From d335ee76ada76d47c4aee30b07f736a4ef3e28df Mon Sep 17 00:00:00 2001 From: snoopy0328 Date: Sat, 22 Mar 2025 14:57:50 -0400 Subject: [PATCH] num4 --- HW03/hw3.ipynb | 174 +++++++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 168 insertions(+), 6 deletions(-) diff --git a/HW03/hw3.ipynb b/HW03/hw3.ipynb index e907674..d6b16bd 100644 --- a/HW03/hw3.ipynb +++ b/HW03/hw3.ipynb @@ -1,5 +1,168 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem 1\n", + "- 2 False: The variance of a Wiener process with scale coefficient sigma = 1 and time t is t2\n", + "- 3 False: \n", + "- 4 False: \n", + "- 5 False: \n", + "- 6 False: \n", + "- 8 False: " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem 3\n", + "Show that the following identity holds for any given prior and posterior:\n", + " Var [θ] = E[Var [θ |y]] + Var [E[θ |y]] \n", + "\n", + "Clarification of terms:\n", + "1. Var [θ] – Prior variance.\n", + "2. E[Var [θ |y]] – Expected posterior variance.\n", + "3. Var [E[θ |y]] – Variance of posterior mean" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem 4\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import norm\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from scipy.stats import norm\n", + "import pandas as pd\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Sample Mean (ybar): 4.84 hours\n", + "Posterior Mean (µ_n): 4.85\n", + "Posterior Standard Deviation (σ_n): 0.15\n" + ] + } + ], + "source": [ + "np.random.seed(42)\n", + "n = 100 #sample size\n", + "mu_true = 5 #avg sleep time\n", + "sigma = 1.5 #standard deviation\n", + "data = np.random.normal(mu_true, sigma, n)\n", + "ybar = np.mean(data) \n", + "print(f\"Sample Mean (ybar): {ybar:.2f} hours\")\n", + "\n", + "# Prior parameters (initial belief about sleep time)\n", + "mu0 = 5 \n", + "sigma0 = 1.0\n", + "\n", + "# Posterior parameters\n", + "sigma_n = np.sqrt(1 / (1 / sigma0**2 + n / sigma**2))\n", + "mu_n = (mu0 / sigma0**2 + n * ybar / sigma**2) / (1 / sigma0**2 + n / sigma**2)\n", + "\n", + "print(f\"Posterior Mean (µ_n): {mu_n:.2f}\")\n", + "print(f\"Posterior Standard Deviation (σ_n): {sigma_n:.2f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Define x-axis range\n", + "x = np.linspace(3, 8, 1000)\n", + "\n", + "# Prior distribution\n", + "prior = norm.pdf(x, mu0, sigma0)\n", + "\n", + "# Likelihood distribution (centered at sample mean)\n", + "likelihood = norm.pdf(x, ybar, sigma / np.sqrt(n))\n", + "\n", + "# Posterior distribution\n", + "posterior = norm.pdf(x, mu_n, sigma_n)\n", + "\n", + "# Plot\n", + "plt.figure(figsize=(10, 6))\n", + "plt.plot(x, prior, label=\"Prior\", linestyle=\"--\")\n", + "plt.plot(x, likelihood, label=\"Likelihood\", linestyle=\"-.\")\n", + "plt.plot(x, posterior, label=\"Posterior\", linestyle=\"-\")\n", + "plt.title(\"College Students Sleep Hours\")\n", + "plt.xlabel(\"Sleep Time (hours)\")\n", + "plt.ylabel(\"Density\")\n", + "plt.legend()\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Prior Data (Sample Mean) Posterior\n", + "0 Precision 1.0 33.333 34.333\n", + "1 SD 1.0 0.173 0.171\n", + "2 Mean 100.0 97.450 97.524\n" + ] + } + ], + "source": [ + "# Create a DataFrame\n", + "df = pd.DataFrame({\n", + " \"\": [\"Precision\", \"SD\", \"Mean\"],\n", + " \"Prior\": [1 / sigma0**2, sigma0, mu0],\n", + " \"Data (Sample Mean)\": [n / sigma**2, sigma / np.sqrt(n), ybar],\n", + " \"Posterior\": [1 / sigma_n**2, sigma_n, mu_n]\n", + "})\n", + "\n", + "# Display the DataFrame\n", + "print(df.round(3))" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -9,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -18,13 +181,13 @@ "" ] }, - "execution_count": 2, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -41,6 +204,7 @@ "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "\n", + "\n", "nest_asyncio.apply() # Allow nested event loops for Jupyter notebooks\n", "# Simulate data\n", "N = 100\n", @@ -55,7 +219,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, "outputs": [ { @@ -128,8 +292,6 @@ } ], "source": [ - "\n", - "\n", "stan_code = \"\"\"\n", "data {\n", " int N; // Number of observations\n",