{
 "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: 0.05290116224852556, Expected: 0.06445521290832805\n"
     ]
    }
   ],
   "source": [
    "pdf = pyhf.simplemodels.hepdata_like(signal_data=[12.0, 11.0], bkg_data=[50.0, 52.0], bkg_uncerts=[3.0, 7.0])\n",
    "CLs_obs, CLs_exp = pyhf.infer.hypotest(1.0, [51, 48] + pdf.config.auxdata, pdf, return_expected=True)\n",
    "print('Observed: {}, Expected: {}'.format(CLs_obs, 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: 0.05290116224852556, CL_sb: 0.023599998519978738, CL_b: 0.4461149342826869\n"
     ]
    }
   ],
   "source": [
    "CLs_obs, p_values = pyhf.infer.hypotest(1.0, [51, 48] + pdf.config.auxdata, pdf, return_tail_probs=True)\n",
    "print('Observed CL_s: {}, CL_sb: {}, CL_b: {}'.format(CLs_obs, p_values[0], 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: 0.05290116224852556\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(1.0, [51, 48] + pdf.config.auxdata, pdf, return_expected_set=True)\n",
    "print('Observed CL_s: {}\\n'.format(CLs_obs))\n",
    "for p_value, n_sigma in enumerate(np.arange(-2,3)):\n",
    "    print('Expected CL_s{}: {}'.format('      ' if n_sigma==0 else '({} σ)'.format(n_sigma),CLs_exp_band[p_value]))"
   ]
  }
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