el-hult/Gelman2.13.ipynb

## Gelman2.13.ipynb
{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "pycharm": {
          "name": "#%% md\n"
        }
      },
      "source": "Discrete data: Table 2.2 gives the number of fatal accidents and deaths on scheduled\nairline flights per year over a ten-year period. We use these data as a numerical example\nfor fitting discrete data models."
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "outputs": [],
      "source": "# load libraries and data\n\nimport io\nimport numpy as np\nimport pandas as pd\nimport matplotlib.pyplot as plt\nimport scipy.stats\nimport scipy.integrate as integrate\nimport importlib",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%%\n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "outputs": [],
      "source": "# add utilities directory to path\nimport os, sys\n#util_path \u003d os.path.abspath(os.path.join(os.path.pardir, \u0027utilities_and_data\u0027))\nlib_path \u003d r\"C:\\Users\\Ludvig\\Google Drive\\Doktorand Uppsala\\Övrningar från böcker\\Gelman et al_2013_Beysesian Data Analysis\"\nif lib_path not in sys.path and os.path.exists(lib_path):\n    sys.path.insert(0, lib_path)\n\n# import from utilities\nimport lib\nif lib is not None:\n    importlib.reload(lib)",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%%\n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "outputs": [
        {
          "data": {
            "text/plain": "   Year  Fatal_accidents  Passenger_Deaths  Death_rate\n0  1976               24               734        0.19\n1  1977               25               516        0.12\n2  1978               31               754        0.15",
            "text/html": "\u003cdiv\u003e\n\u003cstyle scoped\u003e\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n\u003c/style\u003e\n\u003ctable border\u003d\"1\" class\u003d\"dataframe\"\u003e\n  \u003cthead\u003e\n    \u003ctr style\u003d\"text-align: right;\"\u003e\n      \u003cth\u003e\u003c/th\u003e\n      \u003cth\u003eYear\u003c/th\u003e\n      \u003cth\u003eFatal_accidents\u003c/th\u003e\n      \u003cth\u003ePassenger_Deaths\u003c/th\u003e\n      \u003cth\u003eDeath_rate\u003c/th\u003e\n    \u003c/tr\u003e\n  \u003c/thead\u003e\n  \u003ctbody\u003e\n    \u003ctr\u003e\n      \u003cth\u003e0\u003c/th\u003e\n      \u003ctd\u003e1976\u003c/td\u003e\n      \u003ctd\u003e24\u003c/td\u003e\n      \u003ctd\u003e734\u003c/td\u003e\n      \u003ctd\u003e0.19\u003c/td\u003e\n    \u003c/tr\u003e\n    \u003ctr\u003e\n      \u003cth\u003e1\u003c/th\u003e\n      \u003ctd\u003e1977\u003c/td\u003e\n      \u003ctd\u003e25\u003c/td\u003e\n      \u003ctd\u003e516\u003c/td\u003e\n      \u003ctd\u003e0.12\u003c/td\u003e\n    \u003c/tr\u003e\n    \u003ctr\u003e\n      \u003cth\u003e2\u003c/th\u003e\n      \u003ctd\u003e1978\u003c/td\u003e\n      \u003ctd\u003e31\u003c/td\u003e\n      \u003ctd\u003e754\u003c/td\u003e\n      \u003ctd\u003e0.15\u003c/td\u003e\n    \u003c/tr\u003e\n  \u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e"
          },
          "metadata": {},
          "output_type": "execute_result",
          "execution_count": 3
        }
      ],
      "source": "\ntable_2_2 \u003d \"\"\"Year Fatal_accidents Passenger_Deaths Death_rate\n1976 24 734 0.19\n1977 25 516 0.12\n1978 31 754 0.15\n1979 31 877 0.16\n1980 22 814 0.14\n1981 21 362 0.06\n1982 26 764 0.13\n1983 20 809 0.13\n1984 16 223 0.03\n1985 22 1066 0.15\"\"\"\nwith io.StringIO(table_2_2) as f:\n    df \u003d pd.read_csv(f,sep\u003d\" \")\ndf.head(3)\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%%\n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": "# A using conjugate prior\n(a) Assume that the numbers of fatal accidents in each year are independent with a\nPoisson(θ) distribution. Set a prior distribution for θ and determine the posterior\ndistribution based on the data from 1976 through 1985. Under this model, give a 95%\npredictive interval for the number of fatal accidents in 1986. You can use the normal\napproximation to the gamma and Poisson or compute using simulation.\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% md\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "outputs": [
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": 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\u003d\u003d\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": "# assume a conjugate prior\ngamma \u003d scipy.stats.gamma\na \u003d 10\nbeta \u003d a/20\ntheta_prior \u003d gamma(a\u003da,scale\u003d1/beta)\nx \u003d np.linspace(theta_prior.ppf(0.001),theta_prior.ppf(0.999))\nplt.plot(x, theta_prior.pdf(x),\u0027r-\u0027, lw\u003d5, alpha\u003d0.6, label\u003d\u0027prior for theta\u0027)\n\n\na_post \u003d a + df[\u0027Fatal_accidents\u0027].sum()\nbeta_post \u003d beta + df.shape[0]\ntheta_posterior \u003d gamma(a\u003da_post,scale\u003d1/beta_post)\nx_post \u003d np.linspace(theta_posterior.ppf(0.001),theta_posterior.ppf(0.999))\nplt.plot(x_post, theta_posterior.pdf(x),\u0027b-\u0027, lw\u003d3, alpha\u003d0.9, label\u003d\u0027posterior for theta\u0027)\n\n\n\nsimulated_thetas \u003d theta_posterior.rvs(size\u003d1000)\nsimulate_fatalities \u003d lambda theta: scipy.stats.poisson(mu\u003dtheta).rvs(size\u003d1)[0]\nsimulated_fatalities \u003d map(simulate_fatalities,simulated_thetas)\nas_array \u003d np.fromiter(simulated_fatalities,dtype\u003dint)\n\na \u003d lib.plot_histogram_with_95p(as_array,plt.gca(),\u0027simulated fatalities\u0027)\n\nplt.legend(); plt.show()\n\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% \n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": "\n# B\n(b) Assume that the numbers of fatal accidents in each year follow independent Poisson\ndistributions with a constant rate and an exposure in each year proportional to the\nnumber of passenger miles flown. Set a prior distribution for θ and determine the\nposterior distribution based on the data for 1976–1985. (Estimate the number of\npassenger miles flown in each year by dividing the appropriate columns of Table 2.2\nand ignoring round-off errors.) Give a 95% predictive interval for the number of fatal \naccidents in 1986 under the assumption that 8×10¹¹ passenger miles are flown that\nyear.\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% md\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "outputs": [
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": "\ndf[\u0027Miles\u0027] \u003d df[\u0027Passenger_Deaths\u0027] / df[\u0027Death_rate\u0027]\ndf[\u0027Accident_rate\u0027] \u003d df[\u0027Fatal_accidents\u0027] / df[\u0027Miles\u0027]\nmiles_1986 \u003d 8e11 / 1e8\ndf.head()\n\n# i will model a poisson rate, so the rates must be in units larger than 1.\n# to get accident rates large enough, I will inflate then by 1000.\nmiles_2 \u003d df[\u0027Miles\u0027] / 10000\naccident_rate_2 \u003d df[\u0027Accident_rate\u0027] * 10000\nmiles_1986_2 \u003d miles_1986 / 10000\n\nalpha_prior \u003d 10\nbeta_prior \u003d alpha_prior/20\nalpha_posterior \u003d alpha_prior + accident_rate_2.sum()\nbeta_posterior \u003d beta_prior + df.shape[0]\ntheta_posterior \u003d gamma(a\u003dalpha_posterior,scale\u003d1/beta_posterior)\nsimulated_thetas \u003d theta_posterior.rvs(size\u003d1000)\nsimulate_fataly_rate \u003d lambda theta: scipy.stats.poisson(mu\u003dtheta).rvs(size\u003d1)\nsimulated_fatality_rates \u003d np.vectorize(simulate_fataly_rate)(simulated_thetas)\nsimulated_fatal_accidents \u003d simulated_fatality_rates * miles_1986_2\n\nlib.plot_histogram_with_95p(simulated_fatal_accidents,legend\u003d\"Simulated fatal accidents\")\nplt.legend()\nplt.show()\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%%\n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": "# C\n(c) Repeat (a) above, replacing ‘fatal accidents’ with ‘passenger deaths.’\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% md\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "outputs": [
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 2 Axes\u003e",
            "image/png": 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\u003d\u003d\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": "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\u003d\u003d\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": 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\u003d\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": "\nn_samples \u003d 10000\n\nthetas \u003d np.linspace(100,2000,1000) #domain to consider\n\n\nprior_min \u003d 300\npriot_max \u003d 1200\nprior_pdf \u003d ((thetas \u003e\u003d prior_min) \u0026 (thetas \u003c\u003d priot_max)) * 1/(priot_max-prior_min)\nfig,ax1 \u003d plt.subplots()\nax2 \u003d ax1.twinx()\nprior_cdf \u003d np.append(0,integrate.cumtrapz(prior_pdf,thetas))\nax2.plot(thetas,prior_cdf,color\u003d\u0027red\u0027,label\u003d\"prior cdf\")\nax1.plot(thetas,prior_pdf,label\u003d\"prior pdf\")\npick_theta \u003d lambda : np.interp(np.random.random(),prior_cdf,thetas)\nsimulated_prior \u003d np.array([pick_theta() for _ in range(n_samples)])\nax1.hist(simulated_prior,bins\u003d100,label\u003d\u0027simulated prior\u0027,density\u003dTrue)\nax2.set_ylim([0,ax2.get_ylim()[1]])\nax1.set_xlim([thetas.min(),thetas.max()])\nfig.legend();plt.show()\n\ndef prob_y_given_theta(ys,t):\n    probs \u003d scipy.stats.poisson.pmf(ys,mu\u003dt)\n    #print(t,ys,probs)\n    totprob \u003d probs.prod()\n    return totprob\nys \u003d df[\u0027Passenger_Deaths\u0027].to_list()\nconditional_data_prob \u003d np.array([prob_y_given_theta(ys,t) for t in thetas])\nunnormalized_posterior \u003d conditional_data_prob * prior_pdf\nposterior_pdf \u003d unnormalized_posterior / integrate.trapz(unnormalized_posterior,thetas)\nplt.plot(thetas,posterior_pdf) \nplt.gca().set_xlim([thetas.min(),thetas.max()])\nplt.show()\n\nposterior_cdf \u003d np.append(0,integrate.cumtrapz(posterior_pdf,thetas))\npick_theta_post \u003d lambda : np.interp(np.random.random(),posterior_cdf,thetas)\nsimulated_posterior\u003d np.array([pick_theta_post() for _ in range(n_samples)])\n\npick_y_given_theta \u003d lambda t: scipy.stats.poisson.rvs(mu\u003dt)\nsimulated_y \u003d np.array([pick_y_given_theta(t) for t in simulated_posterior])\n\n\n\nlib.plot_histogram_with_95p(simulated_y,legend\u003d\"Simulated accidents\")\nplt.legend()\nplt.show()\n\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% \n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": "\n# D\n(d) Repeat (b) above, replacing ‘fatal accidents’ with ‘passenger deaths.’",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% md\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "outputs": [
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 2 Axes\u003e",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": 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\u003d\u003d\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "text": [
            "the 95 percent interval for death rate (in deaths per 100 million flyer miles) is [0.06,0.21]\n"
          ],
          "output_type": "stream"
        },
        {
          "data": {
            "text/plain": "\u003cFigure size 432x288 with 1 Axes\u003e",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": "\n\n# I will use intensity times 100 as the quantity to model\ny_obs \u003d  (df[\u0027Death_rate\u0027] * 100 ).round().to_list()\n\nn_samples \u003d 10000\n\nthetas \u003d np.linspace(0,40,1000) #domain to consider\n\nprior_min \u003d 3\npriot_max \u003d 20\nprior_pdf \u003d ((thetas \u003e\u003d prior_min) \u0026 (thetas \u003c\u003d priot_max)) * 1/(priot_max-prior_min)\nfig,ax1 \u003d plt.subplots()\nax2 \u003d ax1.twinx()\nprior_cdf \u003d np.append(0,integrate.cumtrapz(prior_pdf,thetas))\nax2.plot(thetas,prior_cdf,color\u003d\u0027red\u0027,label\u003d\"prior cdf\")\nax1.plot(thetas,prior_pdf,label\u003d\"prior pdf\")\npick_theta \u003d lambda : np.interp(np.random.random(),prior_cdf,thetas)\nsimulated_prior \u003d np.array([pick_theta() for _ in range(n_samples)])\nax1.hist(simulated_prior,bins\u003d100,label\u003d\u0027simulated prior\u0027,density\u003dTrue)\nax2.set_ylim([0,ax2.get_ylim()[1]])\nax1.set_xlim([thetas.min(),thetas.max()])\nfig.legend();plt.show()\n\ndef prob_y_given_theta(ys,t):\n    probs \u003d scipy.stats.poisson.pmf(ys,mu\u003dt)\n    totprob \u003d probs.prod()\n    return totprob\n\nconditional_data_prob \u003d np.array([prob_y_given_theta(y_obs,t) for t in thetas])\nunnormalized_posterior \u003d conditional_data_prob * prior_pdf\nposterior_pdf \u003d unnormalized_posterior / integrate.trapz(unnormalized_posterior,thetas)\nplt.plot(thetas,posterior_pdf) \nplt.gca().set_xlim([thetas.min(),thetas.max()])\nplt.show()\n\n\nposterior_cdf \u003d np.append(0,integrate.cumtrapz(posterior_pdf,thetas))\npick_theta_post \u003d lambda : np.interp(np.random.random(),posterior_cdf,thetas)\nsimulated_posterior\u003d np.array([pick_theta_post() for _ in range(n_samples)])\n\npick_y_given_theta \u003d lambda t: scipy.stats.poisson.rvs(mu\u003dt)\nsimulated_y_rate \u003d np.array([pick_y_given_theta(t) for t in simulated_posterior])\nplt.figure()\nplt.hist(simulated_y_rate,bins\u003d20,density\u003dTrue)\nplt.gca().set_xlim([thetas.min(),thetas.max()])\nplt.title(\"Simulated outcome rates\")\nplt.show()\n\nperc1 \u003d np.percentile(simulated_y_rate,2.5)\nperc2 \u003d np.percentile(simulated_y_rate,97.5)\nprint(f\"the 95 percent interval for death rate (in deaths per 100 million flyer miles) is [{perc1/100},{perc2/100}]\")\n\nsimulated_y \u003d (simulated_y_rate / 100) * (8e11 / 1e8)\nlib.plot_histogram_with_95p(simulated_y,legend\u003d\"Simulated accidents\",color\u003d\u0027blue\u0027)\nplt.legend()\nplt.show()\n\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%%\n",
          "is_executing": false
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": "# E\n(e) In which of the cases (a)–(d) above does the Poisson model seem more or less reasonable?\nWhy? Discuss based on general principles, without specific reference to the\nnumbers in Table 2.2.\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% md\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "source": "\nprint(\u0027It makes sense to use a poisson model when the rate is constant. it could be constant per mile, but not per year.\u0027)\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% \n"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": "\nIncidentally, in 1986, there were 22 fatal accidents, 546 passenger deaths, and a death\nrate of 0.06 per 100 million miles flown. We return to this example in Exercises 3.12,\n6.2, 6.3, and 8.14.\n",
      "metadata": {
        "pycharm": {
          "metadata": false,
          "name": "#%% md\n"
        }
      }
    },
    {
      "cell_type": "code",
      "execution_count": 303,
      "outputs": [
        {
          "name": "stdout",
          "text": [
            "The error in death rate is beacuse it is a low number 1986 compared to the mean. Just at the edge of my prediction interval\nThe prediction interval in deaths is just bad. My estimates are underdispersed, following from fewer passenger miles in the 70s.\n"
          ],
          "output_type": "stream"
        }
      ],
      "source": "\nprint(\u0027The error in death rate is beacuse it is a low number 1986 compared to the mean. Just at the edge of my prediction interval\u0027)\nprint(\u0027The prediction interval in deaths is just bad. My estimates are underdispersed, following from fewer passenger miles in the 70s.\u0027)\n\n",
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