6b_cov_CI_tests_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Empirical verification of derived quantities - covariance tests\n",
    "\n",
    "This notebook contains part of the experiments described in Section 6 of the paper \"What is the value of experimentation and measurement?\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "import os\n",
    "from rulu.covariance_CI_test import *\n",
    "from rulu.utils import find_all_tests_in_same_category\n",
    "from matplotlib import pyplot as plt\n",
    "# from scipy.stats import percentileofscore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov_Yr_Ys_tests = find_all_tests_in_same_category(\n",
    "    CovYrYsCITest(sigma_sq_1=0.5**2), \n",
    "    in_dir=\"./output/cov_CI_tests/\")\n",
    "cov_Yr_Ys_second_order_tests = find_all_tests_in_same_category(\n",
    "    CovYrYsSecondOrderCITest(sigma_sq_1=0.5**2), \n",
    "    in_dir=\"./output/cov_CI_tests/\")\n",
    "cov_Yr_Zs_tests = find_all_tests_in_same_category(\n",
    "    CovYrZsCITest(), in_dir=\"./output/cov_CI_tests/\")\n",
    "cov_Yr_Zs_second_order_tests = find_all_tests_in_same_category(\n",
    "    CovYrZsSecondOrderCITest(), in_dir=\"./output/cov_CI_tests/\")\n",
    "cov_XIr_XJs_tests = find_all_tests_in_same_category(\n",
    "    CovXIrXJsCITest(), in_dir=\"./output/cov_CI_tests/\")\n",
    "cov_XIr_XJs_second_order_tests = find_all_tests_in_same_category(\n",
    "    CovXIrXJsSecondOrderCITest(), in_dir=\"./output/cov_CI_tests/\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cov(Y_(r), Y_(s)): 4688/4940 (94.9%) of the tests have the theoretical quantity within the CI.\n",
      "Cov(Y_(r), Y_(s)) - 2nd order: 4940/4940 (100.0%) of the tests have the theoretical quantity within the CI.\n",
      "Cov(Y_(r), Z_(s)): 4663/4940 (94.39%) of the tests have the theoretical quantity within the CI.\n",
      "Cov(Y_(r), Z_(s)) - 2nd order: 4739/4940 (95.93%) of the tests have the theoretical quantity within the CI.\n",
      "Cov(X_I(r), X_J(s)): 4730/4940 (95.75%) of the tests have the theoretical quantity within the CI.\n",
      "Cov(X_I(r), X_J(s)) - 2nd order: 4783/4940 (96.82%) of the tests have the theoretical quantity within the CI.\n"
     ]
    }
   ],
   "source": [
    "for test_collection in [cov_Yr_Ys_tests, cov_Yr_Ys_second_order_tests,\n",
    "                        cov_Yr_Zs_tests, cov_Yr_Zs_second_order_tests, \n",
    "                        cov_XIr_XJs_tests, cov_XIr_XJs_second_order_tests]:\n",
    "    print_test_collection_result(test_collection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_collection = cov_Yr_Ys_tests\n",
    "\n",
    "theoretical_quantity_percentiles = [\n",
    "    test.theoretical_quantity_sample_percentile()\n",
    "    for test in test_collection]\n",
    "\n",
    "plt.hist(theoretical_quantity_percentiles, bins=range(0, 105, 5))\n",
    "plt.xlim(0, 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_collection = cov_Yr_Zs_tests\n",
    "\n",
    "theoretical_quantity_percentiles = [\n",
    "    test.theoretical_quantity_sample_percentile()\n",
    "    for test in test_collection]\n",
    "\n",
    "plt.hist(theoretical_quantity_percentiles, bins=range(0, 102, 2))\n",
    "plt.xlim(0, 100)\n",
    "plt.ylim(0, 400)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_collection = cov_Yr_Zs_second_order_tests\n",
    "\n",
    "theoretical_quantity_percentiles = [\n",
    "    test.theoretical_quantity_sample_percentile()\n",
    "    for test in test_collection]\n",
    "\n",
    "plt.hist(theoretical_quantity_percentiles, bins=range(0, 102, 2))\n",
    "plt.xlim(0, 100)\n",
    "plt.ylim(0, 400)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_collection = cov_XIr_XJs_tests\n",
    "\n",
    "theoretical_quantity_percentiles = [\n",
    "    test.theoretical_quantity_sample_percentile()\n",
    "    for test in test_collection]\n",
    "\n",
    "plt.hist(theoretical_quantity_percentiles, bins=range(0, 102, 2))\n",
    "plt.xlim(0, 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_collection = cov_XIr_XJs_second_order_tests\n",
    "\n",
    "theoretical_quantity_percentiles = [\n",
    "    test.theoretical_quantity_sample_percentile()\n",
    "    for test in test_collection]\n",
    "\n",
    "plt.hist(theoretical_quantity_percentiles, bins=range(0, 102, 2))\n",
    "plt.xlim(0, 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "for test in cov_XIr_XJs_tests:\n",
    "    if test.theoretical_quantity_above_sample_CI():\n",
    "        print(test.N, test.r, test.s,  \"    \\t\",\n",
    "              np.round(test.sigma_sq_X, 3), \n",
    "              np.round(test.sigma_sq_1, 3), np.round(test.sigma_sq_2, 3), \"\\t\",\n",
    "              np.round(test.theoretical_quantity(), 3),\n",
    "              np.round(test.sample_CI(), 3), \"\\t\",\n",
    "              np.round(test.theoretical_quantity() / test.sample_CI(), 4)\n",
    "             )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}