| 
797 | 797 |       "             label = \"$N$: %d, $p$: %.1f\"%(N,p), \n",  | 
798 | 798 |       "             linewidth=3)\n",  | 
799 | 799 |       "    \n",  | 
800 |  | -      "\n",  | 
801 | 800 |       "plt.legend(loc=\"upper left\")\n",  | 
802 | 801 |       "plt.xlim(0, 10.5)\n",  | 
803 | 802 |       "plt.xlabel(\"$k$\")\n",  | 
 | 
1341 | 1340 |       "\n",  | 
1342 | 1341 |       "def logistic( x, beta):\n",  | 
1343 | 1342 |       "    return 1.0/( 1.0 + np.exp( beta*x) )\n",  | 
 | 1343 | +      "\n",  | 
1344 | 1344 |       "x = np.linspace( -4, 4, 100 )\n",  | 
1345 | 1345 |       "plt.plot(x, logistic( x, 1), label = r\"$\\beta = 1$\")\n",  | 
1346 | 1346 |       "plt.plot(x, logistic( x, 3), label = r\"$\\beta = 3$\")\n",  | 
 | 
1430 | 1430 |      "collapsed": false,  | 
1431 | 1431 |      "input": [  | 
1432 | 1432 |       "import scipy.stats as stats\n",  | 
 | 1433 | +      "\n",  | 
1433 | 1434 |       "nor = stats.norm\n",  | 
1434 | 1435 |       "x = np.linspace( -8, 7, 150 )\n",  | 
1435 | 1436 |       "mu = (-2, 0, 3)\n",  | 
 | 
1442 | 1443 |       "        label =\"$\\mu = %d,\\;\\\\tau = %.1f$\"%(_mu, _tau), color = _color )\n",  | 
1443 | 1444 |       "    plt.fill_between( x, nor.pdf( x, _mu, scale =1./_tau ), color = _color, \\\n",  | 
1444 | 1445 |       "         alpha = .33)\n",  | 
1445 |  | -      "    \n",  | 
1446 |  | -      "\n",  | 
1447 | 1446 |       "\n",  | 
1448 | 1447 |       "plt.legend(loc = \"upper right\")\n",  | 
1449 | 1448 |       "plt.xlabel(\"$x$\")\n",  | 
 | 
1634 | 1633 |      "collapsed": false,  | 
1635 | 1634 |      "input": [  | 
1636 | 1635 |       "figsize( 12.5, 4)\n",  | 
 | 1636 | +      "\n",  | 
1637 | 1637 |       "plt.plot( t, mean_prob_t, lw = 3, label = \"average posterior \\nprobability \\\n",  | 
1638 | 1638 |       "of defect\")\n",  | 
1639 | 1639 |       "plt.plot( t, p_t[0, :], ls=\"--\",label=\"realization from posterior\" )\n",  | 
 | 
1671 | 1671 |      "collapsed": false,  | 
1672 | 1672 |      "input": [  | 
1673 | 1673 |       "from scipy.stats.mstats import mquantiles\n",  | 
 | 1674 | +      "\n",  | 
1674 | 1675 |       "# vectorized bottom and top 5% quantiles for \"confidence interval\"\n",  | 
1675 | 1676 |       "qs = mquantiles(p_t,[0.05,0.95],axis=0)\n",  | 
1676 | 1677 |       "plt.fill_between(t[:,0],*qs,alpha = 0.7,\n",  | 
 | 
1723 | 1724 |      "collapsed": false,  | 
1724 | 1725 |      "input": [  | 
1725 | 1726 |       "figsize(12.5, 2.5)\n",  | 
 | 1727 | +      "\n",  | 
1726 | 1728 |       "prob_31 = logistic( 31, beta_samples, alpha_samples )\n",  | 
1727 | 1729 |       "\n",  | 
1728 | 1730 |       "plt.xlim( 0.995, 1)\n",  | 
 | 
1768 | 1770 |       "simulated = mc.Bernoulli( \"bernoulli_sim\", p)\n",  | 
1769 | 1771 |       "N = 10000\n",  | 
1770 | 1772 |       "\n",  | 
1771 |  | -      "\n",  | 
1772 | 1773 |       "mcmc = mc.MCMC( [simulated, alpha, beta, observed ] )\n",  | 
1773 | 1774 |       "mcmc.sample( N )"  | 
1774 | 1775 |      ],  | 
 | 
1798 | 1799 |      "collapsed": false,  | 
1799 | 1800 |      "input": [  | 
1800 | 1801 |       "figsize(12.5, 5)\n",  | 
 | 1802 | +      "\n",  | 
1801 | 1803 |       "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n",  | 
1802 | 1804 |       "print simulations.shape\n",  | 
1803 | 1805 |       "\n",  | 
 | 
1962 | 1964 |      "cell_type": "code",  | 
1963 | 1965 |      "collapsed": false,  | 
1964 | 1966 |      "input": [  | 
1965 |  | -      "figsize( 11., 1.5 )\n",  | 
1966 | 1967 |       "from separation_plot import separation_plot\n",  | 
1967 | 1968 |       "\n",  | 
 | 1969 | +      "figsize( 11., 1.5 )\n",  | 
 | 1970 | +      "\n",  | 
1968 | 1971 |       "separation_plot(posterior_probability, D )"  | 
1969 | 1972 |      ],  | 
1970 | 1973 |      "language": "python",  | 
 | 
2071 | 2074 |      "input": [  | 
2072 | 2075 |       "#type your code here.\n",  | 
2073 | 2076 |       "figsize(12.5, 4 )\n",  | 
 | 2077 | +      "\n",  | 
2074 | 2078 |       "plt.scatter( alpha_samples, beta_samples, alpha = 0.1 )\n",  | 
2075 | 2079 |       "plt.title( \"Why does the plot look like this?\" )\n",  | 
2076 | 2080 |       "plt.xlabel( r\"$\\alpha$\")\n",  | 
 | 
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