Change to predict position based on posterior.

This fixes train_filter() to find the most likely position from the new
estimated state rather than the previous state.

02-Discrete-Bayes.ipynb

@@ -1162,7 +1162,7 @@
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       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -13734,7 +13734,7 @@
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   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 35,
    "metadata": {
     "collapsed": false
    },
@@ -14506,7 +14506,7 @@
     {
      "data": {
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -16252,7 +16252,7 @@
     "\n",
     "        likelihood = lh_hallway(track, m, sensor_accuracy)\n",
     "        posterior = update(likelihood, prior)\n",
-    "        index = np.argmax(prior)\n",
+    "        index = np.argmax(posterior)\n",
     "        if i < iterations - 1:\n",
     "            prior = predict(posterior, move_distance, kernel)       \n",
     "\n",
@@ -17053,7 +17053,7 @@
     {
      "data": {
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -17067,7 +17067,7 @@
      "output_type": "stream",
      "text": [
       "time 0: pos 4, sensed 4, at position 4\n",
-      "        predicted position is 0 with confidence 8.2042%:\n",
+      "        predicted position is 4 with confidence 91.0665%:\n",
       "time 1: pos 8, sensed 8, at position 8\n",
       "        predicted position is 8 with confidence 99.9902%:\n",
       "time 2: pos 2, sensed 2, at position 2\n",
@@ -17871,7 +17871,7 @@
     {
      "data": {
       "text/html": [
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       ],
       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -17889,9 +17889,9 @@
       "time 1: pos 8, sensed 9, at position 8\n",
       "        predicted position is 4 with confidence 59.4728%:\n",
       "time 2: pos 3, sensed 3, at position 3\n",
-      "        predicted position is 8 with confidence 25.7722%:\n",
+      "        predicted position is 3 with confidence 53.5807%:\n",
       "time 3: pos 7, sensed 8, at position 7\n",
-      "        predicted position is 7 with confidence 28.8387%:\n",
+      "        predicted position is 8 with confidence 37.5836%:\n",
       "\n",
       "final position is 7\n",
       "predicted position is 8 with confidence 37.5836%:\n"
@@ -18689,7 +18689,7 @@
     {
      "data": {
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       "text/plain": [
        "<IPython.core.display.HTML object>"
@@ -18849,9 +18849,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python [kalman]",
    "language": "python",
-   "name": "python3"
+   "name": "Python [kalman]"
   },
   "language_info": {
    "codemirror_mode": {
@@ -18863,7 +18863,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.5.1"
+   "version": "3.5.2"
   }
  },
  "nbformat": 4,