGjYbufnx8AmZmZRvtnZmYaHhNCCCGEEKK9umrYfuihhwxBOzIy0uix\nsLAw/Pz8WLt2rWFbSUkJCQkJXHfddc0/WiGEEEIIIVqRK5aRzJ49myVLlrBy5Urc3NwMddguLi44\nOTmh0Wh4+OGHWbBgAdHR0URERPDiiy/i4uLC5MmT6z3vtUzBC9GSdu7cCUDfvn3NPBIhrk5+XkVr\nIz+zIq+whCOp2RxOzeZIWg7H0s9TUlZhtM/4IdFMu6GXmUZYraml0FcM2++++y4ajYYRI0YYbZ83\nbx7PPfccAI8//jjFxcXMnj2b3NxcBgwYwNq1a3FycmrSwIQQQgghROtXUakj+UwuR9JyLoXrbM6e\nL7rqcUdP57TA6EzvimFbp9M16CRz585l7ty5zTIgIYQQQgjReuXkXzQK1sfTcymrqLzqcd5ujkSF\neBIV7EV0iBed/D1aYLSm1+BuJEIIIYQQQtRUVl7JyTO5hmB9ODWH7PyLVz3OxlpLRGAHQ7COCvbE\n082xBUbc8iRsCyGEEEKIq9Lr9WTlXawRrLM5eSaPisqrV0L4dXAyCtZh/h5YWzVquZdWS8K2EEII\nIYSopbSsgmPp59WFjGnZHEnNIbew5KrH2dlYERnkSVSwJ9EhXkQGe+Lh4tACI7ZMFhe29Xo95eXl\nDa4XF8IUQkNDAdXK8mpsbW3RatvHu3MhhBBtV1FxGbuPneHAqSwOp2Zz6mwelTr9VY8L8HS+NGOt\nZq5Dfd2waiez1g1hUWFbr9dTUlKCra0tNjY2DVqpUghTsLe3b9B+VT+z9vb28vMqhBCi1ck8X0ji\n4XS2H0onKfncVcO1o50NkcGq1joqWF3M6Opk10KjbZ0sKmyXl5dja2uLlZWVuYciRINoNBpsbW0p\nKyvDzk5+2QghhLBsOp2eY6dzSDycTuLhdE6dvXIP6RAfV0Owjg7xItjHDa1WJpcaw6LCtk6nw8bG\nxtzDEKJRrKysKC8vN/cwhBBCiDqVllWw5/hZEg+ns+NwxhXrrjsHetA3MoCYjt5EBnni5GDbgiNt\nmywqbAPyUbwQQgghRBPlXihmx+EMth86zZ7jmfX2ubax1tIj3Jf+XYLoFxXQZtvvmZPFhW0hhBBC\nCNE4er2elMx8Eg+p8pAjafWvvujmZEe/qAD6xwTRI9wXBzupKjAlCdtCCCGEEK1QRaWOA8nn2H4p\nYGfm1r8EerC3K/27BBLXJZCoYC+pu25BEraFEEIIIVqJwuIydh3JIPFwOruOnqGopO5rhqy0GmJC\nvQ0B29/TpYVHKqpI2BaiDmvWrGHHjh3MnTvX3EMRQgjRzp3JuWAoDzlwKqve9nyOdjb0ifSnf5dA\nekf64+IoXbIsgYRtIeqwZs0aFi1aJGFbCCFEi9Pp9Bw9ncP2g6dJPJxO6rmCevf1cXekf5cg4roE\nEhvm026WQG9NJGyLZldUVISTk5O5h9Fk0hlHCCFESympas93KJ0dRzLIu0J7vsigDoaAHerrZrr/\nr0pKoIGLvIn6ydufFjBv3jy0Wi2HDx9mypQpuLu74+3tzdNPPw1AWloat956K25ubvj5+bFw4UKj\n40tLS3n++eeJiIjA3t6eoKAgHnnkEYqLi432+/TTTxk5ciT+/v7Y29sTGRnJK6+8gl5v/HHT8ePH\nueOOOwgICMDe3p7AwEAmTJjA2bNnATh16hRarZbFixfXei1arZbnn3++1ms7cOAAd911Fx06dKBb\nt26Gx9euXcuwYcNwcXHBxcWFG264gb179xqdc+rUqTg4OJCWlsZNN92Ei4sLgYGB/Pvf/wZg3759\nDB8+HGdnZ0JDQ1myZEmtceXn5/PII48QEhKCnZ0d4eHhvPjii+h0OsM+Va/r1Vdf5cMPPyQ8PBx7\ne3vi4uLYuXOn0XgWLVqEXq9Hq9UavlJTU+v42xVCCCEaJ6+whD3Hz7Iy4TBvrfidh9/+ickvfs1L\nS7awbtfJWkHb1tqKuOgA5vypH4uf/BOvPzCGO+K70tHP3bQTQ4MGwcCB8PrrcOqU6Z6njZOZ7RY0\nadIkunTpwquvvsoPP/zAyy+/jJubGx999BEjR47ktddeY8mSJTz++OP06dOH+Ph49Ho9t912G5s3\nb2bGjBnExMRw8OBBFi1axIEDB/j5558N51+0aBExMTHcdNNN2Nvb88svv/CPf/yD/Px8Xn75ZUCt\n0jlmzBhKS0uZM2cO/v7+ZGRk8PPPP3PmzBn8/PwM56vvH3Bd2ydOnEinTp1YsGABZWVlACxdupS7\n7rqL0aNH88orr1BSUsIHH3zAkCFD2LFjB1FRUYbjdTod48aNY/DgwSxcuJAlS5bw8MMP4+DgwNy5\nc7nrrruYMGEC7777LlOnTmXgwIGEh4cDUFxcTHx8PKmpqcyaNYuOHTuyfft25s2bR0pKCh9++KHR\nWJctW0ZhYSH3338/AK+99hrjx4/n5MmTWFtbM2vWLM6cOcO6deuMgr2Xl1ej/r6FEEK0b2XllaSe\nyyflbB6nzuaRfDaPlMz8K85aV3F3ticuOoC46EB6dvbDzraFI9uJE7B7t7r9++/w979Dnz4wYQI8\n+ijIIoQNJmG7BfXt29cQ/O677z46duzIk08+yUsvvcRTTz0FwJ133klAQACffPIJ8fHxfPnll/z8\n889s3LiRIUOGGJ1rypQprFu3jlGjRgGwefNm7Gt83DNr1ixmzpzJ22+/zfz587GxseHgwYMkJyez\nYsUKxo8fb9i3apb9WnXp0oWvvvrKcL+oqIg5c+Ywbdo0PvroI8P2e++9l6ioKObPn88XX3xh2F5e\nXs6dd95pGEfV92HmzJl88cUXTJo0CYCRI0cSHR3Np59+ygsvvADAm2++yZEjR/jjjz+IjIwEYPr0\n6YSFhfHMM8/w2GOPGbYDnD59mmPHjuHm5gZAVFQUt956Kz///DM33ngjAwYMICIignXr1jF58uQm\nfV+EEEK0fTqdnqy8Ik5dCtWnMtWfGdmF6PR1X8xYl1BfN9U9JDqQiCDPlmvPd+4c+PgYb9uxA6ys\noLLGYji7dkFBATzxRMuMq41o3WF73jyoUdJgMHeueqyp+zez6dOnG25rtVr69OlDeno69957r2G7\nm5sbUVFRJCcnA7B8+XIiIyOJiYkhOzvbsN/QoUPRaDRs2LDBELargnZlZSUFBQVUVlYydOhQPvzw\nQw4fPky3bt1wdXUF4KeffmLs2LE4OjbPSlFVs8RV1q1bR15eHpMmTTIaN8DgwYPZsGFDrXPU/P64\nubkRGRnJsWPHDEEbIDIyEnd3d8P3B9T3aMiQIXh6eho914gRI3jmmWfYuHGjUdi+/fbbDUG7ajyA\n0TmFEEKIuhQVlxlCdUpmPslnc0k5m09xWUWDz2FnY0VHP3dCfd0I8/cw3DZL95A33oCXXoLvvoPr\nrqvefuedMGoUrFoFX38N69ZBebma2a7rk++MDMjOhm7d6n68HWvdYbuVCQkJMbrv5uaGjY0NPpe9\nm3R1dSUrKwuAo0ePcuTIEby9vWudT6PRGPYDSEhI4B//+AeJiYmGUo4q+fn5AISFhfHII4/wxhtv\nsGTJEgYNGsTNN9/MlClT6NChwzW/tqqSjipHjx4FMLwRuJyVlZXRfVtbW3x9fY22ubm5ERgYWOtY\nV1dXcnNzjZ5r3759DfoeQe2/Bw8PDwCjcwohhGjfKip1ZGRfUOUfZ3JJyczn1Nk8svIvNvgcGg34\nd3AmzN+DUF83Ovq509HPHV8PZ8tYVOZ//1MlIQAjRsD69apGu4qnJ/zlL+orL08F8ri4us/10Udq\n8rJzZxXIJ0yA3r0leCNhu0VdHjCh/rroqosadTodXbt25V//+led+wUEBABw8uRJQ4nFW2+9RUhI\nCPb29uzatYsnnnjC6ELBhQsX8pe//IXVq1ezdu1aHn30UV588UU2bdpEly5d6h1TZc2Pki7j4OBg\ndL/q+RYvXlxnYL5cfc9Z1/cMMLroU6/XM2LECEMpzuXCwsIafU4hhBCmZVVYCJmZqnzBjIFMr9eT\ne6HEKFCfOpvH6ewCyit0Vz/BJa6OdnT0qw7UHf3cCfZxw76la60bav16uPvu6vt9+Line truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtsAAAEWCAYAAAC37ltfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x77da320>"
+       "<matplotlib.figure.Figure at 0x7aa3f28>"
      ]
     },
     "metadata": {},
@@ -2515,9 +2508,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x767f518>"
+       "<matplotlib.figure.Figure at 0x77a0eb8>"
      ]
     },
     "metadata": {},
@@ -2604,9 +2597,9 @@
   "outputs": [
    {
     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAuEAAAEWCAYAAADIP0muAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": 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truncated
      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7682908>"
+       "<matplotlib.figure.Figure at 0x74dbfd0>"
      ]
     },
     "metadata": {},
@@ -2678,7 +2671,7 @@
    "\n",
    "$$P(z|x) = \\frac{1}{\\sqrt{2\\pi\\sigma_z^2}}\\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]$$\n",
    "\n",
-    "$$P(x) = \\frac{1}{\\sqrt{2\\pi\\sigma_p^2}}\\exp \\Big[-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big]$$"
+    "$$P(x) = \\frac{1}{\\sqrt{2\\pi\\sigma_p^2}}\\exp \\Big[-\\frac{(x-\\mu_p)^2}{2\\sigma_p^2}\\Big]$$"
   ]
  },
  {
@@ -2688,9 +2681,9 @@
    "We can drop the leading terms, as they are constants, giving us\n",
    "\n",
    "$$\\begin{aligned}\n",
-    "P(x|z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big]\\\\\n",
-    "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\mu_z)^2}{2\\sigma_p^2}\\Big] \\\\\n",
-    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z-x)^2-\\sigma_z^2(x-\\mu_z)^2]\\Big]\n",
+    "P(x|z) &\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}\\Big]\\exp \\Big[-\\frac{(x-\\mu_p)^2}{2\\sigma_p^2}\\Big]\\\\\n",
+    "&\\propto \\exp \\Big[-\\frac{(z-x)^2}{2\\sigma_z^2}-\\frac{(x-\\mu_p)^2}{2\\sigma_p^2}\\Big] \\\\\n",
+    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z-x)^2-\\sigma_z^2(x-\\mu_p)^2]\\Big]\n",
    "\\end{aligned}$$"
   ]
  },
@@ -2702,7 +2695,7 @@
    "\n",
    "$$\\begin{aligned}\n",
    "P(x|z) &\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[\\sigma_p^2(z^2 -2xz + x^2) + \\sigma_z^2(x^2 - 2x\\mu_z+\\mu_z^2)]\\Big ] \\\\\n",
-    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_z + \\sigma_p^2z) + (\\sigma_p^2z^2+\\sigma_z^2\\mu_z^2)]\\Big ]\n",
+    "&\\propto \\exp \\Big[-\\frac{1}{2\\sigma_z^2\\sigma_p^2}[x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_p + \\sigma_p^2z) + (\\sigma_p^2z^2+\\sigma_z^2\\mu_p^2)]\\Big ]\n",
    "\\end{aligned}$$"
   ]
  },
@@ -2712,7 +2705,7 @@
   "source": [
    "The last parentheses do not contain the posterior $x$, so it can be treated as a constant and discarded.\n",
    "\n",
-    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_z + \\sigma_p^2z)}{\\sigma_z^2\\sigma_p^2}\\Big ]\n",
+    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2(\\sigma_p^2+\\sigma_z^2)-2x(\\sigma_z^2\\mu_p + \\sigma_p^2z)}{\\sigma_z^2\\sigma_p^2}\\Big ]\n",
    "$$"
   ]
  },
@@ -2722,7 +2715,7 @@
   "source": [
    "Divide numerator and denominator by $\\sigma_p^2+\\sigma_z^2$ to get\n",
    "\n",
-    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n",
+    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{x^2-2x(\\frac{\\sigma_z^2\\mu_p + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n",
    "$$"
   ]
  },
@@ -2732,7 +2725,7 @@
   "source": [
    "Proportionality lets us create or delete constants at will, so we can factor this into\n",
    "\n",
-    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n",
+    "$$P(x|z) \\propto \\exp \\Big[-\\frac{1}{2}\\frac{(x-\\frac{\\sigma_z^2\\mu_p + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2})^2}{\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2}}\\Big ]\n",
    "$$"
   ]
  },
@@ -2746,12 +2739,12 @@
    "\n",
    "So we can see that $P(x|z)$ has a mean of\n",
    "\n",
-    "$$\\mu_\\mathtt{posterior} =\\frac{\\sigma_z^2\\mu_z + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2}$$\n",
+    "$$\\mu_\\mathtt{posterior} =\\frac{\\sigma_z^2\\mu_p + \\sigma_p^2z}{\\sigma_p^2+\\sigma_z^2}$$\n",
    "\n",
    "and a variance of\n",
    "$$\\begin{aligned}\n",
-    "\\sigma_\\mathtt{posterior} &=\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2} \\\\\n",
-    "&= \\frac{1}{\\frac{1}{\\sigma_p^2}+\\frac{1}{\\sigma_z^2}}\n",
+    "\\sigma_\\mathtt{posterior} &=\\frac{\\sigma_z^2\\sigma_p^2}{\\sigma_p^2+\\sigma_z^2} \n",
+    "= \\frac{1}{\\frac{1}{\\sigma_p^2}+\\frac{1}{\\sigma_z^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "which are the equations that we have been using."