{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "11d6c31f",
   "metadata": {},
   "source": [
    "# `abcd_pyhf`: Likelihood-based ABCD method for background estimation and hypothesis testing with `pyhf`\n",
    "\n",
    "An introduction to the likelihood-based ABCD method and how to use the Python package `abcd_pyhf` to implement it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76f1102b",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "There are some warnings generated by some of the packages used in this notebook that can safely be ignored in order to keep the output clean. These should disappear in future releases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bc428be8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "warnings.filterwarnings(\n",
    "    'ignore',\n",
    "    r'Assigned errors must be positive\\. Non-positive values are replaced by a heuristic\\.',\n",
    "    UserWarning,\n",
    "    'iminuit'\n",
    ")\n",
    "warnings.filterwarnings(\n",
    "    'ignore',\n",
    "    'invalid value encountered in double_scalars',\n",
    "    RuntimeWarning,\n",
    "    'pyhf'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79492a5f",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "In analyses that are searching for new physics processes, the general idea is usually to look for a potential excess of signal-like events beyond the expected number of events from background processes. The expectations of what signal events might look like and how the background events are distributed are often provided by Monte Carlo (MC) simulation. However, it's often impractical or impossible to generate MC simulations that accurately model the background in the most signal-like regions and/or provide enough statistics to be useful for very low-background analyses. This is especially common for QCD multijet backgrounds, for example. This necessitates the use of data-driven background models, where the background in the signal region is estimated directly from data outside the signal region. Without making any further assumptions about the background, this requires at least two independent discriminant variables."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31bc0ffd",
   "metadata": {},
   "source": [
    "We'll look at an artificial example of signal MC and data to understand this. (This example was randomly generated in the [generate_example_data.ipynb notebook](generate_example_data.ipynb).) First, let's load the \"signal MC\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5ecc23a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8582973c",
   "metadata": {},
   "outputs": [],
   "source": [
    "signal_mc = np.loadtxt('signal_mc.csv', delimiter=',')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93c8d2df",
   "metadata": {},
   "source": [
    "This array consists of pairs of independent observables that I'll call $x$ and $y$. Each row represents one event. We can visualize this distribution in a 2D histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ad70e38e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e6e0b171",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist2d(\n",
    "    *signal_mc.T,\n",
    "    bins=30,\n",
    "    range=((0, 3), (0, 3))\n",
    ")\n",
    "plt.title('Signal Monte Carlo simulation')\n",
    "plt.xlabel('$x$')\n",
    "plt.xlim(0, 3)\n",
    "plt.ylabel('$y$')\n",
    "plt.ylim(0, 3)\n",
    "plt.colorbar(label='Events')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cef877c1",
   "metadata": {},
   "source": [
    "As in a real analysis, we have a relatively high statistics sample of what this potential signal should look like in data if it exists. Of course we don't expect to see nearly this many signal events in real data, and we will have to deal with a distribution of background events in this plane."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a135f4b2",
   "metadata": {},
   "source": [
    "Next, let's look at what our distribution of events in actual \"data\" looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7f0ebd52",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.loadtxt('data.csv', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "64a1929a",
   "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.scatter(*data.T, s=10)\n",
    "plt.title('Data')\n",
    "plt.xlabel('$x$')\n",
    "plt.xlim(0, 3)\n",
    "plt.ylabel('$y$')\n",
    "plt.ylim(0, 3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2649c961",
   "metadata": {},
   "source": [
    "Now the question is: how do we know if there are real signal events here or not? In order to answer, we need a method to estimate how many of these events are from background processes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd5ffcf9",
   "metadata": {},
   "source": [
    "## ABCD method\n",
    "\n",
    "One of the simplest possible ways of estimating background from data is called the \"ABCD method\". In this method, we introduce threshold values in each of the two discriminants, separating this plane into four regions labeled $A$, $B$, $C$, and $D$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b69137b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_threshold = 1\n",
    "y_threshold = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "393edc3d",
   "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.scatter(*data.T, s=10)\n",
    "plt.plot((0, 3), (y_threshold, y_threshold), color='black')\n",
    "plt.plot((x_threshold, x_threshold), (0, 3), color='black')\n",
    "plt.title('Data')\n",
    "plt.xlabel('$x$')\n",
    "plt.xlim(0, 3)\n",
    "plt.ylabel('$y$')\n",
    "plt.ylim(0, 3)\n",
    "region_label_color = 'red'\n",
    "region_label_fontsize = 20\n",
    "region_label_fontweight = 'bold'\n",
    "plt.text(2.95, 2.95, 'A', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight, horizontalalignment='right', verticalalignment='top')\n",
    "plt.text(0.05, 2.95, 'B', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight, verticalalignment='top')\n",
    "plt.text(2.95, 0.05, 'C', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight, horizontalalignment='right')\n",
    "plt.text(0.05, 0.05, 'D', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "162ffbbc",
   "metadata": {},
   "source": [
    "As long as $x$ and $y$ are statistically independent, it's easy to show that the number of events in region $A$, $N_A$ is approximately equal to $N_B N_C / N_D$, where the approximation is only due to finite statistics. Thus if $N_B$, $N_C$, and $N_D$ accurately reflect the number of background events in their respective regions, we have an unbiased estimator of the number of background events in region $A$ that does not rely on any information from region $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3e8cf4e",
   "metadata": {},
   "source": [
    "Now let's look at the distribution of the simulated signal events:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19ff840d",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot((0, 3), (y_threshold, y_threshold), color='black')\n",
    "plt.plot((x_threshold, x_threshold), (0, 3), color='black')\n",
    "plt.hist2d(\n",
    "    *signal_mc.T,\n",
    "    bins=30,\n",
    "    range=((0, 3), (0, 3))\n",
    ")\n",
    "\n",
    "plt.title('Signal Monte Carlo simulaton')\n",
    "plt.xlabel('$x$')\n",
    "plt.xlim(0, 3)\n",
    "plt.ylabel('$y$')\n",
    "plt.ylim(0, 3)\n",
    "region_label_color = 'red'\n",
    "region_label_fontsize = 20\n",
    "region_label_fontweight = 'bold'\n",
    "plt.text(2.95, 2.95, 'A', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight, horizontalalignment='right', verticalalignment='top')\n",
    "plt.text(0.05, 2.95, 'B', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight, verticalalignment='top')\n",
    "plt.text(2.95, 0.05, 'C', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight, horizontalalignment='right')\n",
    "plt.text(0.05, 0.05, 'D', color=region_label_color, fontsize=region_label_fontsize, fontweight=region_label_fontweight)\n",
    "plt.colorbar(label='Events')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a9486bd",
   "metadata": {},
   "source": [
    "There is a significant amount leakage of signal events into regions $B$, $C$, and $D$. So if there really are any signal events observed in data in region $A$, there very likely are signal events in data in the other regions as well. This unfortunately breaks the naive ABCD method, and if we tried to use it, we could end up totally missing our observation of signal in data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4950b42",
   "metadata": {},
   "source": [
    "### Likelihood-based\n",
    "\n",
    "The correct and much more robust way to handle this scenario is to use the \"likelihood-based\" ABCD method. In this method, we set up a system of equations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46725f26",
   "metadata": {},
   "source": [
    "Expected number of signal events in each region:\n",
    "\n",
    "$n_X^\\textrm{signal} = (\\epsilon_X / \\epsilon_A) \\mu$\n",
    "\n",
    "where $\\epsilon_X$ is the signal efficiency of region $X$ ($X \\in \\{A, B, C, D\\}$) estimated from MC and $\\mu$ is the signal strength, defined as the number of signal events in data in region $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c174dbb4",
   "metadata": {},
   "source": [
    "Expected number of background events in each region:\n",
    "\n",
    "$n_A^\\textrm{bkg} = \\mu_b$\n",
    "\n",
    "$n_B^\\textrm{bkg} = \\tau_B \\mu_b$\n",
    "\n",
    "$n_C^\\textrm{bkg} = \\tau_C \\mu_b$\n",
    "\n",
    "$n_D^\\textrm{bkg} = \\tau_B \\tau_C \\mu_b$\n",
    "\n",
    "where $\\mu_b$ is defined to be the number of background events in region $A$ and $\\tau_B$ and $\\tau_C$ are nuisance parameters that enforce the standard ABCD relation $n_A^\\textrm{bkg} = n_B^\\textrm{bkg} n_C^\\textrm{bkg} / n_D^\\textrm{bkg}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbc10e20",
   "metadata": {},
   "source": [
    "Then the total expected number of events in region $X$ is $n_X = n_X^\\textrm{signal} + n_X^\\textrm{bkg}$. For particular values of all these parameters, we can calculate a Poisson likelihood based on the expected number of events and the observed number of events in each region. At this point, we can perform maximum likelihood fits with these parameters in order to do all statistical tests needed to get our analysis results."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "970c91dc",
   "metadata": {},
   "source": [
    "## `abcd_pyhf`\n",
    "\n",
    "`abcd_pyhf` is a Python package that facilitates doing exactly these statistical tests. It's a convenient wrapper around `pyhf`, which is used to build the proper PDFs and run hypothesis tests for the likelihood-based ABCD method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cfa125b",
   "metadata": {},
   "source": [
    "First we need to extract the yields (the number of events in each region for signal MC and data). I'll use a simple function for this counting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "787d3e9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_region_counts(x, y, x_cut, y_cut):\n",
    "    return {\n",
    "        'A': sum((x > x_cut) & (y > y_cut)),\n",
    "        'B': sum((x > 0) & (x < x_cut) & (y > y_cut)),\n",
    "        'C': sum((x > x_cut) & (y > 0) & (y < y_cut)),\n",
    "        'D': sum((x > 0) & (x < x_cut) & (y > 0) & (y < y_cut))\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e54eb32",
   "metadata": {},
   "source": [
    "and then evaluate these yields in data and signal MC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a22d09e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_yields = get_region_counts(*data.T, x_threshold, y_threshold)\n",
    "signal_mc_yields = get_region_counts(*signal_mc.T, x_threshold, y_threshold)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9b726e9",
   "metadata": {},
   "source": [
    "We also need the total systematic uncertainty for this analysis. This is a complicated number that would normally be the product of many dedicated studies. In this example, I'll just arbitrarily set it to 10%:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "15bcf89b",
   "metadata": {},
   "outputs": [],
   "source": [
    "signal_uncertainty = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "192e6978",
   "metadata": {},
   "source": [
    "### `ABCD`\n",
    "\n",
    "The main class used in `abcd_pyhf` is called `ABCD`, which is an object that carries the information about a particular ABCD plane, including the yields from signal MC and data, as well as the systematic uncertainty. I'll pass in this information to make a new `abcd` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1726a96f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from abcd_pyhf import ABCD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "06e2d702",
   "metadata": {},
   "outputs": [],
   "source": [
    "abcd = ABCD(data_yields, signal_mc_yields, signal_uncertainty)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6566dc17",
   "metadata": {},
   "source": [
    "### Parameter fitting\n",
    "\n",
    "One of the lower-level tasks that `abcd_pyhf` can do is extracting the maximum likelihood estimators (MLEs) of the fit parameters and their uncertainty based on the observed data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ddd2263",
   "metadata": {},
   "source": [
    "We can inspect the parameters used in fitting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b0cbe4f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['mu', 'systematic_uncertainty', 'mu_b', 'tau_B', 'tau_C']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.model.config.par_names()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab0a550a",
   "metadata": {},
   "source": [
    "and we can run the fit with the signal strength fixed to zero (a background-only fit):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2b117445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.1       ],\n",
       "       [ 0.        ,  0.1       ],\n",
       "       [27.71897769,  3.56424424],\n",
       "       [ 1.74226533,  0.1602753 ],\n",
       "       [ 5.71076759,  0.71035935]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.bkg_only_fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0477a01e",
   "metadata": {},
   "source": [
    "or fit while allowing all parameters to float, so that the signal strength is at its MLE:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cbec97bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.27676441e+01, 9.22126277e+00],\n",
       "       [5.84459165e-05, 9.93343453e-01],\n",
       "       [2.02291860e+01, 5.70029631e+00],\n",
       "       [1.85885127e+00, 1.94267090e-01],\n",
       "       [7.44703046e+00, 1.88646208e+00]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1b5e8ce",
   "metadata": {},
   "source": [
    "The first column represents the parameter values, and the second column is the uncertainty. The first row is the signal strength, so $\\mu = 13 \\pm 9$ based on the fit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8000ee77",
   "metadata": {},
   "source": [
    "### Likelihood values\n",
    "\n",
    "We can also extract the likelihood at various parameter values."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc6762e9",
   "metadata": {},
   "source": [
    "`twice_nll()` gets the likelihood at several values of $\\mu$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "940da992",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "        13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
       "        26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,\n",
       "        39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51.,\n",
       "        52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62.]),\n",
       " array([[1.82731843e+00],\n",
       "        [1.55778510e+00],\n",
       "        [1.30816135e+00],\n",
       "        [1.07911913e+00],\n",
       "        [8.71050942e-01],\n",
       "        [6.84569046e-01],\n",
       "        [5.20044362e-01],\n",
       "        [3.77801183e-01],\n",
       "        [2.58096057e-01],\n",
       "        [1.61125297e-01],\n",
       "        [8.68509051e-02],\n",
       "        [3.54122377e-02],\n",
       "        [6.71461821e-03],\n",
       "        [6.59226440e-04],\n",
       "        [1.68302247e-02],\n",
       "        [5.51749899e-02],\n",
       "        [1.15282598e-01],\n",
       "        [1.96788824e-01],\n",
       "        [2.99101368e-01],\n",
       "        [4.21955519e-01],\n",
       "        [5.64640277e-01],\n",
       "        [7.26733245e-01],\n",
       "        [9.07619960e-01],\n",
       "        [1.10673018e+00],\n",
       "        [1.32334152e+00],\n",
       "        [1.55698571e+00],\n",
       "        [1.80700479e+00],\n",
       "        [2.07277877e+00],\n",
       "        [2.35378082e+00],\n",
       "        [2.64929129e+00],\n",
       "        [2.95888915e+00],\n",
       "        [3.28199469e+00],\n",
       "        [3.61810438e+00],\n",
       "        [3.96669413e+00],\n",
       "        [4.32732254e+00],\n",
       "        [4.69954877e+00],\n",
       "        [5.08293958e+00],\n",
       "        [5.47708464e+00],\n",
       "        [5.88158300e+00],\n",
       "        [6.29604812e+00],\n",
       "        [6.72007981e+00],\n",
       "        [7.15328930e+00],\n",
       "        [7.59543012e+00],\n",
       "        [8.04561382e+00],\n",
       "        [8.50386620e+00],\n",
       "        [8.96977453e+00],\n",
       "        [9.44285711e+00],\n",
       "        [9.92299959e+00],\n",
       "        [1.04098231e+01],\n",
       "        [1.09031155e+01],\n",
       "        [1.14023413e+01],\n",
       "        [1.19075053e+01],\n",
       "        [1.24182998e+01],\n",
       "        [1.29344730e+01],\n",
       "        [1.34556696e+01],\n",
       "        [1.39818532e+01],\n",
       "        [1.45126826e+01],\n",
       "        [1.50479855e+01],\n",
       "        [1.55876448e+01],\n",
       "        [1.61313433e+01],\n",
       "        [1.66788970e+01],\n",
       "        [1.72302603e+01],\n",
       "        [1.77851699e+01]]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.twice_nll()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b134284",
   "metadata": {},
   "source": [
    "and there's a convenience function (`twice_nll_plot()`) to plot this result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7f48d145",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "abcd.twice_nll_plot()\n",
    "plt.ylim(0, 4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30785a37",
   "metadata": {},
   "source": [
    "While the favored value of $\\mu$ is around 13, we certainly can't exclude a signal-free hypothesis ($\\mu = 0$)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fcffc6f",
   "metadata": {},
   "source": [
    "### $\\textrm{CL}_s$ tests\n",
    "\n",
    "We can easily extract $\\textrm{CL}_b$, $\\textrm{CL}_{s + b}$, and $\\textrm{CL}_s$, which are used by LHC experiments for discovery and setting upper limits on signal strength [[arXiv:1007.1727](https://arxiv.org/abs/1007.1727)]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "66b49631",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "        13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
       "        26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,\n",
       "        39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51.,\n",
       "        52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62.]),\n",
       " array([       nan, 0.54049462, 0.58114728, 0.62097115, 0.65943358,\n",
       "        0.69637113, 0.7313514 , 0.76412622, 0.79449952, 0.82234034,\n",
       "        0.84758169, 0.87022533, 0.89032565, 0.90368121, 0.90291818,\n",
       "        0.90183495, 0.90070848, 0.89953496, 0.89834632, 0.89710649,\n",
       "        0.89585016, 0.8945602 , 0.8932525 , 0.89193117, 0.89060104,\n",
       "        0.88926322, 0.88792381, 0.8865893 , 0.88526165, 0.88393826,\n",
       "        0.88262855, 0.88133203, 0.88004809, 0.87877957, 0.87752291,\n",
       "        0.87627627, 0.8750297 , 0.87379191, 0.87255812, 0.87132787,\n",
       "        0.87010166, 0.86888064, 0.86766039, 0.86646292, 0.86527101,\n",
       "        0.86408463, 0.86291845, 0.8617614 , 0.86061656, 0.85948122,\n",
       "        0.85836446, 0.85725737, 0.85616173, 0.85507638, 0.85400926,\n",
       "        0.85294908, 0.8519015 , 0.85086892, 0.84984534, 0.84882924,\n",
       "        0.84783104, 0.8468414 , 0.84586422]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.clb()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cc8a8190",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "        13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
       "        26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,\n",
       "        39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51.,\n",
       "        52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62.]),\n",
       " array([           nan, 5.00000000e-01, 5.00000000e-01, 5.00000000e-01,\n",
       "        5.00000000e-01, 5.00000000e-01, 5.00000000e-01, 5.00000000e-01,\n",
       "        5.00000000e-01, 5.00000000e-01, 5.00000000e-01, 5.00000000e-01,\n",
       "        5.00000000e-01, 4.89758121e-01, 4.48389487e-01, 4.07145670e-01,\n",
       "        3.67104154e-01, 3.28662698e-01, 2.92223166e-01, 2.57981444e-01,\n",
       "        2.26198312e-01, 1.96972062e-01, 1.70373351e-01, 1.46396920e-01,\n",
       "        1.24996615e-01, 1.06053558e-01, 8.94339759e-02, 7.49740490e-02,\n",
       "        6.24897807e-02, 5.17980363e-02, 4.27032993e-02, 3.50218759e-02,\n",
       "        2.85769803e-02, 2.32044003e-02, 1.87525990e-02, 1.50852687e-02,\n",
       "        1.20811854e-02, 9.63368370e-03, 7.65002996e-03, 6.05037220e-03,\n",
       "        4.76666803e-03, 3.74133149e-03, 2.92582167e-03, 2.28069801e-03,\n",
       "        1.77196333e-03, 1.37241234e-03, 1.05986510e-03, 8.16130761e-04,\n",
       "        6.26733742e-04, 4.80013294e-04, 3.66758007e-04, 2.79541115e-04,\n",
       "        2.12573566e-04, 1.61293018e-04, 1.22133450e-04, 9.22917917e-05,\n",
       "        6.96095556e-05, 5.24060320e-05, 3.93838006e-05, 2.95489210e-05,\n",
       "        2.21353700e-05, 1.65559993e-05, 1.23651676e-05]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.clsb()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b37c40b4",
   "metadata": {},
   "source": [
    "In the case of $\\textrm{CL}_s$, we get the observed values as well as the expected band, which is the median value (assuming the true value of $\\mu$ is zero), $\\pm 1 \\sigma$, and $\\pm 2 \\sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f09d7990",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12.,\n",
       "        13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25.,\n",
       "        26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38.,\n",
       "        39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51.,\n",
       "        52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62.]),\n",
       " array([           nan, 9.25078580e-01, 8.60367105e-01, 8.05190390e-01,\n",
       "        7.58226473e-01, 7.18007935e-01, 6.83665883e-01, 6.54342162e-01,\n",
       "        6.29326997e-01, 6.08020759e-01, 5.89913641e-01, 5.74563829e-01,\n",
       "        5.61592268e-01, 5.41958951e-01, 4.96600353e-01, 4.51463616e-01,\n",
       "        4.07572664e-01, 3.65369565e-01, 3.25290103e-01, 2.87570591e-01,\n",
       "        2.52495697e-01, 2.20188716e-01, 1.90733698e-01, 1.64134772e-01,\n",
       "        1.40350853e-01, 1.19260030e-01, 1.00722579e-01, 8.45645769e-02,\n",
       "        7.05890519e-02, 5.85991561e-02, 4.83819603e-02, 3.97374369e-02,\n",
       "        3.24720669e-02, 2.64052568e-02, 2.13699252e-02, 1.72151971e-02,\n",
       "        1.38066004e-02, 1.10251464e-02, 8.76735863e-03, 6.94385251e-03,\n",
       "        5.47828865e-03, 4.30592113e-03, 3.37208163e-03, 2.63219345e-03,\n",
       "        2.04787091e-03, 1.58828464e-03, 1.22823321e-03, 9.47049566e-04,\n",
       "        7.28238065e-04, 5.58491892e-04, 4.27275387e-04, 3.26087737e-04,\n",
       "        2.48286695e-04, 1.88629954e-04, 1.43011856e-04, 1.08203167e-04,\n",
       "        8.17108028e-05, 6.15911932e-05, 4.63423152e-05, 3.48113845e-05,\n",
       "        2.61082327e-05, 1.95502951e-05, 1.46183836e-05]),\n",
       " array([[1.00000000e+00, 7.82002601e-01, 6.03646409e-01, 4.61477246e-01,\n",
       "         3.49721834e-01, 2.62357190e-01, 1.95011965e-01, 1.43632814e-01,\n",
       "         1.04846253e-01, 7.58696200e-02, 5.44429256e-02, 3.87526636e-02,\n",
       "         2.73723539e-02, 1.91905906e-02, 1.33590602e-02, 9.23822541e-03,\n",
       "         6.34752329e-03, 4.33509799e-03, 2.94386618e-03, 1.98840777e-03,\n",
       "         1.33627902e-03, 8.93853145e-04, 5.95223759e-04, 3.94677700e-04,\n",
       "         2.60716492e-04, 1.71579728e-04, 1.12527021e-04, 7.35552460e-05,\n",
       "         4.79277723e-05, 3.11469603e-05, 2.01835240e-05, 1.30452897e-05,\n",
       "         8.41133259e-06, 5.41111817e-06, 3.47382101e-06, 2.22587740e-06,\n",
       "         1.42410376e-06, 9.09656865e-07, 5.80251639e-07, 3.69668640e-07,\n",
       "         2.35245159e-07, 1.49549415e-07, 9.49843504e-08, 6.02773000e-08,\n",
       "         3.82266466e-08, 2.42309406e-08, 1.53495114e-08, 9.71907498e-09,\n",
       "         6.15168582e-09, 3.89257817e-09, 2.46252656e-09, 1.55758285e-09,\n",
       "         9.85090247e-10, 6.23016578e-10, 3.93996304e-10, 2.49198496e-10,\n",
       "         1.57636934e-10, 9.97248240e-11, 6.31025012e-11, 3.99462084e-11,\n",
       "         2.52910859e-11, 1.60181109e-11, 1.01485850e-11],\n",
       "        [1.00000000e+00, 8.52795126e-01, 7.19387406e-01, 6.01500194e-01,\n",
       "         4.98782292e-01, 4.09781332e-01, 3.33738484e-01, 2.69446367e-01,\n",
       "         2.15671205e-01, 1.71171086e-01, 1.34735016e-01, 1.05203370e-01,\n",
       "         8.15071079e-02, 6.26705503e-02, 4.78349028e-02, 3.62581041e-02,\n",
       "         2.72967329e-02, 2.04175624e-02, 1.51777229e-02, 1.12160801e-02,\n",
       "         8.24186149e-03, 6.02431200e-03, 4.38081428e-03, 3.17002559e-03,\n",
       "         2.28357862e-03, 1.63770650e-03, 1.16959310e-03, 8.31926448e-04,\n",
       "         5.89442716e-04, 4.16208665e-04, 2.92836758e-04, 2.05351498e-04,\n",
       "         1.43550829e-04, 1.00048053e-04, 6.95329913e-05, 4.81977774e-05,\n",
       "         3.33328490e-05, 2.29983991e-05, 1.58344621e-05, 1.08804477e-05,\n",
       "         7.46250675e-06, 5.10934438e-06, 3.49251698e-06, 2.38364350e-06,\n",
       "         1.62460502e-06, 1.10595191e-06, 7.51892918e-07, 5.10609374e-07,\n",
       "         3.46394769e-07, 2.34769752e-07, 1.58976196e-07, 1.07565182e-07,\n",
       "         7.27265071e-08, 4.91406033e-08, 3.31815653e-08, 2.23948252e-08,\n",
       "         1.51077116e-08, 1.01867051e-08, 6.86618391e-09, 4.62728037e-09,\n",
       "         3.11720265e-09, 2.09949968e-09, 1.41378230e-09],\n",
       "        [1.00000000e+00, 9.19010750e-01, 8.37705447e-01, 7.58057706e-01,\n",
       "         6.81132833e-01, 6.07257732e-01, 5.37297202e-01, 4.71747568e-01,\n",
       "         4.11000950e-01, 3.55319314e-01, 3.04836622e-01, 2.59549333e-01,\n",
       "         2.19348704e-01, 1.84015815e-01, 1.53265551e-01, 1.26768049e-01,\n",
       "         1.04134453e-01, 8.49762484e-02, 6.88982057e-02, 5.55159399e-02,\n",
       "         4.44650510e-02, 3.54101293e-02, 2.80416446e-02, 2.20865441e-02,\n",
       "         1.73080986e-02, 1.34957692e-02, 1.04729611e-02, 8.08971692e-03,\n",
       "         6.22077340e-03, 4.76402579e-03, 3.63315949e-03, 2.75978806e-03,\n",
       "         2.08843798e-03, 1.57464143e-03, 1.18313700e-03, 8.86039890e-04,\n",
       "         6.61564843e-04, 4.92472643e-04, 3.65573813e-04, 2.70650888e-04,\n",
       "         1.99867837e-04, 1.47240018e-04, 1.08220749e-04, 7.93665815e-05,\n",
       "         5.80869446e-05, 4.24333860e-05, 3.09381344e-05, 2.25172133e-05,\n",
       "         1.63609726e-05, 1.18691248e-05, 8.59761529e-06, 6.21900842e-06,\n",
       "         4.49244750e-06, 3.24122847e-06, 2.33557595e-06, 1.68118481e-06,\n",
       "         1.20888931e-06, 8.68362315e-07, 6.23186969e-07, 4.46904551e-07,\n",
       "         3.20193704e-07, 2.29239039e-07, 1.64003133e-07],\n",
       "        [1.00000000e+00, 9.69272753e-01, 9.35101669e-01, 8.97992383e-01,\n",
       "         8.58265232e-01, 8.15978624e-01, 7.71592423e-01, 7.25505087e-01,\n",
       "         6.78183483e-01, 6.30137453e-01, 5.81904346e-01, 5.34013405e-01,\n",
       "         4.86983915e-01, 4.41281729e-01, 3.97330926e-01, 3.55510179e-01,\n",
       "         3.16091877e-01, 2.79301584e-01, 2.45284087e-01, 2.14114427e-01,\n",
       "         1.85802878e-01, 1.60309233e-01, 1.37531155e-01, 1.17336631e-01,\n",
       "         9.95768353e-02, 8.40620496e-02, 7.06042029e-02, 5.90071251e-02,\n",
       "         4.90758788e-02, 4.06304176e-02, 3.34839920e-02, 2.74730810e-02,\n",
       "         2.24452947e-02, 1.82618685e-02, 1.47991219e-02, 1.19470767e-02,\n",
       "         9.61025980e-03, 7.70301550e-03, 6.15346691e-03, 4.89968509e-03,\n",
       "         3.88920814e-03, 3.07786085e-03, 2.42875105e-03, 1.91119853e-03,\n",
       "         1.49997329e-03, 1.17431649e-03, 9.17058742e-04, 7.14479582e-04,\n",
       "         5.55398357e-04, 4.30808011e-04, 3.33475837e-04, 2.57621916e-04,\n",
       "         1.98644235e-04, 1.52893681e-04, 1.17469848e-04, 9.01070503e-05,\n",
       "         6.90088728e-05, 5.27676354e-05, 4.02905135e-05, 3.07241521e-05,\n",
       "         2.33960785e-05, 1.77935022e-05, 1.35160562e-05],\n",
       "        [1.00000000e+00, 9.93781700e-01, 9.86121127e-01, 9.76898497e-01,\n",
       "         9.65954682e-01, 9.53043388e-01, 9.38022216e-01, 9.20737885e-01,\n",
       "         9.01074662e-01, 8.78961103e-01, 8.54380038e-01, 8.27366603e-01,\n",
       "         7.98020316e-01, 7.66489437e-01, 7.32983521e-01, 6.97778049e-01,\n",
       "         6.61162239e-01, 6.23480358e-01, 5.85093136e-01, 5.46372385e-01,\n",
       "         5.07688209e-01, 4.69407827e-01, 4.31854622e-01, 3.95331896e-01,\n",
       "         3.60129845e-01, 3.26457461e-01, 2.94504778e-01, 2.64410114e-01,\n",
       "         2.36267361e-01, 2.10157072e-01, 1.86074084e-01, 1.64013344e-01,\n",
       "         1.43934545e-01, 1.25770984e-01, 1.09439428e-01, 9.48401228e-02,\n",
       "         8.18685134e-02, 7.03976309e-02, 6.03084546e-02, 5.14782444e-02,\n",
       "         4.37866363e-02, 3.71172277e-02, 3.13596217e-02, 2.64098997e-02,\n",
       "         2.21727713e-02, 1.85605085e-02, 1.54908737e-02, 1.28925435e-02,\n",
       "         1.07008343e-02, 8.85836291e-03, 7.31446671e-03, 6.02478250e-03,\n",
       "         4.95069396e-03, 4.05882168e-03, 3.32011902e-03, 2.71013203e-03,\n",
       "         2.20766218e-03, 1.79469293e-03, 1.45617616e-03, 1.17941203e-03,\n",
       "         9.53474473e-04, 7.69494523e-04, 6.19974382e-04]]))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.cls()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "997a17b2",
   "metadata": {},
   "source": [
    "### Brazil plot\n",
    "\n",
    "There's another convenience function for plotting the $\\textrm{CL}_s$ band, sometimes called a \"Brazil plot\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "50eaaa4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "abcd.brazil_plot()\n",
    "plt.xlim(0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4672ecd",
   "metadata": {},
   "source": [
    "### Upper limits\n",
    "\n",
    "And finally we can extract the observed and expected upper limit band for the signal strength (where the lines in the plot above cross 0.05, for a 95% confidence level):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f3e01596",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(29.84163563742085,\n",
       " [10.283164525558307,\n",
       "  13.854061161638194,\n",
       "  19.499139929855087,\n",
       "  27.90694811529501,\n",
       "  39.19218925297826])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abcd.upper_limit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ff10a3",
   "metadata": {},
   "source": [
    "## Summary and outlook\n",
    "\n",
    "- The ABCD method\n",
    "    - One of the simplest and most common data-driven background estimation methods\n",
    "    - Really a family of many methods using very similar techniques, but almost all that are actually used in modern analyses are some variant of the likelihood-based method described here\n",
    "- `abcd_pyhf`\n",
    "    - A small, pure-Python package\n",
    "    - Depends only on NumPy, Matplotlib, and `pyhf`\n",
    "        - No dependence on experiment-specific formats or code\n",
    "    - Works out of the box for most simple cases\n",
    "        - Intended to be extensible to accommodate more complicated cases\n",
    "    - Using this for my own ATLAS analysis, and a few other ATLAS analyses now also using or trying out this package"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed2e6bdd",
   "metadata": {},
   "source": [
    "## Links\n",
    "\n",
    "- [GitHub repository](https://github.com/masonproffitt/abcd-pyhf)\n",
    "- [PyPI package](https://pypi.org/project/abcd-pyhf/)\n",
    "- [ACAT 2021 poster](https://indico.cern.ch/event/855454/contributions/4596707/)"
   ]
  }
 ],
 "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",
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