docs/source/notebooks/cox_model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
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   "source": [
    "%matplotlib inline\n",
    "from pymc3 import Gamma, Poisson, Normal, Model, sample, forestplot, NUTS, Metropolis, find_MAP, starting, traceplot\n",
    "import theano.tensor as tt\n",
    "from theano import function as fn\n",
    "from theano import printing\n",
    "import numpy as np\n",
    "import scipy as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is the original model, implemented in BUGS:\n",
    "\n",
    "```R\n",
    "model\n",
    "{   \n",
    "    # Set up data\n",
    "        for(i in 1:Nsubj) {\n",
    "            for(j in 1:T) {\n",
    "    # risk set = 1 if obs.t >= t\n",
    "                Y[i,j] <- step(obs.t[i] - t[j] + eps)\n",
    "    # counting process jump = 1 if obs.t in [ t[j], t[j+1] )\n",
    "    #                      i.e. if t[j] <= obs.t < t[j+1]\n",
    "                dN[i, j] <- Y[i, j] * step(t[j + 1] - obs.t[i] - eps) * FAIL[i]\n",
    "            }\n",
    "        }\n",
    "\n",
    "    # Model \n",
    "        for(j in 1:T) {\n",
    "            for(i in 1:Nsubj) {\n",
    "                dN[i, j]   ~ dpois(Idt[i, j])              # Likelihood\n",
    "                Idt[i, j] <- Y[i, j] * exp(beta[1]*pscenter[i] + beta[2]*\n",
    "                hhcenter[i] + beta[3]*ncomact[i] + beta[4]*rleader[i] + beta[5]*dleader[i] + beta[6]*inter1[i] + beta[7]*inter2[i]) * dL0[j]    # Intensity\n",
    "            }     \n",
    "            dL0[j] ~ dgamma(mu[j], c)\n",
    "            mu[j] <- dL0.star[j] * c    # prior mean hazard \n",
    "        }\n",
    "\n",
    "\n",
    "    c ~ dgamma(0.0001, 0.00001)\n",
    "    r ~ dgamma(0.001, 0.0001)\n",
    "\n",
    "\n",
    "    for (j in 1 : T) {  dL0.star[j] <- r * (t[j + 1] - t[j])  } \n",
    "    # next line indicates number of covariates and is for the corresponding betas\n",
    "    for(i in 1:7) {beta[i] ~ dnorm(0.0,0.00001)} \n",
    "\n",
    "\n",
    "}\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dta = dict(T=73, Nsubj=430, eps=0.0,  t=[1, 21, 85, 128, 129, 148, 178, 204,\n",
    "                                         206, 210, 211, 212, 225, 238, 241,\n",
    "                                         248, 259, 273, 275, 281, 286, 289,\n",
    "                                         301, 302, 303, 304, 313, 317, 323,\n",
    "                                         344, 345, 349, 350, 351, 355, 356,\n",
    "                                         359, 364, 385, 386, 389, 390, 391,\n",
    "                                         392, 394, 395, 396, 397, 398, 399,\n",
    "                                         400, 406, 415, 416, 426, 427, 434,\n",
    "                                         435, 437, 441, 447, 448, 449, 450,\n",
    "                                         451, 453, 455, 456, 458, 459, 460,\n",
    "                                         461, 462, 463],\n",
    "obs_t = [460, 313, 435, 350, 435, 350, 350, 460, 460, 448, 225, 225, 396, 435, 396, 396, 453, 396, 456, 397, 397, 396, 395, 275, 449, 395, 395, 462, 302, 302, 458, 461, 396, 241, 389, 458, 304, 304, 395, 395, 364, 460, 415, 463, 396, 459, 441, 435, 396, 458, 437, 396, 356, 356, 396, 455, 396, 462, 399, 400, 350, 350, 395, 395, 441, 355, 85, 458, 128, 396, 386, 386, 386, 462, 458, 390, 390, 396, 396, 396, 427, 458, 395, 275, 275, 395, 359, 395, 395, 441, 395, 463, 178, 275, 463, 396, 396, 259, 396, 396, 458, 441, 396, 463, 396, 463, 435, 396, 437, 396, 398, 463, 460, 462, 460, 460, 210, 396, 435, 458, 385, 323, 323, 359, 396, 396, 460, 238, 441, 450, 392, 458, 396, 458, 396, 396, 462, 435, 396, 394, 396, 435, 458, 1, 395, 395, 451, 462, 458, 462, 396, 286, 396, 349, 449, 462, 455, 21, 463, 461, 461, 456, 435, 396, 460, 462, 462, 435, 435, 460, 386, 396, 458, 386, 461, 441, 435, 435, 463, 456, 396, 275, 460, 406, 460, 406, 317, 406, 461, 396, 359, 458, 463, 435, 462, 458, 396, 396, 273, 396, 435, 281, 275, 396, 447, 225, 447, 396, 435, 416, 396, 248, 396, 435, 435, 396, 461, 385, 396, 458, 458, 396, 461, 396, 448, 396, 396, 460, 455, 456, 463, 462, 458, 463, 396, 462, 395, 456, 396, 463, 396, 435, 459, 396, 396, 396, 395, 435, 455, 395, 461, 344, 396, 395, 396, 317, 396, 395, 426, 461, 396, 289, 441, 395, 396, 458, 396, 396, 435, 396, 395, 396, 441, 345, 396, 359, 435, 435, 396, 396, 395, 458, 461, 458, 212, 301, 458, 456, 395, 396, 395, 435, 396, 396, 303, 458, 460, 400, 396, 462, 359, 458, 396, 206, 441, 396, 458, 396, 462, 396, 396, 275, 396, 395, 435, 435, 462, 225, 458, 462, 396, 396, 289, 396, 303, 455, 400, 400, 359, 461, 396, 462, 460, 463, 463, 463, 204, 435, 435, 396, 396, 396, 463, 458, 396, 455, 435, 396, 396, 463, 396, 461, 463, 460, 441, 460, 435, 435, 460, 455, 460, 395, 460, 460, 460, 435, 449, 463, 462, 129, 391, 396, 391, 391, 434, 356, 462, 396, 349, 225, 396, 435, 461, 391, 391, 351, 211, 461, 212, 434, 148, 356, 458, 456, 455, 435, 463, 463, 462, 435, 463, 437, 460, 396, 406, 451, 460, 435, 396, 460, 455, 396, 398, 456, 458, 396, 456, 449, 396, 128, 396, 462, 463, 396, 396, 396, 435, 460, 396, 458],\n",
    "FAIL= [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],\n",
    "pscenter= [\n",
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    "inter1= [ -.01434325, -.01460965, 0, 0, 0, -.01113493, 0, 0, 0, -.0553269, -.03238896, 0, 0, -.07062459, -.07464545, -.07032613, 0, 0, -.01408955, 0, -.00219072, 0, 0, 0, 0, 0, .07300876, .01394272, 0, 0, 0, 0, 0, 0, .05120398, 0, -.00550709, -.02062663, -.03077685, -.01688493, 0, .01149963, 0, .01149963, .01149963, 0, 0, 0, 0, 0, 0, 0, 0, 0, .01149963, .0034338, .0376236, .00733331, 0, .03832785, .03832785, -.02622275, -.02622275, -.02622275, -.01492678, 0, 0, -.02897806, -.02847666, 0, 0, -.04224754, -.04743705, -.0510477, -.031893, 0, 0, 0, -.01503116, .003101, -.00083466, .02395027, -.07952866, 0, 0, -.06586029, 0, -.0613939, -.081205, -.07540084, -.08488011, -.08488011, 0, -.07492433, -.08907269, -.09451609, 0, -.08980743, 0, -.0771635, 0, 0, -.0771635, -.08204606, 0, -.05263504, 0, -.05109092, -.04696729, 0, -.04696729, 0, -.05303248, -.05348096, 0, 0, .00584956, -.00792241, -.01719816, 0, -.01576016, 0, -.04014061, 0, 0, 0, 0, 0, .0471441, 0, .04233112, 0, .04233112, 0, 0, .0493324, .04512087, .03205975, .02913185, 0, .05324252, 0, 0, 0, 0, .05054695, 0, .14026688, .01734403, .06078221, 0, 0, 0, -.03138622, 0, .01637333, 0, 0, 0, 0, .01897239, .01591935, 0, -.0619156, 0, -.06851645, 0, -.03889525, -.05023452, -.05013452, 0, 0, -.01362136, 0, 0, -.02634164, 0, 0, 0, 0, -.00890537, -.00611669, 0, 0, 0, -.01513384, 0, -.03551984, 0, -.01978032, 0, .06706496, .10551275, 0, .03092981, .06556855, 0, 0, 0, .09362991, 0, 0, 0, 0, 0, 0, .02610553, .03546937, 0, 0, .034415, 0, 0, 0, .07546701, 0, 0, 0, 0, -.02919447, -.01016712, 0, 0, 0, 0, -.04845615, -.05010044, 0, 0, 0, 0, 0, 0, -.07666632, 0, 0, -.07226554, -.08216553, -.0777643, 0, 0, -.04727952, 0, -.06870384, -.05999847, 0, 0, 0, .02772475, .02883079, .03642944, 0, .04148949, 0, 0, 0, .04268012, .03225577, 0, -.05140995, -.05399637, 0, 0, .02432223, 0, .0490674, .0490674, .0490674, 0, 0, 0, 0, 0, 0, 0, 0, .10476315, 0, 0, 0, 0, 0, .07008056, 0, 0, .01667466, 0, .05253941, .04293926, 0, .02692172, 0, 0, .08742411, .04533176, 0, .01831875, 0, .09834951, .09952456, 0, .02945534, .038731, 0, .04435538, 0, -.02357505, 0, 0, -.02357505, .09324722, 0, 0, 0, -.03490683, 0, -.05054474, 0, -.0474724, -.04905931, 0, .02879751, 0, 0, 0, 0, 0, 0, 0, .04439012, 0, .02989959, .02989959, .05468828, .04463226, 0, 0, 0, 0, 0, .01231324, -.01399783, .04595331, .00145386, 0, .06459354, -.0007196, 0, -.07614055, -.08435525, 0, -.10299519, 0, 0, 0, -.00210284, -.00797183, 0, 0, 0, 0, -.03545086, 0, 0, 0, 0, -.061286, -.07666647, 0, -.05902354, -.07652324, -.07645561, 0, 0, 0, -.03292062, 0, 0, 0, 0, -.075417, 0, -.07922532, 0, -.08583414, -.07450142, -.08066016, 0, 0, -.06249051, 0, 0, 0, 0, -.0618688, 0, -.06524737, -.04419825, -.04489509, 0, 0, 0, -.04520512, -.04187583, 0, 0, -.03753508, 0, 0, 0, 0, 0, 0, 0, 0, .06862645, 0, 0, -.00120631, .01947345, 0, 0, .03561932, 0, .03158225, .03608047, 0, 0, 0, -.02899643],\n",
    "\n",
    "inter2= [-.78348798, -.63418788, 0, 0, 0, .11481193, 0, 0, 0, -.88128799, -1.109488, 0, 0, -.30888793, .29651192, -.36688802, 0, 0, -.59088796, 0, .50561196, 0, 0, 0, 0, 0, 2.1662121, .08891205, 0, 0, 0, 0, 0, 0, -.23918791, 0, -.9575879, -.07728811, .29641202, 1.2273121, 0, 1.5764117, 0, .72131211, 1.279212, 0, 0, 0, 0, 0, 0, 0, 0, 0, .36481193, 1.5480118, -.03078791, 1.389112, 0, .70901209, -.16668792, 1.435812, .47001198, 2.0838118, 1.1673121, 0, 0, 1.4470119, .23301201, 0, 0, -.61948794, -.41388795, .263212, .66171199, 0, 0, 0, 1.6920118, 1.334012, 1.2101121, .41591194, -.48498794, 0, 0, .09911207, 0, -.46908805, .0205119, .0535119, -.14228792, -.55708808, 0, -.54008788, -.30998799, -.10958811, 0, -.01338812, 0, -.51788801, 0, 0, .13271193, -.11208793, 0, -.54508799, 0, .16641192, .95871216, 0, 1.6281118, 0, -.49718806, -.41348812, 0, 0, -.11718794, -.57058805, -.59488791, 0, -.65658802, 0, -.52698797, 0, 0, 0, 0, 0, 1.3500118, 0, 1.665812, 0, 1.963912, 0, 0, 1.9371119, .90991193, -.39558789, .39521196, 0, -.05268808, 0, 0, 0, 0, -.12458798, 0, -.28228804, .79281193, -.26358792, 0, 0, 0, -.72828788, 0, .355912, 0, 0, 0, 0, -.43538806, -1.566388, 0, -.28388807, 0, -.69028801, 0, -.78128809, -.54648799, -.92738789, 0, 0, .61571199, 0, 0, 1.012012, 0, 0, 0, 0, .43991187, .9404121, 0, 0, 0, .61671191, 0, 2.6073117, 0, -.60438794, 0, -.18108793, -.48178813, 0, -.22628804, -.07398792, 0, 0, 0, 1.830512, 0, 0, 0, 0, 0, 0, -.36918804, 1.3247118, 0, 0, 1.163012, 0, 0, 0, 1.3241119, 0, 0, 0, 0, -.90038794, -1.250888, 0, 0, 0, 0, -1.048188, -.90138787, 0, 0, 0, 0, 0, 0, -.00878807, 0, 0, .46301201, -.22048803, -.71518797, 0, 0, -.4952881, 0, -.83718795, .57951194, 0, 0, 0, 1.054112, .61721212, 2.2717118, 0, 2.0280118, 0, 0, 0, 2.6503119, 2.3914118, 0, -.36418793, -.9259879, 0, 0, .16971211, 0, 1.9360118, 2.5344119, 2.0171118, 0, 0, 0, 0, 0, 0, 0, 0, .77211195, 0, 0, 0, 0, 0, 1.952312, 0, 0, .25901201, 0, -.5028879, .03641204, 0, .38571194, 0, 0, -.44528791, -.55918807, 0, .39721206, 0, -.34038803, -.05988808, 0, -.03518792, .045512, 0, -.039288, 0, .01431207, 0, 0, .030412, -.31918809, 0, 0, 0, -.324388, 0, -1.232188, 0, -.23678799, -.89188808, 0, -.6766879, 0, 0, 0, 0, 0, 0, 0, -.67818803, 0, 1.099412, 1.2767119, -.64068788, -.50678796, 0, 0, 0, 0, 0, .68371207, .11251191, -.17128797, .17081194, 0, -.48708794, .09591202, 0, -.20108791, -.02158805, 0, -.3012881, 0, 0, 0, -.87638801, -.54488796, 0, 0, 0, 0, -.14738794, 0, 0, 0, 0, -.75718802, -.37418792, 0, 1.0981121, 1.1441121, .47381189, 0, 0, 0, -.33498809, 0, 0, 0, 0, -.91838807, 0, -.34488794, 0, .12971191, .99381214, -.91608804, 0, 0, .98171192, 0, 0, 0, 0, -.01528808, 0, -.41458794, .25691202, .18601207, 0, 0, 0, -.35608789, .79691201, 0, 0, 1.548912, 0, 0, 0, 0, 0, 0, 0, 0, 1.1663117, 0, 0, -.009088, -.49578807, 0, 0, -.2677879, 0, -.25468799, .68631202, 0, 0, 0, -.36198804])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data_cox(dta):\n",
    "    array = lambda x : np.array(dta[x], dtype=float)\n",
    "    t = array('t')\n",
    "    obs_t = array('obs_t')\n",
    "    pscenter = array('pscenter')\n",
    "    hhcenter = array('hhcenter')\n",
    "    ncomact = array('ncomact')\n",
    "    rleader = array('rleader')\n",
    "    dleader = array('dleader')\n",
    "    inter1 = array('inter1')\n",
    "    inter2 = array('inter2')\n",
    "    fail = array('FAIL')\n",
    "    return (t, obs_t, pscenter, hhcenter, ncomact,\n",
    "            rleader, dleader, inter1, inter2, fail)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "(t, obs_t, pscenter, hhcenter, ncomact, rleader,\n",
    "     dleader, inter1, inter2, fail) = load_data_cox(dta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([pscenter, hhcenter, ncomact, rleader, dleader, inter1, inter2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7, 430)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "with Model() as model:\n",
    "    \n",
    "    T = len(t) - 1\n",
    "    nsubj = len(obs_t)\n",
    "\n",
    "    # risk set equals one if obs_t >= t\n",
    "    Y = np.array([[int(obs >= time) for time in t] for obs in obs_t])\n",
    "    # counting process. jump = 1 if obs_t \\in [t[j], t[j+1])\n",
    "    dN = np.array([[Y[i,j]*int(t[j+1] >= obs_t[i])*fail[i] for j in range(T)] for i in\n",
    "                    range(nsubj)])\n",
    "\n",
    "    c = Gamma('c', .0001, .00001)\n",
    "    r = Gamma('r', .001, .0001)\n",
    "    \n",
    "    dL0_star = r*np.diff(t)\n",
    "    \n",
    "    # prior mean hazard\n",
    "    mu = dL0_star * c \n",
    "    \n",
    "    dL0 = Gamma('dL0', mu, c, shape=T)\n",
    "\n",
    "    beta = Normal('beta', np.zeros(7),\n",
    "                  np.ones(7)*100, shape=7)\n",
    "\n",
    "    linear_model = tt.exp(tt.dot(X.T, beta))\n",
    "    idt = Y[:, :-1] * tt.outer(linear_model, dL0)\n",
    "\n",
    "    dn_like = Poisson('dn_like', idt, observed=dN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using advi_map...\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n",
      "         Current function value: 2811.898224\n",
      "         Iterations: 899\n",
      "         Function evaluations: 999\n",
      "         Gradient evaluations: 989\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Average Loss = 85,779: 100%|██████████| 10000/10000 [00:06<00:00, 1476.40it/s]   \n",
      "Finished [100%]: Average Loss = 85,557\n",
      "100%|██████████| 2500/2500 [01:07<00:00, 36.90it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = sample(2000, n_init=10000, init='advi_map')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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++JU43lPbwtjCrKjuE8l6UZEoP9RK+aHQDdBIY8lwO3sampFs0+b2Ll7ZWHW4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13aba62b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "traceplot(trace, varnames=['c', 'r']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x13af01eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(trace, varnames=['beta'], \n",
    "           ylabels=['pscenter', 'hhcenter', 'ncomact', 'rleader', 'dleader', 'inter1', 'inter2']);"
   ]
  }
 ],
 "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": "3.6.1"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}