Normal Test.ipynb

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   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import numpy as np\n",
    "import pymc3 as pm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate data from Gaussian with mean=2 and SD=5 and try to recover these parameters with PyMC3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "x = np.random.normal(2, 5, size=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "Applied log-transform to sigma and added transformed sigma_log to model.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    \n",
    "    mu = pm.Normal('mu', 0, sd=1e4)\n",
    "    sigma = pm.HalfCauchy('sigma', 25)\n",
    "    \n",
    "    likelihood = pm.Normal('likelihood', mu, sd=sigma, observed=x)"
   ]
  },
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   "execution_count": 5,
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     "text": [
      "Assigned NUTS to mu\n",
      "Assigned NUTS to sigma_log\n",
      " [-----------------100%-----------------] 1000 of 1000 complete in 0.7 sec"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    tr = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "\n",
      "mu:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  2.174            0.203            0.008            [1.851, 2.509]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  1.836          2.069          2.184          2.301          2.497\n",
      "\n",
      "\n",
      "sigma_log:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  1.609            0.042            0.001            [1.563, 1.651]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  1.565          1.592          1.609          1.623          1.655\n",
      "\n",
      "\n",
      "sigma:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  5.003            0.280            0.009            [4.774, 5.212]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  4.782          4.912          4.996          5.069          5.231\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pm.summary(tr)"
   ]
  }
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