Untitled1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import reshape, sum\n",
    "\n",
    "melanoma_data = reshape([1.57808, 0.00000, 2, 1.27, 35.9945, 1, 1.48219,\n",
    "                         0.00000, 2, 0.76, 41.9014, 1, 0.0, 7.33425, 1, 35.00, 70.2164, 2, 2.23288,\n",
    "                         0.00000, 1, 1.70, 33.7096, 1, 0.0, 9.38356, 2, 1.00, 47.9726, 1, 3.27671,\n",
    "                         0.00000, 1, 11.00, 31.8219, 2, 0.0, 9.64384, 1, 6.50, 32.9479, 1, 1.66575,\n",
    "                         0.00000, 2, 3.62, 35.9205, 1, 0.94247, 0.00000, 1, 8.50, 40.5068, 2,\n",
    "                         1.68767, 0.00000, 2, 4.20, 57.0384, 1, 2.34247, 0.00000, 2, 5.00, 62.0630, 1,\n",
    "                         0.89863, 0.00000, 1, 2.25, 56.5342, 1, 0.0, 9.03288, 2, 2.30, 22.9945, 2,\n",
    "                         0.0, 9.63014, 2, 10.00, 18.4712, 1, 0.52603, 0.00000, 1, 3.35, 41.2521, 1,\n",
    "                         1.82192, 0.00000, 2, 3.80, 29.5178, 1, 0.93425, 0.00000, 1, 0.75, 59.0493, 2,\n",
    "                         0.0, 8.98630, 2, 0.50, 32.2877, 1, 3.35068, 0.00000, 1, 0.46, 26.4822, 1,\n",
    "                         8.67397, 0.00000, 1, 2.55, 55.0411, 1, 0.41096, 0.00000, 2, 1.95, 55.1233, 2,\n",
    "                         2.78630, 0.00000, 1, 2.50, 22.4055, 2, 2.56438, 0.00000, 1, 2.10, 50.8466, 1,\n",
    "                         0.0, 8.75342, 2, 9.00, 56.0274, 1, 0.56986, 0.00000, 2, 5.00, 55.4767, 1,\n",
    "                         0.0, 8.40000, 1, 0.55, 41.2411, 1, 0.0, 7.25205, 1, 12.50, 32.7425, 1,\n",
    "                         4.38630, 0.00000, 2, 1.16, 45.3479, 1, 0.0, 8.36712, 2, 4.25, 42.8438, 2,\n",
    "                         0.0, 8.99178, 2, 15.00, 51.1068, 1, 0.86575, 0.00000, 2, 0.72, 30.1808, 1,\n",
    "                         0.0, 4.76986, 1, 1.50, 58.7014, 2, 1.15616, 0.00000, 2, 6.50, 51.5397, 1,\n",
    "                         0.0, 7.28767, 1, 2.75, 27.1973, 1, 3.13151, 0.00000, 1, 3.83, 67.6740, 1,\n",
    "                         0.0, 8.55068, 2, 1.80, 64.4274, 2, 0.0, 8.45753, 2, 4.75, 35.4411, 1,\n",
    "                         4.59452, 0.00000, 1, 5.80, 35.9452, 1, 2.88219, 0.00000, 2, 0.51, 48.1370, 1,\n",
    "                         0.89589, 0.00000, 1, 3.25, 58.6082, 1, 1.76164, 0.00000, 2, 0.90, 40.0137, 2,\n",
    "                         0.0, 7.81370, 1, 3.45, 26.0055, 1, 0.0, 8.33425, 2, 1.38, 36.9616, 1,\n",
    "                         2.62192, 0.00000, 1, 5.28, 25.9068, 2, 0.16164, 0.00000, 2, 3.00, 63.8055, 1,\n",
    "                         0.0, 8.24658, 1, 2.20, 29.6986, 2, 1.52603, 0.00000, 1, 7.00, 61.6384, 1,\n",
    "                         5.30959, 0.00000, 1, 4.00, 49.9918, 1, 0.87123, 0.00000, 2, 2.36, 37.1068, 1,\n",
    "                         0.41644, 0.00000, 1, 1.06, 53.4658, 2, 4.24110, 0.00000, 1, 6.50, 57.7425, 2,\n",
    "                         0.13699, 0.00000, 1, 10.00, 29.1479, 1, 7.07671, 0.00000, 2, 1.20, 59.2466,\n",
    "                         1, 0.13151, 0.00000, 2, 15.00, 61.3507, 2, 0.0, 8.02740, 1, 0.49, 33.9205,\n",
    "                         2, 0.0, 6.16164, 2, 1.60, 43.1918, 1, 1.29863, 0.00000, 2, 11.50, 34.1890,\n",
    "                         2, 1.29041, 0.00000, 2, 1.90, 58.3808, 2, 0.0, 7.99726, 1, 4.80, 21.9479,\n",
    "                         2, 0.0, 8.34795, 1, 0.55, 35.1151, 1, 0.0, 7.30137, 2, 6.50, 31.6493, 1,\n",
    "                         2.32877, 0.00000, 2, 12.00, 56.1890, 1, 0.56438, 0.00000, 1, 7.00, 60.7123,\n",
    "                         1, 5.62740, 0.00000, 2, 6.50, 58.8329, 2, 1.23014, 0.00000, 1, 1.60,\n",
    "                         44.4849, 2, 0.0, 7.94521, 1, 1.15, 51.1315, 2, 5.06301, 0.00000, 1, 2.65,\n",
    "                         34.2164, 1, 3.27671, 0.00000, 2, 2.00, 35.2301, 1, 0.0, 0.60822, 2, 2.50,\n",
    "                         32.7425, 2, 0.65753, 0.00000, 1, 4.38, 38.0986, 2, 0.84110, 0.00000, 2,\n",
    "                         2.93, 45.7699, 1, 0.0, 8.40000, 2, 3.00, 44.2000, 1, 0.18356, 0.00000, 1,\n",
    "                         2.50, 71.3260, 1, 2.62466, 0.00000, 2, 2.30, 59.0795, 1, 0.0, 7.96438, 2,\n",
    "                         2.00, 35.3836, 2, 0.0, 7.77808, 1, 0.75, 58.0438, 2, 0.22192, 0.00000, 1,\n",
    "                         5.00, 43.2164, 1, 2.33973, 0.00000, 1, 10.00, 60.4932, 1, 0.52329, 0.00000,\n",
    "                         1, 0.87, 32.4795, 2, 0.0, 8.04110, 2, 1.33, 60.2986, 1, 0.0, 7.83288, 1,\n",
    "                         5.60, 47.1342, 1, 0.64110, 0.00000, 1, 2.55, 42.3233, 1, 0.38356, 0.00000,\n",
    "                         1, 6.50, 54.4164, 1, 0.0, 7.82192, 2, 1.20, 51.4219, 1, 0.51781, 0.00000,\n",
    "                         2, 3.00, 46.5973, 1, 0.0, 8.09863, 2, 2.55, 58.3562, 1, 0.0, 8.16712, 2,\n",
    "                         1.61, 25.6712, 2, 4.42740, 0.00000, 1, 1.40, 29.1726, 1, 0.88493, 0.00000,\n",
    "                         1, 2.25, 18.6795, 1, 2.78356, 0.00000, 1, 4.50, 60.9671, 2, 2.64658,\n",
    "                         0.00000, 2, 0.81, 63.8849, 2, 0.0, 8.21370, 2, 1.30, 37.9808, 2, 0.0,\n",
    "                         7.41918, 2, 3.20, 32.3507, 2, 0.99726, 0.00000, 1, 1.29, 42.9589, 1,\n",
    "                         5.88493, 0.00000, 2, 4.40, 40.9562, 1, 0.41644, 0.00000, 1, 6.00, 61.9753, 1,\n",
    "                         3.53699, 0.00000, 1, 3.93, 55.3315, 2, 0.0, 7.56164, 1, 0.60, 36.0767, 1,\n",
    "                         0.0, 7.53151, 1, 0.75, 50.6795, 1, 0.27671, 0.00000, 1, 0.73, 66.6986, 1,\n",
    "                         0.76986, 0.00000, 2, 0.20, 29.3479, 2, 0.0, 7.62192, 2, 3.88, 33.1863, 1,\n",
    "                         0.0, 7.79726, 1, 2.48, 48.6356, 2, 0.64110, 0.00000, 1, 2.50, 29.4877, 1,\n",
    "                         1.14521, 0.00000, 2, 10.00, 42.6685, 1, 2.01644, 0.00000, 1, 16.00, 24.4055,\n",
    "                         2, 2.84384, 0.00000, 1, 4.00, 40.3890, 1, 0.0, 7.00000, 2, 1.35, 45.4192,\n",
    "                         1, 1.27397, 0.00000, 2, 3.00, 65.3945, 1, 0.0, 7.09589, 1, 10.72, 47.5753,\n",
    "                         2, 2.04110, 0.00000, 1, 1.50, 58.4438, 2, 0.83562, 0.00000, 1, 3.50,\n",
    "                         59.2767, 2, 0.92329, 0.00000, 1, 1.10, 30.2630, 2, 0.07397, 0.00000, 1,\n",
    "                         1.00, 40.7370, 1, 0.0, 7.30685, 2, 5.10, 44.7452, 1, 2.07671, 0.00000, 2,\n",
    "                         0.50, 67.8329, 1, 0.0, 7.70959, 2, 4.03, 27.7452, 1, 0.0, 6.15890, 1,\n",
    "                         1.80, 25.9260, 2, 0.0, 6.89315, 2, 3.50, 31.2740, 1, 3.30685, 0.00000, 1,\n",
    "                         1.15, 58.8822, 2, 0.36164, 0.00000, 1, 1.75, 57.0575, 1, 1.97808, 0.00000,\n",
    "                         2, 2.50, 59.8137, 1, 1.23836, 0.00000, 2, 2.10, 77.5151, 1, 0.10685,\n",
    "                         0.00000, 1, 1.35, 43.4219, 1, 0.0, 7.63836, 1, 4.50, 52.2082, 1, 2.06301,\n",
    "                         0.00000, 1, 0.50, 36.3205, 2, 0.0, 7.42466, 2, 2.30, 25.9781, 1, 0.50959,\n",
    "                         0.00000, 1, 4.00, 49.4411, 1, 0.65753, 0.00000, 1, 5.40, 57.9589, 1, 0.0,\n",
    "                         6.93151, 1, 6.00, 65.5644, 1, 0.0, 7.23288, 2, 5.10, 72.3425, 1, 6.01096,\n",
    "                         0.00000, 1, 4.50, 68.8548, 1, 0.33699, 0.00000, 1, 1.45, 50.4438, 2, 0.0,\n",
    "                         6.47123, 2, 3.38, 48.2877, 1, 0.94795, 0.00000, 1, 3.00, 46.9479, 2,\n",
    "                         2.91781, 0.00000, 2, 1.20, 33.6000, 2, 1.59726, 0.00000, 2, 7.30, 51.1644, 2,\n",
    "                         0.84932, 0.00000, 2, 1.67, 47.7836, 1, 1.38356, 0.00000, 1, 4.00, 53.8795, 2,\n",
    "                         3.81644, 0.00000, 2, 2.10, 38.7068, 2, 0.0, 7.06849, 1, 10.00, 69.3205, 2,\n",
    "                         0.0, 7.04110, 2, 3.50, 66.0219, 1, 1.00274, 0.00000, 2, 1.10, 36.0329, 2,\n",
    "                         0.0, 6.34795, 2, 0.40, 63.4603, 1, 1.18082, 0.00000, 1, 0.70, 48.8986, 2,\n",
    "                         0.97534, 0.00000, 1, 5.00, 45.0575, 1, 2.16712, 0.00000, 1, 0.85, 57.6712, 2,\n",
    "                         0.0, 6.85479, 1, 4.80, 45.2000, 1, 1.38356, 0.00000, 1, 1.20, 49.0438, 1,\n",
    "                         1.71507, 0.00000, 2, 1.30, 51.4630, 1, 0.79452, 0.00000, 2, 5.80, 34.5479, 1,\n",
    "                         0.0, 6.86301, 2, 6.00, 47.6438, 2, 0.0, 6.50411, 1, 3.00, 38.7233, 2,\n",
    "                         0.42466, 0.00000, 2, 1.88, 54.0658, 1, 0.98630, 0.00000, 1, 2.60, 45.7397, 1,\n",
    "                         0.0, 6.13699, 2, 2.70, 47.2822, 2, 3.80000, 0.00000, 2, 6.00, 62.6411, 1,\n",
    "                         0.0, 6.48493, 1, 4.00, 62.0192, 2, 0.0, 6.96438, 2, 1.71, 41.0904, 2, 0.0,\n",
    "                         6.78082, 2, 1.60, 50.2712, 2, 0.56164, 0.00000, 2, 1.50, 49.5288, 2,\n",
    "                         2.67123, 0.00000, 1, 3.00, 70.8192, 1, 1.56712, 0.00000, 2, 0.90, 59.0712, 1,\n",
    "                         2.07397, 0.00000, 2, 4.00, 53.9041, 1, 0.33973, 0.00000, 1, 2.80, 44.7342, 1,\n",
    "                         3.37808, 0.00000, 2, 0.80, 22.1397, 1, 3.15068, 0.00000, 1, 0.70, 72.8575, 1,\n",
    "                         0.0, 6.81096, 2, 0.90, 61.4521, 1, 3.20822, 0.00000, 2, 12.00, 61.2904, 1,\n",
    "                         0.62740, 0.00000, 1, 5.78, 34.7507, 1, 1.64384, 0.00000, 1, 0.60, 67.4164, 2,\n",
    "                         1.40822, 0.00000, 1, 12.00, 53.2493, 1, 0.0, 6.06575, 1, 4.00, 49.0082, 1,\n",
    "                         1.66301, 0.00000, 2, 0.45, 56.7699, 1, 1.36986, 0.00000, 2, 1.30, 34.0247, 2,\n",
    "                         5.46849, 0.00000, 1, 0.81, 34.3014, 2, 0.42740, 0.00000, 1, 3.20, 45.0712, 2,\n",
    "                         1.13973, 0.00000, 2, 4.00, 54.7671, 2, 1.73699, 0.00000, 2, 4.77, 42.8548, 2,\n",
    "                         0.0, 5.54521, 2, 2.20, 36.6301, 2, 0.85205, 0.00000, 1, 3.00, 43.2466, 1,\n",
    "                         0.43014, 0.00000, 1, 3.00, 53.3562, 1, 1.20822, 0.00000, 2, 0.80, 35.3534, 1,\n",
    "                         4.36164, 0.00000, 1, 4.00, 36.5233, 1, 0.52877, 0.00000, 2, 5.00, 52.7863, 1,\n",
    "                         0.0, 6.51507, 1, 2.00, 24.4329, 2, 2.89863, 0.00000, 2, 3.85, 58.7178, 1,\n",
    "                         0.0, 6.20274, 2, 0.76, 45.5479, 1, 1.21644, 0.00000, 2, 0.75, 43.3014, 2,\n",
    "                         0.0, 6.00000, 2, 6.50, 51.4055, 2, 0.0, 6.25479, 1, 0.85, 38.9671, 2, 0.0,\n",
    "                         6.49863, 1, 4.30, 68.2658, 1, 1.13699, 0.00000, 2, 2.10, 59.4493, 2,\n",
    "                         1.69589, 0.00000, 1, 1.50, 30.0192, 1, 0.0, 6.41096, 2, 2.00, 22.1562, 2,\n",
    "                         0.0, 6.02192, 1, 11.00, 54.7671, 1, 3.04932, 0.00000, 2, 4.88, 45.0384, 1,\n",
    "                         0.0, 5.62740, 2, 5.20, 39.7589, 1, 0.72603, 0.00000, 1, 3.04, 41.3808, 1,\n",
    "                         0.73425, 0.00000, 2, 8.00, 34.9671, 1, 1.47945, 0.00000, 2, 1.60, 46.3479, 1,\n",
    "                         0.37808, 0.00000, 2, 1.10, 29.9233, 2, 0.0, 5.75890, 2, 3.00, 32.8740, 1,\n",
    "                         1.48219, 0.00000, 2, 10.00, 39.5397, 2, 0.0, 5.88493, 1, 1.95, 55.4822, 1,\n",
    "                         0.0, 1.80274, 1, 2.00, 32.3562, 1, 1.40548, 0.00000, 2, 3.70, 41.8027, 2,\n",
    "                         0.0, 4.74795, 1, 2.90, 35.3452, 2, 0.0, 5.24658, 1, 1.80, 50.4795, 1,\n",
    "                         0.29041, 0.00000, 1, 6.00, 61.3507, 2, 0.0, 5.83836, 1, 1.50, 67.3562, 1,\n",
    "                         0.0, 5.32055, 2, 1.75, 53.8548, 2, 5.16712, 0.00000, 2, 5.00, 78.7315, 2,\n",
    "                         0.0, 5.59178, 2, 0.63, 62.7233, 1, 0.0, 5.77808, 1, 1.15, 65.1507, 1,\n",
    "                         0.53425, 0.00000, 2, 1.50, 34.8274, 1, 0.0, 2.22466, 1, 0.98, 33.8466, 2,\n",
    "                         3.59726, 0.00000, 1, 5.00, 67.8822, 1, 0.0, 5.32329, 1, 5.50, 66.0712, 2,\n",
    "                         1.78630, 0.00000, 2, 1.00, 55.0658, 2, 0.70411, 0.00000, 2, 10.00, 50.5123,\n",
    "                         1, 0.0, 4.94795, 2, 5.00, 42.4055, 2, 0.0, 5.45479, 2, 3.75, 58.1068, 2,\n",
    "                         4.32877, 0.00000, 1, 10.00, 26.0137, 1, 1.16164, 0.00000, 2, 3.00, 54.4685,\n",
    "                         1, 0.0, 5.20274, 2, 8.00, 54.0630, 2, 0.0, 4.40822, 1, 1.64, 34.5589, 1,\n",
    "                         1.41096, 0.00000, 1, 4.95, 58.5068, 1, 0.0, 4.92877, 2, 1.45, 63.9370, 1,\n",
    "                         0.0, 5.42192, 2, 12.00, 49.8274, 2, 0.98904, 0.00000, 1, 2.05, 50.5562, 1,\n",
    "                         0.36438, 0.00000, 1, 3.60, 40.4795, 2, 0.0, 4.38082, 1, 8.30, 61.7479, 2,\n",
    "                         0.77260, 0.00000, 2, 0.45, 41.6712, 1, 4.90959, 0.00000, 2, 3.00, 25.5096, 1,\n",
    "                         1.26849, 0.00000, 1, 4.40, 61.2000, 1, 0.58082, 0.00000, 2, 1.10, 53.1260, 1,\n",
    "                         0.0, 4.95616, 1, 1.05, 40.4658, 1, 0.0, 5.12329, 1, 1.71, 60.3068, 1, 0.0,\n",
    "                         4.74795, 1, 6.30, 48.7425, 2, 0.0, 4.90685, 2, 0.50, 46.7562, 2, 1.41918,\n",
    "                         0.00000, 1, 5.10, 34.8932, 2, 0.44110, 0.00000, 1, 6.00, 33.3096, 1, 0.0,\n",
    "                         4.29863, 2, 1.50, 35.7589, 1, 0.0, 4.63836, 2, 0.36, 49.8575, 1, 0.0,\n",
    "                         4.81370, 1, 3.00, 57.3726, 2, 4.50137, 0.00000, 2, 1.24, 29.7726, 2,\n",
    "                         3.92329, 0.00000, 2, 0.70, 51.8822, 2, 0.0, 4.86027, 2, 0.80, 65.3123, 2,\n",
    "                         0.52603, 0.00000, 1, 1.00, 52.0658, 2, 2.10685, 0.00000, 2, 3.38, 60.9534, 2,\n",
    "                         0.0, 4.24384, 1, 1.52, 32.6055, 2, 3.39178, 0.00000, 1, 2.20, 51.5123, 2,\n",
    "                         0.0, 4.36164, 2, 2.10, 48.6548, 1, 0.0, 4.81918, 2, 1.40, 43.8438, 2],\n",
    "                        (255, 6))\n",
    "\n",
    "# Censoring indicator\n",
    "censored = (melanoma_data[:, 0] == 0).astype(int)\n",
    "# Time\n",
    "t = sum(melanoma_data[:, 0:2], 1)\n",
    "# Treatment\n",
    "treat = melanoma_data[:, 2].astype(int) - 1\n",
    "# Breslow scale\n",
    "breslow = melanoma_data[:, 3]\n",
    "# Age and sex\n",
    "age = melanoma_data[:, 4]\n",
    "sex = melanoma_data[:, 5].astype(int) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.57808,   0.     ,   2.     ,   1.27   ,  35.9945 ,   1.     ],\n",
       "       [  1.48219,   0.     ,   2.     ,   0.76   ,  41.9014 ,   1.     ],\n",
       "       [  0.     ,   7.33425,   1.     ,  35.     ,  70.2164 ,   2.     ],\n",
       "       ..., \n",
       "       [  3.39178,   0.     ,   1.     ,   2.2    ,  51.5123 ,   2.     ],\n",
       "       [  0.     ,   4.36164,   2.     ,   2.1    ,  48.6548 ,   1.     ],\n",
       "       [  0.     ,   4.81918,   2.     ,   1.4    ,  43.8438 ,   2.     ]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "melanoma_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 10000 of 10000 complete in 1.4 secPlotting beta0\n",
      "Plotting beta1\n"
     ]
    },
    {
     "data": {
      "image/png": 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32ULmJ5SY1bZQl12WeNyvv5L2QhAEITjpuiyXArgQwIc+5Z4CMIWZWwBoDWBF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\nR3neefz7kxByuBuwIUIRNhYXmcNFGAiBgzUYAyPHQuzaB1C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tYR5XX72dv/qrcoxI5XUO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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf2baa3a828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+3/+D555zhGpQ2Ibvvgu3gDU15W4/5L2eKEp1wg/yAYOsANt449rZ9klVTw85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\nTcAZOcfUgmreAYxRzTuABqp5BzBGNe8AxqjmHcAY1bwDyIwTMDOziR0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      "text/plain": [
       "<matplotlib.figure.Figure at 0xf2bac6ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Exponential survival model for melanoma data, taken from\n",
    "Bayesian Data Analysis (Ibrahim et al 2000) Example 2.1\n",
    "# JAGS model\n",
    "model {\n",
    "    for(i in 1:N) {\n",
    "        z[i] ~ dinterval(t[i], t.cen[i])\n",
    "        t[i] ~ dweib(1,mu[i])\n",
    "        eta[i] <- beta0 + beta[1]*trt[i]\n",
    "        mu[i] <- exp(eta[i])\n",
    "     }\n",
    "     # Priors\n",
    "     for(j in 1:p) {\n",
    "         beta[j] ~ dnorm(0,.0001)\n",
    "     }\n",
    "     beta0 ~ dnorm(0,.0001)\n",
    "}\n",
    "\"\"\"\n",
    "%matplotlib inline  \n",
    "from pymc import Normal, Lambda, observed\n",
    "from numpy import exp, log\n",
    "\n",
    "# Convert censoring indicators to indicators for failure event\n",
    "failure = (censored == 0).astype(int)\n",
    "\n",
    "# Intercept for survival rate\n",
    "beta0 = Normal('beta0', mu=0.0, tau=0.0001, value=0.0)\n",
    "# Treatment effect\n",
    "beta1 = Normal('beta1', mu=0.0, tau=0.0001, value=0.0)\n",
    "\n",
    "# Survival rates\n",
    "lam = Lambda('lam', lambda b0=beta0, b1=beta1, t=treat: exp(b0 + b1 * t))\n",
    "\n",
    "\n",
    "@observed\n",
    "def survival(value=t, lam=lam, f=failure):\n",
    "    \"\"\"Exponential survival likelihood, accounting for censoring\"\"\"\n",
    "    return sum(f * log(lam) - lam * value)\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    from pymc import MCMC, Matplot\n",
    "\n",
    "    # Instantiate model\n",
    "    M = MCMC([beta0, beta1, lam, survival])\n",
    "    # Sample\n",
    "    M.sample(10000, 5000)\n",
    "    # Plot traces\n",
    "    Matplot.plot(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0\n",
      " 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1\n",
      " 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1\n",
      " 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0\n",
      " 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1\n",
      " 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0\n",
      " 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "print(failure)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1\n",
      " 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1\n",
      " 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0\n",
      " 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 0\n",
      " 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1\n",
      " 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1\n",
      " 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "print(treat)"
   ]
  },
  {
   "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": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}