{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hello World, `pyhf` style"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Two bin counting experiment with a background uncertainty**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyhf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Returning the observed and expected** $\\mathrm{CL}_{s}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed: 0.052515541856109765, Expected: 0.06445521290832805\n"
     ]
    }
   ],
   "source": [
    "model = pyhf.simplemodels.uncorrelated_background(\n",
    "    signal=[12.0, 11.0], bkg=[50.0, 52.0], bkg_uncertainty=[3.0, 7.0]\n",
    ")\n",
    "data = [51, 48] + model.config.auxdata\n",
    "test_mu = 1.0\n",
    "CLs_obs, CLs_exp = pyhf.infer.hypotest(\n",
    "    test_mu, data, model, test_stat=\"qtilde\", return_expected=True\n",
    ")\n",
    "print(f\"Observed: {CLs_obs}, Expected: {CLs_exp}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Returning the observed** $\\mathrm{CL}_{s}$, $\\mathrm{CL}_{s+b}$, **and** $\\mathrm{CL}_{b}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed CL_s: 0.052515541856109765, CL_sb: 0.023324961200974572, CL_b: 0.44415349012077077\n"
     ]
    }
   ],
   "source": [
    "CLs_obs, p_values = pyhf.infer.hypotest(\n",
    "    test_mu, data, model, test_stat=\"qtilde\", return_tail_probs=True\n",
    ")\n",
    "print(f\"Observed CL_s: {CLs_obs}, CL_sb: {p_values[0]}, CL_b: {p_values[1]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A reminder that \n",
    "$$\n",
    "\\mathrm{CL}_{s} = \\frac{\\mathrm{CL}_{s+b}}{\\mathrm{CL}_{b}} = \\frac{p_{s+b}}{1-p_{b}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert CLs_obs == p_values[0] / p_values[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Returning the expected** $\\mathrm{CL}_{s}$ **band values**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed CL_s: 0.052515541856109765\n",
      "\n",
      "Expected CL_s(-2 σ): 0.0026064088679947964\n",
      "Expected CL_s(-1 σ): 0.013820657528619273\n",
      "Expected CL_s      : 0.06445521290832805\n",
      "Expected CL_s(1 σ): 0.23526103626937836\n",
      "Expected CL_s(2 σ): 0.5730418174887743\n"
     ]
    }
   ],
   "source": [
    "CLs_obs, CLs_exp_band = pyhf.infer.hypotest(\n",
    "    test_mu, data, model, test_stat=\"qtilde\", return_expected_set=True\n",
    ")\n",
    "print(f\"Observed CL_s: {CLs_obs}\\n\")\n",
    "for p_value, n_sigma in enumerate(np.arange(-2, 3)):\n",
    "    print(\n",
    "        \"Expected CL_s{}: {}\".format(\n",
    "            \"      \" if n_sigma == 0 else f\"({n_sigma} σ)\",\n",
    "            CLs_exp_band[p_value],\n",
    "        )\n",
    "    )"
   ]
  }
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