CP6_Combined_PDFs_syst.&stat._errors_H-tests.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1603cd99",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Making the necessary imports\n",
    "import os\n",
    "import numpy as np\n",
    "from numpy import matrix\n",
    "import scipy.optimize as theMinimiser\n",
    "from iminuit import Minuit\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import scipy.integrate as integrate\n",
    "from iminuit.cost import UnbinnedNLL\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c10c3e0a",
   "metadata": {},
   "source": [
    "## Part 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cd1936d",
   "metadata": {},
   "source": [
    "### Plotting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "035c126e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load the masses\n",
    "mass_samples = np.loadtxt(\"datafile-higgs.txt\", dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "27aa8b7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(mass_samples, bins=100)\n",
    "plt.title(\"Mass distribution\")\n",
    "plt.xlabel(\"Mass\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ea43e21",
   "metadata": {},
   "source": [
    "### Maximum likelihood fit to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7f803602",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the normalised exponential PDF\n",
    "def Generate_exp_PDF(mass_samples,tau,mass_low,mass_high):\n",
    "    C = np.exp(-mass_low/tau)-np.exp(-mass_high/tau) # Calculate the normalisation constant\n",
    "    return (1/(tau*C))*np.exp(-mass_samples/tau) # Return the normalised exponential PDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "28e285ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the guassian PDF\n",
    "# No need to normalise the guassian PDF as the range of data on each side of the mean is many standard deviations away\n",
    "# and therefore the data range can be accurately approximated as infinite\n",
    "def Generate_gauss_PDF(mass_samples, mu):\n",
    "    return scipy.stats.norm.pdf(mass_samples,mu,sigma) # Return the normalised gaussian PDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ea39e21d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the combined PDF of the normalised exponential and normalised gaussian PDFs\n",
    "# This PDF is also normalised as the fraction it takes of the normalised gaussian and exponential PDFs adds up to 1\n",
    "def PDF_combined(mass_samples,tau,mu,F,mass_low,mass_high):\n",
    "    PDF1 = Generate_exp_PDF(mass_samples,tau,mass_low,mass_high)\n",
    "    PDF2 = Generate_gauss_PDF(mass_samples,mu)\n",
    "    \n",
    "    return (F * PDF1) + ((1-F) * PDF2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dbb17f97",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the negative of the log of the joint likelihood\n",
    "# This is the function we are trying to minimise with the minimiser, given different values of tau, mu and F\n",
    "def NLL(tau,mu,F):\n",
    "    P = PDF_combined(mass_samples,tau,mu,F,mass_low,mass_high)\n",
    "    return -np.sum(np.log(P))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "20930287",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = 0.2 # Using a fixed gaussian width of 0.2\n",
    "\n",
    "# Setting the range of our mass data for use in normalisation\n",
    "mass_low = 0 \n",
    "mass_high = 10\n",
    "\n",
    "# Set the minimisation parameters\n",
    "m = Minuit(NLL, tau=5, mu=2, F=0.98)\n",
    "m.limits[\"F\"] = (0.0,1.0) \n",
    "m.limits[\"tau\"] = (0.0,10.0) \n",
    "m.limits[\"mu\"] = (1.0,9.0) # Limits on mu set many standard deviations away from data boundaries to accurately\n",
    "                           # approximate infinite data range \n",
    "\n",
    "# Set the errors on the initial start values\n",
    "m.errors=[0.1,0.1,0.1]\n",
    "\n",
    "# Set the increase in NLL for the 1-SD error calculation\n",
    "m.errordef=0.5\n",
    "\n",
    "# Run the minimisation\n",
    "m = m.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "804e2e23",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau =   5.008  +/-  0.031\n",
      "\n",
      "\n",
      "mu =   2.499  +/-  0.015\n",
      "\n",
      "\n",
      "F  =   0.9796  +/-  0.0012\n"
     ]
    }
   ],
   "source": [
    "# Printing the final results and their error\n",
    "fstr = \"{0:2.2}\"\n",
    "val = m.values[\"tau\",\"mu\",\"F\"]\n",
    "err = m.errors[\"tau\",\"mu\",\"F\"]\n",
    "print(\"{:2s}\".format(\"tau\"), \"=  \", \"{0:2.3f}\".format(val[0]), \" +/- \", fstr.format(err[0]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"mu\"), \"=  \", \"{0:2.3f}\".format(val[1]), \" +/- \", fstr.format(err[1]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"F\"), \"=  \", \"{0:2.4f}\".format(val[2]), \" +/- \", fstr.format(err[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e250d435",
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_exp = m.values[\"mu\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bb9c2c7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plotting the fitted mass distribution\n",
    "x = np.linspace(mass_low, mass_high, 1000)\n",
    "y = PDF_combined(x, m.values[\"tau\"],m.values[\"mu\"],m.values[\"F\"], mass_low, mass_high)\n",
    "\n",
    "counts = plt.hist(mass_samples, bins = 100, color=\"orange\",density=True)\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Fitted Mass Distribution\")\n",
    "plt.xlabel(\"Mass\")\n",
    "plt.ylabel(\"Scaled counts\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd6865f9",
   "metadata": {},
   "source": [
    "## Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "26920774",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the normalised polynomial PDF\n",
    "def Generate_polynomial_PDF(mass_samples,b,c):\n",
    "    norm_const = ((c/3)*(mass_high**3)) + ((b/2)*(mass_high**2)) + (a*mass_high) # Calculate normalisation constant\n",
    "    return (1/norm_const)*(a + b*mass_samples + c*(mass_samples**2)) # Return the normalised polynomial PDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c0f4e38d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the combined PDF of the normalised polynomial and normalised gaussian PDFs\n",
    "# This PDF is also normalised as the fraction it takes of the normalised gaussian and polynomial PDFs adds up to 1\n",
    "def PDF_combined(mass_samples,b,c,mu,F):\n",
    "    PDF1 = Generate_polynomial_PDF(mass_samples,b,c)\n",
    "    PDF2 = Generate_gauss_PDF(mass_samples,mu)\n",
    "    \n",
    "    return (F * PDF1) + ((1-F) * PDF2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d22a61b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the negative of the log of the joint likelihood\n",
    "# This is the function we are trying to minimise with the minimiser, given different values of b, c, mu and F\n",
    "NLL = UnbinnedNLL(mass_samples, PDF_combined)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7b8ea513",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = 0.2 # Using a fixed gaussian width of 0.2\n",
    "a = 1 # Using a fixed constant polynomial term of 1\n",
    "\n",
    "# Setting the range of our mass data for use in normalisation\n",
    "mass_low = 0 \n",
    "mass_high = 10\n",
    "\n",
    "# Set the minimisation parameters\n",
    "m = Minuit(NLL, b=-0.016, c=0.007, mu=2.5, F=0.98)\n",
    "m.limits[\"F\"] = (0.0,1.0) \n",
    "m.limits[\"b\"] = (-0.5,0.5) \n",
    "m.limits[\"c\"] = (-0.5,0.5) \n",
    "m.limits[\"mu\"] = (1.0,9.0) # Limits on mu set many standard deviations away from data boundaries to accurately\n",
    "                           # approximate infinite data range \n",
    "\n",
    "# Set the errors on the initial start values\n",
    "m.errors=[0.1,0.001,0.001,0.1]\n",
    "\n",
    "# Set the increase in NLL for the 1-SD error calculation\n",
    "m.errordef=0.5\n",
    "\n",
    "# Run the minimisation\n",
    "m = m.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "677916f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b  =   -0.15779  +/-  0.00075\n",
      "\n",
      "\n",
      "c  =   0.007295  +/-  8.4e-05\n",
      "\n",
      "\n",
      "M  =   2.494  +/-  0.011\n",
      "\n",
      "\n",
      "F  =   0.98202  +/-  0.00082\n"
     ]
    }
   ],
   "source": [
    "fstr = \"{0:2.2}\"\n",
    "val = m.values[\"b\",\"c\",\"mu\",\"F\"]\n",
    "err = m.errors[\"b\",\"c\",\"mu\",\"F\"]\n",
    "print(\"{:2s}\".format(\"b\"), \"=  \", \"{0:2.5f}\".format(val[0]), \" +/- \", fstr.format(err[0]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"c\"), \"=  \", \"{0:2.6f}\".format(val[1]), \" +/- \", fstr.format(err[1]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"M\"), \"=  \", \"{0:2.3f}\".format(val[2]), \" +/- \", fstr.format(err[2]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"F\"), \"=  \", \"{0:2.5f}\".format(val[3]), \" +/- \", fstr.format(err[3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "775bb6bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_poly = m.values[\"mu\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "43b7cdce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plotting the fitted mass distribution\n",
    "x = np.linspace(mass_low, mass_high, 1000)\n",
    "y = PDF_combined(x, mu = m.values[\"mu\"], b = m.values[\"b\"],c = m.values[\"c\"] ,F=m.values[\"F\"])\n",
    "\n",
    "counts = plt.hist(mass_samples, bins = 100, color=\"orange\",density=True)\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Fitted Mass Distribution\")\n",
    "plt.xlabel(\"Mass\")\n",
    "plt.ylabel(\"Scaled counts\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "d63ef121",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "systematic error:  0.0041915972630870435\n"
     ]
    }
   ],
   "source": [
    "## Calculating the systematic error using the \"shift\" method\n",
    "\n",
    "syst_error = mean_exp-mean_poly\n",
    "print(\"systematic error: \", syst_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d2c46368",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistical error:  0.011048175540001148\n"
     ]
    }
   ],
   "source": [
    "## Getting the statistical error on the mean\n",
    "\n",
    "stat_error = m.errors[\"mu\"]\n",
    "print(\"statistical error: \", stat_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "33372c23",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Calculating total error by adding in quadrature\n",
    "total_error = np.sqrt((syst_error**2)+(stat_error**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e7073248",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M  =   2.494  +/-  0.011  +/-  0.004\n"
     ]
    }
   ],
   "source": [
    "## Display result of mean with all individual errors\n",
    "\n",
    "print(\"{:2s}\".format(\"M\"), \"=  \", \"{0:2.3f}\".format(m.values[\"mu\"]), \" +/- \", fstr.format(stat_error),\n",
    "      \" +/- \", \"{0:2.3f}\".format(syst_error))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "2c1d9c9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M  =   2.494  +/-  0.012\n"
     ]
    }
   ],
   "source": [
    "## Display result of mean with total combined errors in quadrature\n",
    "\n",
    "print(\"{:2s}\".format(\"M\"), \"=  \", \"{0:2.3f}\".format(m.values[\"mu\"]), \" +/- \", fstr.format(total_error))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdf1536a",
   "metadata": {},
   "source": [
    "#### The importance of the systematic error compared to the statistical error for the measurement of M "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0ff897f",
   "metadata": {},
   "source": [
    "Statistical error in our measurement of M is mainly goverened by the total number of mass sample measurements we have as they limit the accuracy of our sub-sample of data which is supposed to represent the true underlying distribution. This type of error can mainly be reduced by increasing the number of mass sample measurements as this will allow us to obtain a more truely representative distribution of the underlying true distribution. With more samples our data will be less prone to the effects of statistical fluctuations. \n",
    "\n",
    "On the other hand, systematic error in our measurement of M is mainly goverened by the how much the value of M varies as different models are used to fit the data distribution. A small systematic error means the variation in our the value of M is small when using different assumed models for the fit. \n",
    "\n",
    "It is desired for the statistical error to be larger than the systematic error as this means the error on the M value is mainly affected by the amount of data we have rather than the quality of our fit model. For our experiment we calculated a statistical error that is significantly larger than the systematic error. This means we have a relatively good fit model to the data, even though we know it is not the exact one.\n",
    "\n",
    "Obtained results are meaningless without also quoting their statistial and systematic errors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "930c0e02",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ade68214",
   "metadata": {},
   "source": [
    "## Part 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "08b72e0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the normalised linear PDF\n",
    "def Linear_PDF(x,b):\n",
    "    linear_dist = lambda x: a + b*(x)\n",
    "    area, _ = integrate.quad(linear_dist,mass_low,mass_high) # Calculate the normalisation constant\n",
    "    return (1/area)*(a + b*(x))  # Return the normalised linear PDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2ed1173d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate the combined PDF of the normalised linear and normalised gaussian PDFs\n",
    "# This PDF is also normalised as the fraction it takes of the normalised gaussian and linear PDFs adds up to 1\n",
    "def PDF_combined(mass_samples,b,mu,F):\n",
    "    PDF1 = Linear_PDF(mass_samples,b)\n",
    "    PDF2 = Generate_gauss_PDF(mass_samples,mu)\n",
    "    \n",
    "    return (F * PDF1) + ((1-F) * PDF2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "39adc76c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the negative of the log of the joint likelihood\n",
    "# This is the function we are trying to minimise with the minimiser, given different values of b, mu and F\n",
    "NLL = UnbinnedNLL(mass_samples, PDF_combined)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "aed96ecb",
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma = 0.2 # Using a fixed gaussian width of 0.2\n",
    "a = 1 # Using a fixed constant term of 1\n",
    "\n",
    "# Setting the range of our mass data for use in normalisation\n",
    "mass_low = 0 \n",
    "mass_high = 10\n",
    "\n",
    "# Set the minimisation parameters\n",
    "m = Minuit(NLL, b=-0.09, mu=2.5, F=0.98)\n",
    "m.limits[\"F\"] = (0.0,1.0) \n",
    "m.limits[\"b\"] = (-0.5,0.5) \n",
    "m.limits[\"mu\"] = (1.0,9.0) # Limits on mu set many standard deviations away from data boundaries to accurately\n",
    "                           # approximate infinite data range \n",
    "\n",
    "# Set the errors on the initial start values\n",
    "m.errors=[0.01,0.01,0.01]\n",
    "\n",
    "# Set the increase in NLL for the 1-SD error calculation\n",
    "m.errordef=0.5\n",
    "\n",
    "# Run the minimisation\n",
    "m = m.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bddb04bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b  =   -0.09041  +/-  0.00016\n",
      "\n",
      "\n",
      "M  =   2.465  +/-  0.011\n",
      "\n",
      "\n",
      "F  =   0.98013  +/-  0.00082\n"
     ]
    }
   ],
   "source": [
    "fstr = \"{0:2.2}\"\n",
    "val = m.values[\"b\",\"mu\",\"F\"]\n",
    "err = m.errors[\"b\",\"mu\",\"F\"]\n",
    "print(\"{:2s}\".format(\"b\"), \"=  \", \"{0:2.5f}\".format(val[0]), \" +/- \", fstr.format(err[0]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"M\"), \"=  \", \"{0:2.3f}\".format(val[1]), \" +/- \", fstr.format(err[1]))\n",
    "print(\"\\n\")\n",
    "print(\"{:2s}\".format(\"F\"), \"=  \", \"{0:2.5f}\".format(val[2]), \" +/- \", fstr.format(err[2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "09415fa9",
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_linear = m.values[\"mu\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "249b8359",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Plotting the fitted mass distribution\n",
    "x = np.linspace(0, 10, 1000)\n",
    "y = PDF_combined(x,m.values[\"b\"],m.values[\"mu\"],m.values[\"F\"])\n",
    "\n",
    "counts = plt.hist(mass_samples, bins = 100, color=\"orange\",density=True)\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Fitted Mass Distribution\")\n",
    "plt.xlabel(\"Mass\")\n",
    "plt.ylabel(\"Scaled counts\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "385725e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0041915972630870435\n",
      "0.03308164284112669\n",
      "0.028890045578039647\n"
     ]
    }
   ],
   "source": [
    "## Calculating the difference in mean between all of the models\n",
    "\n",
    "diff_1_2 = np.abs(mean_exp-mean_poly)\n",
    "\n",
    "diff_1_3 = np.abs(mean_exp-mean_linear)\n",
    "\n",
    "diff_2_3 = np.abs(mean_poly-mean_linear)\n",
    "\n",
    "print(diff_1_2)\n",
    "print(diff_1_3)\n",
    "print(diff_2_3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "53a6e549",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "systematic error:  0.03308164284112669\n"
     ]
    }
   ],
   "source": [
    "## Taking the largest difference between the mean values as the systematic uncertainty\n",
    "\n",
    "syst_error = diff_1_3\n",
    "print(\"systematic error: \", syst_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "62cbdc0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "statistical error:  0.010704145512545393\n"
     ]
    }
   ],
   "source": [
    "## Getting the statistical error on the mean\n",
    "\n",
    "stat_error = m.errors[\"mu\"]\n",
    "print(\"statistical error: \", stat_error)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "98e8f455",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Calculating total error by adding in quadrature\n",
    "total_error = np.sqrt((syst_error**2)+(stat_error**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "637227a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M  =   2.465  +/-  0.011  +/-  0.033\n"
     ]
    }
   ],
   "source": [
    "## Display result of mean with all individual errors\n",
    "\n",
    "print(\"{:2s}\".format(\"M\"), \"=  \", \"{0:2.3f}\".format(m.values[\"mu\"]), \" +/- \", fstr.format(stat_error),\n",
    "      \" +/- \", \"{0:2.3f}\".format(syst_error))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f3118755",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M  =   2.465  +/-  0.035\n"
     ]
    }
   ],
   "source": [
    "## Display result of mean with total combined errors in quadrature\n",
    "\n",
    "print(\"{:2s}\".format(\"M\"), \"=  \", \"{0:2.3f}\".format(m.values[\"mu\"]), \" +/- \", fstr.format(total_error))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef9a245f",
   "metadata": {},
   "source": [
    "The statistical error for this fit has remained very similar to the previous fits.\n",
    "\n",
    "The systematic error is governed by how well the model fits the data compared to the best fitting model. The systematic error of this model fit is the largest of the three fits as the model we are using fits the data most poorly. This results in the obtained value of M to deviate by the largest amount from the true value based on the fit.\n",
    "\n",
    "It is desired for the statistical error to be larger than the systematic error as this means the error on the value of M is mainly affected by the amount of data we have rather than the quality of our fit model. For this fit we calculated a systematic error that is larger than the statistical error. This means that the deviation in the value of M that we calculate away from the true value mainly comes from using a model that fits poorly to the data rather than the limited number of samples.\n",
    "\n",
    "\n",
    "\n",
    "The value of M we obtained is meaningless without also quoting its statistical and systematic errors. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4eb5cf75",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cdf387b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ba02507a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31ba6c8e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
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 },
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