{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confidence intervals\n",
    "\n",
    "In this notebook, we look at the confidence interval methods in `resample`. We try them on the median of an exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false,
     "source_hidden": false
    },
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from resample.bootstrap import confidence_interval as ci, bootstrap\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false,
     "source_hidden": false
    },
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(1)\n",
    "\n",
    "# generate data\n",
    "data = rng.exponential(size=1000)\n",
    "\n",
    "# generate confidence intervals\n",
    "cis = {\n",
    "    m: ci(np.median, data, cl=0.68, size=100, ci_method=m, random_state=rng)\n",
    "    for m in (\"percentile\", \"bca\")\n",
    "}\n",
    "\n",
    "# compute mean and std. deviation of replicates\n",
    "rep = bootstrap(np.median, data, size=1000, random_state=rng)\n",
    "mr = np.mean(rep)\n",
    "sr = np.std(rep)\n",
    "\n",
    "# draw everything\n",
    "for i, (m, v) in enumerate(cis.items()):\n",
    "    for j in (0, 1):\n",
    "        plt.axvline(v[j], color=f\"C{i}\", label=m if j == 0 else None)\n",
    "\n",
    "plt.hist(rep, facecolor=\"0.8\")\n",
    "plt.axvline(np.log(2), lw=3, color=\"k\")\n",
    "plt.errorbar(mr, 100, 0, sr, fmt=\"o\") \n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of the replicates and its standard deviation is shown with the dot and the horizontal error bar. The three interval methods are shown as thin vertical lines. The thick black line is the true value of the median for an exponential distribution."
   ]
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "python3"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.9"
  },
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