HMM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pymc\n",
    "import pdb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def unconditionalProbability(Ptrans):\n",
    "   \"\"\"Compute the unconditional probability for the states of a\n",
    "   Markov chain.\"\"\"\n",
    "\n",
    "   m = Ptrans.shape[0]\n",
    "\n",
    "   P = np.column_stack((Ptrans, 1. - Ptrans.sum(axis=1)))\n",
    "\n",
    "   I = np.eye(m)\n",
    "   U = np.ones((m, m))\n",
    "   u = np.ones(m)\n",
    "\n",
    "   return np.linalg.solve((I - P + U).T, u)\n",
    "\n",
    "data = np.loadtxt('test_data.txt',\n",
    "                 dtype=np.dtype([('state', np.uint8),\n",
    "                                 ('emission', np.float)]),\n",
    "                 delimiter=',',\n",
    "                 skiprows=1)\n",
    "\n",
    "# Two state model for simplicity.\n",
    "N_states = 2\n",
    "N_chain = len(data)\n",
    "\n",
    "# Transition probability stochastic\n",
    "theta = np.ones(N_states) + 1.\n",
    "\n",
    "def Ptrans_logp(value, theta):\n",
    "   logp = 0.\n",
    "   for i in range(value.shape[0]):\n",
    "       logp = logp + pymc.dirichlet_like(value[i], theta)\n",
    "   return logp\n",
    "\n",
    "def Ptrans_random(theta):\n",
    "   return pymc.rdirichlet(theta, size=len(theta))\n",
    "\n",
    "Ptrans = pymc.Stochastic(logp=Ptrans_logp,\n",
    "                        doc='Transition matrix',\n",
    "                        name='Ptrans',\n",
    "                        parents={'theta': theta},\n",
    "                        random=Ptrans_random)\n",
    "\n",
    "#Hidden states stochastic\n",
    "def states_logp(value, Ptrans=Ptrans):\n",
    "    \n",
    "    if sum(value>1):\n",
    "        return -np.inf\n",
    "\n",
    "    P = np.column_stack((Ptrans, 1. - Ptrans.sum(axis=1)))\n",
    "\n",
    "    Pinit = unconditionalProbability(Ptrans)\n",
    "\n",
    "    logp = pymc.categorical_like(value[0], Pinit)\n",
    "\n",
    "    for i in range(1, len(value)):\n",
    "       try:\n",
    "          logp = logp + pymc.categorical_like(value[i], P[value[i-1]])\n",
    "       except:\n",
    "          pdb.set_trace()\n",
    "\n",
    "    return logp\n",
    "\n",
    "def states_random(Ptrans=Ptrans, N_chain=N_chain):\n",
    "   P = np.column_stack((Ptrans, 1. - Ptrans.sum(axis=1)))\n",
    "\n",
    "   Pinit = unconditionalProbability(Ptrans)\n",
    "\n",
    "   states = np.empty(N_chain, dtype=np.uint8)\n",
    "\n",
    "   states[0] = pymc.rcategorical(Pinit)\n",
    "\n",
    "   for i in range(1, N_chain):\n",
    "       states[i] = pymc.rcategorical(P[states[i-1]])\n",
    "\n",
    "   return states\n",
    "\n",
    "states = pymc.Stochastic(logp=states_logp,\n",
    "                        doc='Hidden states',\n",
    "                        name='states',\n",
    "                        parents={'Ptrans': Ptrans},\n",
    "                        random=states_random,\n",
    "                        dtype=np.uint8)\n",
    "\n",
    "# Gaussian emission parameters\n",
    "mu = pymc.Normal('mu', 0., 1.e-6, value=np.random.randn(N_states))\n",
    "sigma = pymc.Uniform('sigma', 0., 100.,\n",
    "value=np.random.rand(N_states))\n",
    "\n",
    "y = pymc.Normal('y', mu[states], 1./sigma[states]**2,\n",
    "value=data['emission'], observed=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "M = pymc.MCMC([Ptrans, states, mu, sigma, y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 100000 of 100000 complete in 6483.2 sec"
     ]
    }
   ],
   "source": [
    "M.sample(iter=100000, burn=10000, thin=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "mu:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t1.007            0.011            0.001            [ 0.983  1.028]\n",
      "\t-0.335           0.263            0.026              [-0.67  0.1 ]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.982            1.0             1.008          1.015         1.027\n",
      "\t-0.664           -0.593          -0.406         -0.077        0.115\n",
      "\t\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/hstrey/anaconda/envs/python3/lib/python3.5/site-packages/numpy/core/fromnumeric.py:225: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n",
      "  return reshape(newshape, order=order)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "states:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.714            0.452            0.042                  [ 0.  1.]\n",
      "\t0.12             0.325            0.03                   [ 0.  1.]\n",
      "\t0.093            0.29             0.027                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.109            0.312            0.03                   [ 0.  1.]\n",
      "\t0.149            0.356            0.035                  [ 0.  1.]\n",
      "\t0.026            0.16             0.015                  [ 0.  0.]\n",
      "\t0.073            0.26             0.026                  [ 0.  1.]\n",
      "\t0.014            0.119            0.01                   [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.045            0.207            0.018                  [ 0.  0.]\n",
      "\t0.038            0.192            0.018                  [ 0.  0.]\n",
      "\t0.029            0.169            0.015                  [ 0.  0.]\n",
      "\t0.212            0.408            0.04                   [ 0.  1.]\n",
      "\t0.191            0.393            0.038                  [ 0.  1.]\n",
      "\t0.343            0.475            0.046                  [ 0.  1.]\n",
      "\t0.192            0.394            0.038                  [ 0.  1.]\n",
      "\t0.233            0.423            0.041                  [ 0.  1.]\n",
      "\t0.09             0.286            0.027                  [ 0.  1.]\n",
      "\t0.111            0.314            0.03                   [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.094            0.291            0.027                  [ 0.  1.]\n",
      "\t0.141            0.348            0.033                  [ 0.  1.]\n",
      "\t0.111            0.314            0.029                  [ 0.  1.]\n",
      "\t0.103            0.304            0.03                   [ 0.  1.]\n",
      "\t0.052            0.222            0.019                  [ 0.  1.]\n",
      "\t0.21             0.407            0.039                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.503            0.5              0.048                  [ 0.  1.]\n",
      "\t0.073            0.26             0.024                  [ 0.  1.]\n",
      "\t0.093            0.29             0.027                  [ 0.  1.]\n",
      "\t0.007            0.084            0.005                  [ 0.  0.]\n",
      "\t0.012            0.111            0.008                  [ 0.  0.]\n",
      "\t0.086            0.28             0.027                  [ 0.  1.]\n",
      "\t0.048            0.213            0.02                   [ 0.  0.]\n",
      "\t0.1              0.3              0.029                  [ 0.  1.]\n",
      "\t0.128            0.334            0.032                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.886            0.317            0.029                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.28             0.449            0.043                  [ 0.  1.]\n",
      "\t0.202            0.401            0.038                  [ 0.  1.]\n",
      "\t0.27             0.444            0.043                  [ 0.  1.]\n",
      "\t0.638            0.481            0.047                  [ 0.  1.]\n",
      "\t0.692            0.462            0.044                  [ 0.  1.]\n",
      "\t0.964            0.187            0.017                  [ 1.  1.]\n",
      "\t0.602            0.49             0.047                  [ 0.  1.]\n",
      "\t0.274            0.446            0.043                  [ 0.  1.]\n",
      "\t0.409            0.492            0.047                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.993            0.081            0.005                  [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.351            0.477            0.045                  [ 0.  1.]\n",
      "\t0.373            0.484            0.047                  [ 0.  1.]\n",
      "\t0.076            0.264            0.025                  [ 0.  1.]\n",
      "\t0.054            0.226            0.021                  [ 0.  1.]\n",
      "\t0.171            0.376            0.036                  [ 0.  1.]\n",
      "\t0.177            0.382            0.036                  [ 0.  1.]\n",
      "\t0.452            0.498            0.048                  [ 0.  1.]\n",
      "\t0.206            0.404            0.04                   [ 0.  1.]\n",
      "\t0.158            0.365            0.035                  [ 0.  1.]\n",
      "\t0.117            0.321            0.031                  [ 0.  1.]\n",
      "\t0.129            0.335            0.032                  [ 0.  1.]\n",
      "\t0.282            0.45             0.044                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.252            0.434            0.041                  [ 0.  1.]\n",
      "\t0.057            0.232            0.021                  [ 0.  1.]\n",
      "\t0.02             0.138            0.011                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.106            0.308            0.029                  [ 0.  1.]\n",
      "\t0.262            0.44             0.042                  [ 0.  1.]\n",
      "\t0.058            0.234            0.022                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.119            0.323            0.031                  [ 0.  1.]\n",
      "\t0.043            0.203            0.019                  [ 0.  0.]\n",
      "\t0.146            0.353            0.034                  [ 0.  1.]\n",
      "\t0.081            0.273            0.027                  [ 0.  1.]\n",
      "\t0.094            0.292            0.028                  [ 0.  1.]\n",
      "\t0.123            0.329            0.031                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.959            0.199            0.018                  [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.403            0.49             0.045                  [ 0.  1.]\n",
      "\t0.088            0.283            0.027                  [ 0.  1.]\n",
      "\t0.064            0.244            0.024                  [ 0.  1.]\n",
      "\t0.091            0.288            0.028                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.004            0.061            0.003                  [ 0.  0.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.299            0.458            0.045                  [ 0.  1.]\n",
      "\t0.371            0.483            0.047                  [ 0.  1.]\n",
      "\t0.192            0.394            0.039                  [ 0.  1.]\n",
      "\t0.236            0.425            0.042                  [ 0.  1.]\n",
      "\t0.24             0.427            0.043                  [ 0.  1.]\n",
      "\t0.283            0.451            0.044                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.751            0.432            0.041                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.841            0.365            0.034                  [ 0.  1.]\n",
      "\t0.37             0.483            0.047                  [ 0.  1.]\n",
      "\t0.292            0.455            0.044                  [ 0.  1.]\n",
      "\t0.179            0.384            0.037                  [ 0.  1.]\n",
      "\t0.112            0.315            0.031                  [ 0.  1.]\n",
      "\t0.085            0.279            0.026                  [ 0.  1.]\n",
      "\t0.248            0.432            0.043                  [ 0.  1.]\n",
      "\t0.301            0.459            0.044                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.795            0.403            0.037                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.279            0.448            0.043                  [ 0.  1.]\n",
      "\t0.302            0.459            0.044                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.167            0.373            0.035                  [ 0.  1.]\n",
      "\t0.002            0.042            0.001                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.034            0.181            0.017                  [ 0.  0.]\n",
      "\t0.022            0.148            0.014                  [ 0.  0.]\n",
      "\t0.076            0.264            0.025                  [ 0.  1.]\n",
      "\t0.102            0.302            0.029                  [ 0.  1.]\n",
      "\t0.018            0.134            0.012                  [ 0.  0.]\n",
      "\t0.001            0.03             0.001                  [ 0.  0.]\n",
      "\t0.142            0.349            0.034                  [ 0.  1.]\n",
      "\t0.111            0.314            0.03                   [ 0.  1.]\n",
      "\t0.236            0.425            0.04                   [ 0.  1.]\n",
      "\t0.144            0.352            0.033                  [ 0.  1.]\n",
      "\t0.044            0.205            0.02                   [ 0.  0.]\n",
      "\t0.065            0.247            0.023                  [ 0.  1.]\n",
      "\t0.145            0.353            0.034                  [ 0.  1.]\n",
      "\t0.232            0.422            0.041                  [ 0.  1.]\n",
      "\t0.145            0.352            0.034                  [ 0.  1.]\n",
      "\t0.14             0.347            0.033                  [ 0.  1.]\n",
      "\t0.065            0.246            0.024                  [ 0.  1.]\n",
      "\t0.034            0.181            0.017                  [ 0.  0.]\n",
      "\t0.037            0.189            0.018                  [ 0.  0.]\n",
      "\t0.02             0.139            0.013                  [ 0.  0.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.946            0.226            0.021                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.519            0.5              0.049                  [ 0.  1.]\n",
      "\t0.131            0.338            0.032                  [ 0.  1.]\n",
      "\t0.019            0.137            0.012                  [ 0.  0.]\n",
      "\t0.005            0.07             0.005                  [ 0.  0.]\n",
      "\t0.027            0.163            0.016                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.017            0.128            0.011                  [ 0.  0.]\n",
      "\t0.136            0.342            0.033                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.958            0.2              0.018                  [ 1.  1.]\n",
      "\t0.027            0.161            0.015                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.176            0.381            0.038                  [ 0.  1.]\n",
      "\t0.029            0.168            0.015                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.014            0.116            0.009                  [ 0.  0.]\n",
      "\t0.0              0.018            0.0                    [ 0.  0.]\n",
      "\t0.036            0.186            0.017                  [ 0.  0.]\n",
      "\t0.324            0.468            0.046                  [ 0.  1.]\n",
      "\t0.623            0.485            0.047                  [ 0.  1.]\n",
      "\t0.478            0.5              0.048                  [ 0.  1.]\n",
      "\t0.574            0.494            0.048                  [ 0.  1.]\n",
      "\t0.559            0.496            0.048                  [ 0.  1.]\n",
      "\t0.664            0.472            0.044                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.351            0.477            0.046                  [ 0.  1.]\n",
      "\t0.208            0.406            0.039                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.024            0.153            0.012                  [ 0.  0.]\n",
      "\t0.041            0.197            0.019                  [ 0.  0.]\n",
      "\t0.061            0.24             0.023                  [ 0.  1.]\n",
      "\t0.034            0.181            0.017                  [ 0.  0.]\n",
      "\t0.121            0.326            0.032                  [ 0.  1.]\n",
      "\t0.092            0.289            0.028                  [ 0.  1.]\n",
      "\t0.089            0.284            0.027                  [ 0.  1.]\n",
      "\t0.188            0.391            0.038                  [ 0.  1.]\n",
      "\t0.137            0.343            0.033                  [ 0.  1.]\n",
      "\t0.118            0.323            0.031                  [ 0.  1.]\n",
      "\t0.109            0.312            0.029                  [ 0.  1.]\n",
      "\t0.097            0.296            0.028                  [ 0.  1.]\n",
      "\t0.014            0.117            0.01                   [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
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      "\t0.182            0.386            0.038                  [ 0.  1.]\n",
      "\t0.126            0.332            0.032                  [ 0.  1.]\n",
      "\t0.057            0.231            0.021                  [ 0.  1.]\n",
      "\t0.012            0.11             0.009                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.169            0.375            0.035                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.244            0.429            0.042                  [ 0.  1.]\n",
      "\t0.138            0.345            0.033                  [ 0.  1.]\n",
      "\t0.069            0.253            0.024                  [ 0.  1.]\n",
      "\t0.001            0.026            0.001                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.064            0.245            0.023                  [ 0.  1.]\n",
      "\t0.207            0.405            0.039                  [ 0.  1.]\n",
      "\t0.068            0.252            0.024                  [ 0.  1.]\n",
      "\t0.05             0.218            0.02                   [ 0.  1.]\n",
      "\t0.075            0.263            0.026                  [ 0.  1.]\n",
      "\t0.685            0.464            0.045                  [ 0.  1.]\n",
      "\t0.52             0.5              0.048                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.138            0.345            0.033                  [ 0.  1.]\n",
      "\t0.105            0.306            0.029                  [ 0.  1.]\n",
      "\t0.108            0.311            0.03                   [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.259            0.438            0.043                  [ 0.  1.]\n",
      "\t0.078            0.269            0.026                  [ 0.  1.]\n",
      "\t0.046            0.209            0.019                  [ 0.  0.]\n",
      "\t0.007            0.083            0.006                  [ 0.  0.]\n",
      "\t0.007            0.083            0.005                  [ 0.  0.]\n",
      "\t0.195            0.396            0.038                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.487            0.5              0.048                  [ 0.  1.]\n",
      "\t0.419            0.493            0.049                  [ 0.  1.]\n",
      "\t0.276            0.447            0.043                  [ 0.  1.]\n",
      "\t0.055            0.227            0.022                  [ 0.  1.]\n",
      "\t0.0              0.018            0.0                    [ 0.  0.]\n",
      "\t0.292            0.455            0.044                  [ 0.  1.]\n",
      "\t0.245            0.43             0.042                  [ 0.  1.]\n",
      "\t0.339            0.473            0.046                  [ 0.  1.]\n",
      "\t0.273            0.445            0.043                  [ 0.  1.]\n",
      "\t0.116            0.32             0.029                  [ 0.  1.]\n",
      "\t0.13             0.337            0.033                  [ 0.  1.]\n",
      "\t0.026            0.16             0.015                  [ 0.  0.]\n",
      "\t0.026            0.16             0.015                  [ 0.  0.]\n",
      "\t0.039            0.193            0.018                  [ 0.  0.]\n",
      "\t0.182            0.386            0.036                  [ 0.  1.]\n",
      "\t0.395            0.489            0.048                  [ 0.  1.]\n",
      "\t0.354            0.478            0.047                  [ 0.  1.]\n",
      "\t0.347            0.476            0.047                  [ 0.  1.]\n",
      "\t0.131            0.337            0.032                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.028            0.165            0.016                  [ 0.  0.]\n",
      "\t0.104            0.306            0.029                  [ 0.  1.]\n",
      "\t0.094            0.291            0.028                  [ 0.  1.]\n",
      "\t0.006            0.08             0.005                  [ 0.  0.]\n",
      "\t0.027            0.161            0.015                  [ 0.  0.]\n",
      "\t0.029            0.168            0.015                  [ 0.  0.]\n",
      "\t0.087            0.282            0.027                  [ 0.  1.]\n",
      "\t0.115            0.319            0.031                  [ 0.  1.]\n",
      "\t0.148            0.356            0.035                  [ 0.  1.]\n",
      "\t0.685            0.464            0.044                  [ 0.  1.]\n",
      "\t0.405            0.491            0.046                  [ 0.  1.]\n",
      "\t0.5              0.5              0.047                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.444            0.497            0.048                  [ 0.  1.]\n",
      "\t0.243            0.429            0.04                   [ 0.  1.]\n",
      "\t0.185            0.389            0.037                  [ 0.  1.]\n",
      "\t0.362            0.481            0.046                  [ 0.  1.]\n",
      "\t0.545            0.498            0.048                  [ 0.  1.]\n",
      "\t0.41             0.492            0.048                  [ 0.  1.]\n",
      "\t0.174            0.379            0.037                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.132            0.339            0.033                  [ 0.  1.]\n",
      "\t0.218            0.413            0.041                  [ 0.  1.]\n",
      "\t0.113            0.317            0.03                   [ 0.  1.]\n",
      "\t0.128            0.335            0.032                  [ 0.  1.]\n",
      "\t0.166            0.372            0.036                  [ 0.  1.]\n",
      "\t0.24             0.427            0.042                  [ 0.  1.]\n",
      "\t0.103            0.304            0.03                   [ 0.  1.]\n",
      "\t0.181            0.385            0.038                  [ 0.  1.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.024            0.153            0.014                  [ 0.  0.]\n",
      "\t0.169            0.375            0.035                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.216            0.412            0.039                  [ 0.  1.]\n",
      "\t0.024            0.152            0.014                  [ 0.  0.]\n",
      "\t0.0              0.0              0.0                    [ 0.  0.]\n",
      "\t0.058            0.234            0.021                  [ 0.  1.]\n",
      "\t0.178            0.382            0.037                  [ 0.  1.]\n",
      "\t0.046            0.209            0.019                  [ 0.  0.]\n",
      "\t0.294            0.456            0.044                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.667            0.471            0.045                  [ 0.  1.]\n",
      "\t0.397            0.489            0.048                  [ 0.  1.]\n",
      "\t0.213            0.409            0.04                   [ 0.  1.]\n",
      "\t0.141            0.348            0.034                  [ 0.  1.]\n",
      "\t0.041            0.199            0.019                  [ 0.  0.]\n",
      "\t0.004            0.066            0.003                  [ 0.  0.]\n",
      "\t0.065            0.246            0.023                  [ 0.  1.]\n",
      "\t0.086            0.28             0.027                  [ 0.  1.]\n",
      "\t0.251            0.434            0.042                  [ 0.  1.]\n",
      "\t0.352            0.478            0.047                  [ 0.  1.]\n",
      "\t0.374            0.484            0.047                  [ 0.  1.]\n",
      "\t0.575            0.494            0.047                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.405            0.491            0.047                  [ 0.  1.]\n",
      "\t0.077            0.266            0.024                  [ 0.  1.]\n",
      "\t0.114            0.318            0.03                   [ 0.  1.]\n",
      "\t0.24             0.427            0.041                  [ 0.  1.]\n",
      "\t0.596            0.491            0.048                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.256            0.436            0.041                  [ 0.  1.]\n",
      "\t0.348            0.476            0.047                  [ 0.  1.]\n",
      "\t0.237            0.426            0.041                  [ 0.  1.]\n",
      "\t0.01             0.101            0.01                   [ 0.  0.]\n",
      "\t0.02             0.139            0.013                  [ 0.  0.]\n",
      "\t0.066            0.248            0.023                  [ 0.  1.]\n",
      "\t0.091            0.287            0.027                  [ 0.  1.]\n",
      "\t0.139            0.346            0.034                  [ 0.  1.]\n",
      "\t0.055            0.228            0.022                  [ 0.  1.]\n",
      "\t0.051            0.221            0.022                  [ 0.  1.]\n",
      "\t0.15             0.357            0.035                  [ 0.  1.]\n",
      "\t0.11             0.313            0.03                   [ 0.  1.]\n",
      "\t0.046            0.21             0.018                  [ 0.  0.]\n",
      "\t0.023            0.15             0.013                  [ 0.  0.]\n",
      "\t0.167            0.373            0.036                  [ 0.  1.]\n",
      "\t0.163            0.37             0.036                  [ 0.  1.]\n",
      "\t0.1              0.301            0.029                  [ 0.  1.]\n",
      "\t0.039            0.194            0.018                  [ 0.  0.]\n",
      "\t0.048            0.215            0.02                   [ 0.  0.]\n",
      "\t0.266            0.442            0.042                  [ 0.  1.]\n",
      "\t0.389            0.488            0.047                  [ 0.  1.]\n",
      "\t1.0              0.0              0.0                    [ 1.  1.]\n",
      "\t0.287            0.452            0.043                  [ 0.  1.]\n",
      "\t0.069            0.253            0.024                  [ 0.  1.]\n",
      "\t0.139            0.346            0.034                  [ 0.  1.]\n",
      "\t0.027            0.162            0.015                  [ 0.  0.]\n",
      "\t0.055            0.228            0.021                  [ 0.  1.]\n",
      "\t0.005            0.074            0.004                  [ 0.  0.]\n",
      "\t0.002            0.048            0.002                  [ 0.  0.]\n",
      "\t0.043            0.203            0.018                  [ 0.  0.]\n",
      "\t0.13             0.336            0.033                  [ 0.  1.]\n",
      "\t0.032            0.176            0.016                  [ 0.  0.]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
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      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t1.0              1.0             1.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            1.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           0.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t0.0              0.0             0.0            0.0           1.0\n",
      "\t\n",
      "\n",
      "sigma:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.222            0.014            0.001            [ 0.191  0.246]\n",
      "\t1.157            0.057            0.004            [ 1.045  1.265]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.187            0.216           0.225          0.232         0.243\n",
      "\t1.043            1.118           1.159          1.197         1.263\n",
      "\t\n",
      "\n",
      "Ptrans:\n",
      " \n",
      "\tMean             SD               MC Error        95% HPD interval\n",
      "\t------------------------------------------------------------------\n",
      "\t0.837            0.076            0.007            [ 0.643  0.925]\n",
      "\t0.24             0.031            0.002            [ 0.179  0.3  ]\n",
      "\t\n",
      "\t\n",
      "\tPosterior quantiles:\n",
      "\t\n",
      "\t2.5             25              50              75             97.5\n",
      "\t |---------------|===============|===============|---------------|\n",
      "\t0.607            0.821           0.861          0.889         0.912\n",
      "\t0.183            0.217           0.238          0.26          0.305\n",
      "\t\n"
     ]
    }
   ],
   "source": [
    "M.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.75,  0.25])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "myP=np.array([[0.9],[0.3]])\n",
    "unconditionalProbability(myP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.46391414],\n",
       "       [ 0.35178629]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ptrans_random(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
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}