{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Use of conjugate priors\n",
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "std = 5  # MPa\n",
    "sample = [30.1, 28.7, 21.2, 28.6, 25.8, 25.1, 24.2, 27.3, 20.0, 34.8]  # MPa\n",
    "n = len(sample)\n",
    "\n",
    "prior_mu_mean = 40  # MPa\n",
    "prior_mu_std = 100  # MPa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the mean of the sample\n",
    "mean_sample = ...\n",
    "print(f\"Mean of the sample: {mean_sample:.2f} MPa\")\n",
    "\n",
    "# Posterior distribution with conjugate prior\n",
    "posterior_mu_mean = ...\n",
    "posterior_mu_std = ...\n",
    "print(f\"Posterior mean: {posterior_mu_mean:.2f} MPa\")\n",
    "print(f\"Posterior standard deviation: {posterior_mu_std:.2f} MPa\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate prior and posterior values for x using scipy\n",
    "x = np.linspace(0, 100, 1000)\n",
    "prior = ...\n",
    "posterior = ...\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, prior, label=\"Prior\")\n",
    "ax.plot(x, posterior, label=\"Posterior\")\n",
    "ax.set_xlim(0, 100)\n",
    "ax.set_ylim(0, 0.3)\n",
    "ax.set_xlabel(\"Mean (MPa)\")\n",
    "ax.set_ylabel(\"Density\")\n",
    "ax.set_title(\"Distribution of the Mean\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
 ],
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