365 lines
101 KiB
Plaintext
365 lines
101 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "471768dc",
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"metadata": {},
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"source": [
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"## Import Required Libraries"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "9f71be99",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy.special import comb"
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]
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},
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{
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"cell_type": "markdown",
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"id": "6256adf9",
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"metadata": {},
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"source": [
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"# Exercise 1: Binomial Distribution MLE\n",
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"\n",
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"## Problem Statement\n",
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"\n",
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"Consider the binomial distribution of the number $k$ of successes in $n$ independent trials:\n",
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"\n",
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"$$\\sum_{i=1}^{n} X_i \\sim \\text{Binomial}(n, p)$$\n",
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"\n",
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"The log-likelihood function is:\n",
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"\n",
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"$$\\log L(p) = \\log \\binom{n}{k} + k \\log(p) + (n-k) \\log(1-p)$$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4fd73405",
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"metadata": {},
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"source": [
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"## Part 1: Plot the Log-Likelihood Function\n",
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"\n",
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"**Given:** $n = 100$, $k = 10$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"id": "619eb285",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Parameters\n",
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"n = 100\n",
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"k = 10"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 23,
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"id": "f6ab6a08",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"MLE of p: 0.15\n"
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]
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}
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],
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"source": [
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"# Create a sequence of p values\n",
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"p_values = np.linspace(0.01, 0.99, 100)\n",
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"\n",
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"# Define the log-likelihood function\n",
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"def log_likelihood(p, n, k):\n",
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" return np.log(comb(n, k)) + k * np.log(p) + (n - k) * np.log(1 - p)\n",
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"\n",
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"# Calculate log-likelihood for each p\n",
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"log_lik_values = [log_likelihood(p, n, k) for p in p_values]\n",
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"\n",
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"# Update parameters for MLE calculation\n",
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"k = 15\n",
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"n = 100\n",
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"\n",
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"# Calculate MLE\n",
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"p_MLE = k / n\n",
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"print(f\"MLE of p: {p_MLE}\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 24,
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"id": "202b759a",
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"metadata": {},
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"outputs": [
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{
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"data": {
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",
|
|
"text/plain": [
|
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"<Figure size 1000x600 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Plot the log-likelihood function\n",
|
|
"plt.figure(figsize=(10, 6))\n",
|
|
"plt.plot(p_values, log_lik_values, 'b-', linewidth=2)\n",
|
|
"plt.xlabel('p', fontsize=12)\n",
|
|
"plt.ylabel('Log-Likelihood', fontsize=12)\n",
|
|
"plt.title('Log-Likelihood Function for Binomial(100, p) with k=10', fontsize=14)\n",
|
|
"plt.grid(True, alpha=0.3)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"id": "341b9966",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"==================================================\n",
|
|
"Summary of Results\n",
|
|
"==================================================\n",
|
|
"Sample size (n): 100\n",
|
|
"Observed successes (k): 15\n",
|
|
"MLE of p: 0.15\n",
|
|
"Comparison p: 0.10\n",
|
|
"\n",
|
|
"Log-likelihood at p = 0.15: -2.1974\n",
|
|
"Log-likelihood at p = 0.10: -3.4209\n",
|
|
"==================================================\n",
|
|
"\n",
|
|
"The MLE p̂ = 0.15 maximizes the log-likelihood function\n",
|
|
"This is simply the sample proportion of successes\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Summary results\n",
|
|
"print(\"=\" * 50)\n",
|
|
"print(\"Summary of Results\")\n",
|
|
"print(\"=\" * 50)\n",
|
|
"print(f\"Sample size (n): {n}\")\n",
|
|
"print(f\"Observed successes (k): {k}\")\n",
|
|
"print(f\"MLE of p: {p_MLE}\")\n",
|
|
"print(f\"Comparison p: 0.10\")\n",
|
|
"print(f\"\\nLog-likelihood at p = {p_MLE}: {log_likelihood(p_MLE, n, k):.4f}\")\n",
|
|
"print(f\"Log-likelihood at p = 0.10: {log_likelihood(0.10, n, k):.4f}\")\n",
|
|
"print(\"=\" * 50)\n",
|
|
"print(f\"\\nThe MLE p̂ = {p_MLE} maximizes the log-likelihood function\")\n",
|
|
"print(\"This is simply the sample proportion of successes\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "87447f70",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Summary of Results\n",
|
|
"\n",
|
|
"Let's create a summary table of our findings:"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"id": "6e27150b",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 1200x700 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Recalculate log-likelihood values with updated k\n",
|
|
"p_values = np.linspace(0.01, 0.99, 100)\n",
|
|
"log_lik_values = [log_likelihood(p, n, k) for p in p_values]\n",
|
|
"\n",
|
|
"# Create the plot\n",
|
|
"plt.figure(figsize=(12, 7))\n",
|
|
"plt.plot(p_values, log_lik_values, 'b-', linewidth=2, label='Log-Likelihood')\n",
|
|
"\n",
|
|
"# Add vertical lines for p = 0.10 and p = p_MLE\n",
|
|
"plt.axvline(x=0.10, color='red', linewidth=2, linestyle='--', label='p = 0.10')\n",
|
|
"plt.axvline(x=p_MLE, color='green', linewidth=2, linestyle='--', label=f'p = {p_MLE} (MLE)')\n",
|
|
"\n",
|
|
"# Add points at specific p values\n",
|
|
"plt.plot(0.10, log_likelihood(0.10, n, k), 'ro', markersize=10)\n",
|
|
"plt.plot(p_MLE, log_likelihood(p_MLE, n, k), 'go', markersize=10)\n",
|
|
"\n",
|
|
"# Labels and formatting\n",
|
|
"plt.xlabel('p', fontsize=12)\n",
|
|
"plt.ylabel('Log-Likelihood', fontsize=12)\n",
|
|
"plt.title('Log-Likelihood with Binomial Distributions', fontsize=14)\n",
|
|
"plt.legend(loc='upper right', fontsize=10)\n",
|
|
"plt.grid(True, alpha=0.3)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "64e200dc",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Part 3: Compare Log-Likelihood at Different p Values\n",
|
|
"\n",
|
|
"Let's visualize the log-likelihood function with the MLE and compare it to $p = 0.10$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"id": "9b6ae903",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"MLE of p: 0.15\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Update parameters for MLE calculation\n",
|
|
"k = 15\n",
|
|
"n = 100\n",
|
|
"\n",
|
|
"# Calculate MLE\n",
|
|
"p_MLE = k / n\n",
|
|
"print(f\"MLE of p: {p_MLE}\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "880ba7a0",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Part 2: Compute the MLE\n",
|
|
"\n",
|
|
"**Given:** $\\sum_{i=1}^{n} x_i = 15$ with $n = 100$ trials\n",
|
|
"\n",
|
|
"### Finding the MLE\n",
|
|
"\n",
|
|
"To find the maximum likelihood estimator, we take the derivative of the log-likelihood with respect to $p$ and set it equal to zero:\n",
|
|
"\n",
|
|
"$$\\frac{d}{dp} \\log L(p) = \\frac{k}{p} - \\frac{n-k}{1-p} = 0$$\n",
|
|
"\n",
|
|
"Solving for $p$:\n",
|
|
"\n",
|
|
"$$\\frac{k}{p} = \\frac{n-k}{1-p}$$\n",
|
|
"\n",
|
|
"$$k(1-p) = p(n-k)$$\n",
|
|
"\n",
|
|
"$$k - kp = pn - pk$$\n",
|
|
"\n",
|
|
"$$k = pn$$\n",
|
|
"\n",
|
|
"$$\\hat{p}_{MLE} = \\frac{k}{n}$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"id": "50234cc2",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Create a sequence of p values\n",
|
|
"p_values = np.linspace(0.01, 0.99, 100)\n",
|
|
"\n",
|
|
"# Calculate log-likelihood for each p\n",
|
|
"log_lik_values = [log_likelihood(p, n, k) for p in p_values]"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"id": "49c125fc",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Define the log-likelihood function\n",
|
|
"def log_likelihood(p, n, k):\n",
|
|
" return np.log(comb(n, k)) + k * np.log(p) + (n - k) * np.log(1 - p)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 30,
|
|
"id": "79e4c1ce",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# Define the log-likelihood function\n",
|
|
"def log_likelihood(p, n, k):\n",
|
|
" return np.log(comb(n, k)) + k * np.log(p) + (n - k) * np.log(1 - p)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"id": "01412dff",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
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"MLE of p: 0.15\n",
|
|
"Log-likelihood at p = 0.15: -2.1974\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(f\"MLE of p: {p_MLE}\")\n",
|
|
"\n",
|
|
"print(f\"Log-likelihood at p = {p_MLE}: {log_likelihood(p_MLE, n, k):.4f}\")"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": ".venv",
|
|
"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": "3.13.7"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|