{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c1b1b572-0a13-48f7-a6df-6c6e93a2f712",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Binomial Efficiency: 0.0000  +/- 0.0000\n",
      " Poisson Efficiency: 0.0000  +/- 0.0000\n",
      "Bayesian Efficiency: 0.0000  + 0.0092 - -0.0009\n",
      " Anterior: Mean=0.5000  Var=0.0833\n",
      "Posterior: Mean=0.0050  Var=0.0000  Mode=0.0000\n",
      "Bayesian 68.0% confidence interval for efficiency: [0.0009, 0.0092]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def bayesian_efficiency_confidence_interval(k, n, alpha_prior=1, beta_prior=1, confidence_level=0.95):\n",
    "    \"\"\"\n",
    "    Compute the Bayesian confidence interval for efficiency.\n",
    "    \n",
    "    Parameters:\n",
    "    k (int): Number of successes.\n",
    "    n (int): Number of trials.\n",
    "    alpha_prior (float): Alpha parameter of the Beta prior distribution.\n",
    "    beta_prior (float): Beta parameter of the Beta prior distribution.\n",
    "    confidence_level (float): Desired confidence level (e.g., 0.95 for 95%).\n",
    "    \n",
    "    Returns:\n",
    "    (float, float): Lower and upper bounds of the confidence interval.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Posterior parameters\n",
    "    alpha_post = alpha_prior + k\n",
    "    beta_post = beta_prior + (n - k)\n",
    "    \n",
    "    # Compute the confidence interval\n",
    "    lower_bound = stats.beta.ppf((1 - confidence_level) / 2, alpha_post, beta_post)\n",
    "    upper_bound = stats.beta.ppf(1 - (1 - confidence_level) / 2, alpha_post, beta_post)\n",
    "    \n",
    "    return lower_bound, upper_bound\n",
    "\n",
    "########\n",
    "# Data\n",
    "########\n",
    "k =0 # number of successes\n",
    "n = 197  # number of trials\n",
    "alpha_prior = 1.0\n",
    "beta_prior = 1.0\n",
    "confidence_level = 0.68  # % confidence level\n",
    "x = np.linspace(0, 1, 1000)\n",
    "\n",
    "\n",
    "##########\n",
    "# Binomial \n",
    "##########\n",
    "eff_bin = k/n\n",
    "err_bin = (1/n)*np.sqrt(k*(1-k/n))\n",
    "\n",
    "print(f\"Binomial Efficiency: {eff_bin:.4f}  +/- {err_bin:.4f}\")\n",
    "\n",
    "##########\n",
    "# Poisson \n",
    "##########\n",
    "eff_poi = k/n\n",
    "err_poi = np.sqrt(k/n**2+k**2/n**3)\n",
    "\n",
    "print(f\" Poisson Efficiency: {eff_poi:.4f}  +/- {err_poi:.4f}\")\n",
    "\n",
    "\n",
    "###########\n",
    "# Bayesian\n",
    "###########\n",
    "# Anterior distribution\n",
    "anterior_pdf = stats.beta.pdf(x, alpha_prior, beta_prior)\n",
    "mean_prior = stats.beta.mean(alpha_prior, beta_prior)\n",
    "var_prior = stats.beta.var(alpha_prior, beta_prior)\n",
    "\n",
    "# Posterior distribution\n",
    "alpha_post = k + alpha_prior\n",
    "beta_post = n - k + beta_prior\n",
    "posterior_pdf = stats.beta.pdf(x, alpha_post, beta_post)\n",
    "mean_post = stats.beta.mean(alpha_post, beta_post)\n",
    "var_post = stats.beta.var(alpha_post, beta_post)\n",
    "mode_post = (alpha_post - 1) / (alpha_post + beta_post - 2)\n",
    "\n",
    "# Confidence interval\n",
    "lower, upper = bayesian_efficiency_confidence_interval(k, n, alpha_prior=alpha_prior, beta_prior=beta_prior, confidence_level=confidence_level)\n",
    "\n",
    "print(f\"Bayesian Efficiency: {mode_post:.4f}  + {upper-mode_post:.4f} - {mode_post-lower:.4f}\")\n",
    "print(f\" Anterior: Mean={mean_prior:.4f}  Var={var_prior:.4f}\")\n",
    "print(f\"Posterior: Mean={mean_post:.4f}  Var={var_post:.4f}  Mode={mode_post:.4f}\")\n",
    "print(f\"Bayesian {confidence_level*100}% confidence interval for efficiency: [{lower:.4f}, {upper:.4f}]\")\n",
    "\n",
    "# Create a figure and a set of subplots (1 row, 2 columns)\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))\n",
    "# plt.figure(figsize=(8, 5))\n",
    "\n",
    "#Anterior\n",
    "ax1.plot(x, anterior_pdf, label=f'Beta({alpha_prior},{beta_prior}) Anterior') \n",
    "ax1.set_title('Anterior Distribution')\n",
    "if (alpha_prior == 1) and (beta_prior ==1):\n",
    "    ax1.set_ylim(0.0, 1.1*max(anterior_pdf))  # Set y-axis limits from -0.5 to 0.5\n",
    "ax1.set_xlabel('Efficiency')\n",
    "ax1.set_ylabel('Density')\n",
    "#ax1.legend()\n",
    "\n",
    "# Posterior\n",
    "ax2.plot(x, posterior_pdf, label=f'Beta({alpha_post},{beta_post}) Posterior')\n",
    "ax2.fill_between(x, posterior_pdf, where=(x > lower) & (x < upper), color='skyblue', alpha=0.4, label='95% CI')\n",
    "ax2.axvline(lower, color='red', linestyle='--', label=f'Lower bound: {lower:.4f}')\n",
    "ax2.axvline(upper, color='green', linestyle='--', label=f'Upper bound: {upper:.4f}')\n",
    "ax2.set_title('Posterior Distribution with 95% Confidence Interval')\n",
    "ax2.set_xlabel('Efficiency')\n",
    "ax2.set_ylabel('Density')\n",
    "ax2.legend()\n",
    "\n",
    "#plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "30929c37-ff38-4147-9843-933213b29f41",
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "69d2dc74-2618-4004-b217-c8c1a594298c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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