{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bac76a34-05b0-4084-b6d2-e87fac6fcc00",
   "metadata": {},
   "source": [
    "# Frequentist vs Bayesian Approach"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97e2c7f8-2529-4809-875f-ddadf4320ee0",
   "metadata": {},
   "source": [
    "## How did JWST data change our understanding\n",
    "\n",
    "Before JWST, the Hubble Space Telescope (HST) measured the ultraviolet luminosity function (UV LF), from which astrophysicists inferred that early star formation dropped off steeply. However, early JWST deep-field data revealed an unexpectedly high number of bright, massive galaxies at high redshift, challenging previous standard models.\n",
    "\n",
    "Let $\\epsilon$ represent the Star Formation Efficiency (the fraction of available gas converted into stars) in high-redshift $z \\sim 10$ galaxies. Historically, models suggested early galaxies were highly inefficient *$\\epsilon \\sim 0.1$*. JWST observations analyzed a targeted cosmic volume and found **16 highly luminous galaxies out of 20 surveyed candidates** \n",
    "\n",
    "How does this change our understanding? Compare Frequentist vs Bayesian approaches, and give interpretation accordingly"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d6f014b-48a3-42e2-9d31-5cd4f75f3de3",
   "metadata": {},
   "source": [
    "## Frequentist approach\n",
    "\n",
    "- Calculate the efficiency from JWST data\n",
    "- Compare with previous expectation ($H_0$)\n",
    "- Confidence with which we can rule out $H_0$\n",
    "\n",
    "This distribution is a binomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "66d15e01-135d-4dba-aa1e-791a91aa65a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b1944fb7-e665-47b1-b9c5-b229085d6670",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_obs = 20\n",
    "n_detect = 16\n",
    "\n",
    "frac_obs = 16/20\n",
    "frac_obs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5adf5509-e90a-4aea-8817-d0c51756d1ed",
   "metadata": {},
   "source": [
    "#### Compute error on `frac_obs`\n",
    "\n",
    "1. Analytically: $\\sqrt{(p(1-p)/n)}$ (Derive it! from the normal approximation of Binomial)\n",
    "2. From the likelihood profiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e1fd7d56-2b51-4272-8cfd-2efb60cc4a53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.08944271909999157)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# analytically - Wald Interval\n",
    "\n",
    "frac_err1 = np.sqrt(frac_obs*(1-frac_obs)/n_obs)\n",
    "frac_err1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7cda867-4c1f-4308-9e9d-cffa3261311e",
   "metadata": {},
   "source": [
    "The  upper bound of the analytically error is clearly overestimated - 3-sigma confidence interval will be > 100%!\n",
    "Thus, it is better to use the likelihood profile"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7607494-47e3-4445-bb1a-2e203b71c558",
   "metadata": {},
   "source": [
    "Numerically:\n",
    "\n",
    "To compute the 68% (or 95%) confidence interval directly from the likelihood profile (corresponding to a 1-sigma (or 2-sigma) error), we use the log-likelihood drop threshold dictated by the Chi-squared distribution for 1 degree of freedom:\n",
    "\n",
    "$\\Delta \\ln L=\\frac{1}{2}\\chi _{1}^{2}(p)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7d27287f-f6f9-415c-b128-1d264000015f",
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon_grid = np.linspace(0.1, 0.99, 1000)\n",
    "\n",
    "# 3. Calculate Log-Likelihood and find the peak\n",
    "log_likelihood = binom.logpmf(n_detect, n_obs, epsilon_grid)\n",
    "max_log_l = np.max(log_likelihood)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9b0ffc2e-247f-4558-91dc-1d3fa0f46ce2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_interval(perc):\n",
    "    \"\"\"\n",
    "    perc: what % confidence interval\n",
    "    \"\"\"\n",
    "    delL = 0.5*chi2.ppf(perc, 1)\n",
    "    valid_indices = np.where(log_likelihood >= (max_log_l - delL))\n",
    "    low = epsilon_grid[valid_indices[0][0]]\n",
    "    high = epsilon_grid[valid_indices[0][-1]]\n",
    "    return low, high"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0909a005-5091-445c-a74d-7e8d14300c9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.7022422422422422), np.float64(0.8777477477477477))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 68% interval\n",
    "find_interval(0.68)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7d4935e0-e634-4afe-b3fe-af9f397710f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.5953353353353353), np.float64(0.932982982982983))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 95% interval\n",
    "find_interval(0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2ab04c9e-5503-46f5-8a3b-0db51d3b49e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.37528528528528526), np.float64(0.9864364364364364))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 99.99% interval\n",
    "find_interval(0.9999)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "eaf247bf-6610-4314-a29e-b8f060bdbe77",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLE 95%% (2-sigma) Analysis:\n",
      "  Maximum Likelihood Estimate (MLE): 0.800\n",
      "  95% Confidence Interval Bounds:  0.595, 0.933\n",
      "  Asymmetric Error Bar:   0.205, 0.133\n"
     ]
    }
   ],
   "source": [
    "print(\"MLE 95%% (2-sigma) Analysis:\")\n",
    "print(f\"  Maximum Likelihood Estimate (MLE): {frac_obs:.3f}\")\n",
    "print(f\"  95% Confidence Interval Bounds:  {find_interval(0.95)[0]:.3f}, {find_interval(0.95)[1]:.3f}\")  \n",
    "print(f\"  Asymmetric Error Bar:   {frac_obs - find_interval(0.95)[0]:.3f}, {find_interval(0.95)[1]-frac_obs:.3f}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a6439bbe-2824-456b-a69f-6d732f9d0b8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "norm_likelihood = np.exp(log_likelihood - max_log_l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c980010d-c74c-40db-8861-b375d62a53df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"JWST Likelihood Profile\")\n",
    "plt.xlabel(\"Star Formation Efficiency (epsilon)\", fontsize=11)\n",
    "plt.ylabel(\"Normalized Relative Likelihood\", fontsize=11)\n",
    "\n",
    "plt.plot(epsilon_grid, norm_likelihood, color='blue', linewidth=2.5)\n",
    "\n",
    "plt.axvline(x=frac_obs, color='red', linestyle=':', linewidth=1.5, label=f'MLE Peak ({frac_obs:.2f})')\n",
    "plt.xlim(0.01, 1.0)\n",
    "\n",
    "plt.axvspan(find_interval(0.68)[0], find_interval(0.68)[1], alpha=0.30, color='skyblue', label='68% Interval')\n",
    "plt.axvspan(find_interval(0.95)[0], find_interval(0.95)[1], alpha=0.15, color='teal', label='95%% Interval')\n",
    "\n",
    "plt.axvline(x=0.1, color='red', label=\"Expected\")\n",
    "\n",
    "plt.legend()\n",
    "plt.grid(True, linestyle=':', alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b2075ed2-ec8a-4757-871c-2d897042a415",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hypothesis Testing against legacy HST model (H0: epsilon = 10%):\n",
      "  Calculated p-value: 3.262945E-13\n",
      "Result: Reject H0. The JWST observation is statistically incompatible with the HST model at 53.0-sigma\n",
      "-----------------\n"
     ]
    }
   ],
   "source": [
    "# Hypothesis Testing\n",
    "# Null Hypothesis (H0): Early efficiency matches HST predictions (epsilon = 10% or 0.10)\n",
    "null_epsilon = 0.1\n",
    "p_value = 1 - binom.cdf(n_detect - 1, n_obs, null_epsilon)\n",
    "print(f\"Hypothesis Testing against legacy HST model (H0: epsilon = 10%):\")\n",
    "print(f\"  Calculated p-value: {p_value:.6E}\")\n",
    "sigma= chi2.isf(p_value, 1)\n",
    "\n",
    "print(f\"Result: Reject H0. The JWST observation is statistically incompatible with the HST model at {sigma:.1f}-sigma\")\n",
    "print(\"-----------------\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1888d170-35d5-43ad-b545-0a5011dea190",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "902c06d0-cd31-432b-a1d6-b3908cdc5c00",
   "metadata": {},
   "source": [
    "## Bayesian outlook\n",
    "\n",
    "Construct two different priors:\n",
    "\n",
    "1. Agnostic - Uniform prior\n",
    "2. HST inferred - two priors\n",
    "\n",
    "We will take a beta distribution as a prior\n",
    "To match HST, we need $\\mu = \\alpha/(\\alpha + \\beta) \\sim 0.1$\n",
    "\n",
    "Lets take $\\alpha = 2, \\beta=18$ \n",
    "\n",
    "Advantages of beta distribution:\n",
    "\n",
    "- Defined between 0 and 1\n",
    "- conjugate prior to a Binomial distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aeefe0c1-ff82-4f47-8209-b0969be6d9ce",
   "metadata": {},
   "source": [
    "Lets plot the two beta distributions taken. We know the mean and mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "033af304-e591-4d58-8789-00b3a920c507",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x720e7ff3a570>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 1, 1000)\n",
    "p1 = beta.pdf(x, 1, 1)\n",
    "p2 = beta.pdf(x, 2, 18)\n",
    "plt.plot(x, p1, label=\"Agnostic\")\n",
    "plt.plot(x, p2, label=\"HST\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67572a71-9ee7-4fe6-be3e-3469cc876ab3",
   "metadata": {},
   "source": [
    "$\\beta(1,1)$ = Uniform distribution!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "d9854493-2c16-42e2-9f96-ac9d5eb5abc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mode(a, b):\n",
    "    if a <=1:\n",
    "        return 0.5\n",
    "    return (a-1)/(a+b-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "6afeb2b4-646a-4967-8356-ac83968d7eb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mode(1,9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "60408ede-f16c-4f46-b336-f4f808d05ea0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mode(1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2c1140e3-a474-425a-8724-235c12ff2464",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HST1:\n",
      "  Prior Peak Efficiency: 5.6%\n",
      "  Posterior Peak Efficiency: 44.7%\n",
      "\n",
      "Agnostic:\n",
      "  Prior Peak Efficiency: 50.0%\n",
      "  Posterior Peak Efficiency: 80.0%\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:36: SyntaxWarning: invalid escape sequence '\\e'\n",
      "<>:36: SyntaxWarning: invalid escape sequence '\\e'\n",
      "/tmp/ipykernel_82935/2391991521.py:36: SyntaxWarning: invalid escape sequence '\\e'\n",
      "  plt.xlabel(\"Star Formation Efficiency ($\\epsilon$)\", fontsize=12)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "  \n",
    "n_nond = n_obs - n_detect\n",
    "\n",
    "# 2. Prior beliefs about Star Formation Efficiency (epsilon)\n",
    "priors = {\n",
    "    \"HST1\": (2, 18),\n",
    "    \"Agnostic\": (1, 1)\n",
    "}\n",
    "\n",
    "\n",
    "epsilon_grid = np.linspace(0, 1, 1000)\n",
    "\n",
    "\n",
    "# 4. Bayesian Update Loop\n",
    "for label, (alpha_p, beta_p) in priors.items():\n",
    "    # Conjugate updating rule: posterior parameters\n",
    "    alpha_post = alpha_p + n_detect #conjuagte!\n",
    "    beta_post = beta_p + n_nond\n",
    "    \n",
    "    # Calculate modes (peak probabilities)\n",
    "    prior_mode = mode(alpha_p, beta_p)\n",
    "    post_mode = mode(alpha_post, beta_post)\n",
    "    \n",
    "    print(f\"{label}:\")\n",
    "    print(f\"  Prior Peak Efficiency: {prior_mode*100:.1f}%\")\n",
    "    print(f\"  Posterior Peak Efficiency: {post_mode*100:.1f}%\\n\")\n",
    "    \n",
    "    # Generate Curves\n",
    "    prior_curve = beta.pdf(epsilon_grid, alpha_p, beta_p)\n",
    "    post_curve = beta.pdf(epsilon_grid, alpha_post, beta_post)\n",
    "    \n",
    "    # Plotting\n",
    "    line, = plt.plot(epsilon_grid, prior_curve, linestyle=\"--\", alpha=0.5, label=f\"{label} Prior\")\n",
    "    plt.plot(epsilon_grid, post_curve, color=line.get_color(), linewidth=2.5, label=f\"{label} Posterior\")\n",
    "\n",
    "# 5. Graph Annotations\n",
    "plt.xlabel(\"Star Formation Efficiency ($\\epsilon$)\", fontsize=12)\n",
    "plt.ylabel(\"Probability Density\", fontsize=12)\n",
    "plt.axvline(x=0.80, color=\"purple\", linestyle=\":\", label=\"JWST Sample Mean (16/20)\")\n",
    "plt.legend()\n",
    "plt.grid(True, alpha=0.2)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abbb8e5a-25d1-43f0-bcaa-1e53e6b72df1",
   "metadata": {},
   "source": [
    "Try playing around with different priors!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aed9f27e-93eb-4320-a1c9-928f3afb951e",
   "metadata": {},
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    "### Conclusion\n",
    "\n",
    "\n",
    "| Feature | Frequentist Interpretation | Bayesian Interpretation (Agnostic Prior) | Bayesian Interpretation (Conservative Prior) |\n",
    "| :--- | :--- | :--- | :--- |\n",
    "| **Point Estimate** | **MLE = 80.0%**. The exact observed ratio in the data sample. | **Posterior Mode = 80.0%**. Overlaps with frequentist output due to flat prior. | **Posterior Mode = 44.1%**. Dragged down by decades of legacy physics. |\n",
    "| **Interval Meaning** | **Confidence Interval (59% to 93%)**. If we repeat this survey infinitely, 95% of generated intervals will contain the true cosmic value. | **Credible Interval**. There is a 95% subjective probability that the true cosmic parameter sits within these boundary marks. | **Credible Interval**. Adjusted dynamically based on physical constraints. |\n",
    "| **Handling of Legacy Knowledge** | Ignores legacy data. Evaluates the new dataset strictly in isolation. | Considers flat assumption. All values initially held equal. | Mathematically enforces legacy bounds, requiring massive data pools to shift. |\n"
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