{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lecture 3\n",
    "## Likelihoods & numerical minimizer fitting\n",
    "_(Written by Jean-Loup Tastet, 2019-02-11)_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import division # For those using Python 2, to avoid having 2/3==0.\n",
    "from __future__ import print_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.random import rand, seed # Uniform RNG\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.colors # To create custom colormaps\n",
    "from iminuit import Minuit # The Minuit minimizer, from the ROOT project"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the **normalized** PDF $f(x; \\alpha, \\beta)$ over $[-1, +1]$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x; \\alpha, \\beta) = \\frac{1 + \\alpha x + \\beta x^2}{2 + \\frac{2}{3} \\beta} \\qquad x \\in [-1, +1]$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Properly normalized PDF, returning zero outside the allowed range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pdf(x, alpha, beta):\n",
    "    in_interval = (x >= -1) & (x <= +1)\n",
    "    # Value inside the interval. Outside, we return zero.\n",
    "    val = (1 + alpha*x + beta*x**2) / (2 + (2/3)*beta)\n",
    "    return np.where(in_interval, val, 0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's write a convenience function to create a PDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_pdf(alpha, beta):\n",
    "    # Return a function depending only on x.\n",
    "    return lambda x: pdf(x, alpha, beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "true_alpha = 0.6\n",
    "true_beta  = 0.5\n",
    "f = make_pdf(true_alpha, true_beta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample from $f(x; \\alpha, \\beta)$ using Monte-Carlo rejection sampling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to know an upper bound on $f(x; \\alpha, \\beta)$.\n",
    "\n",
    "Here, we have an analytical value. If $\\beta < 0$, it is located at $-\\frac{\\alpha}{2\\beta}$, otherwise it is at one of the edges $x = \\pm 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pdf_maximum(alpha, beta):\n",
    "    f = make_pdf(alpha, beta)\n",
    "    return f(-alpha/(2*beta)) if beta < 0 else max(f(-1), f(+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample(Npoints, interval, f, f_max, batchsize=None):\n",
    "    if batchsize is None:\n",
    "        batchsize = Npoints // 2 # Integer division\n",
    "    xmin, xmax = interval\n",
    "    x = np.zeros(Npoints)\n",
    "    N = 0\n",
    "    while N < Npoints:\n",
    "        # Draw one batch of uniformly distributed points in [xmin, xmax]\n",
    "        this_batch_size = min(batchsize, Npoints - N)\n",
    "        batch = xmin + rand(this_batch_size) * (xmax-xmin)\n",
    "        # Do rejection sampling for each point\n",
    "        accepted = f(batch) > (rand(this_batch_size) * f_max)\n",
    "        # Count the accepted points and add them to the output array\n",
    "        N_accepted = np.sum(accepted)\n",
    "        x[N:N+N_accepted] = batch[accepted]\n",
    "        N += N_accepted\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_from_pdf(Npoints, alpha, beta, **kwargs):\n",
    "    f = make_pdf(alpha, beta)\n",
    "    f_max = pdf_maximum(alpha, beta)\n",
    "    return sample(Npoints, (-1, +1), f, f_max, **kwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check that our Monte-Carlo gives meaningful results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Npoints = 2000\n",
    "data = sample_from_pdf(Npoints, true_alpha, true_beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 372,
       "width": 494
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_mc_check, ax_mc_check = plt.subplots(figsize=(8,6))\n",
    "x_range = np.linspace(-1, +1, 200)\n",
    "ax_mc_check.plot(x_range, f(x_range), 'k-', label='True PDF')\n",
    "# The `density=True` argument automatically normalizes the histogram\n",
    "# so that it can be interpreted as a probability density.\n",
    "ax_mc_check.hist(data, density=True, label='MC data')\n",
    "ax_mc_check.set_xlabel('$x$')\n",
    "ax_mc_check.legend()\n",
    "ax_mc_check.autoscale(enable=True, axis='x', tight=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems to work!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum likelihood estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generic log-likelihood definition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def llh(data, pdf):\n",
    "    return np.sum(np.log(pdf(data)), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a target function $-2\\mathrm{LLH}(\\alpha, \\beta)$ which only depends on $\\alpha$ and $\\beta$, and has a minimum where the likelihood has a maximum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_target(data):\n",
    "    return lambda alpha, beta: -2*llh(data, make_pdf(alpha, beta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "target = make_target(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's minimize!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.7/site-packages/ipykernel_launcher.py:1: InitialParamWarning: Parameter alpha does not have initial value. Assume 0.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/usr/lib/python3.7/site-packages/ipykernel_launcher.py:1: InitialParamWarning: Parameter alpha is floating but does not have initial step size. Assume 1.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/usr/lib/python3.7/site-packages/ipykernel_launcher.py:1: InitialParamWarning: Parameter beta does not have initial value. Assume 0.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/usr/lib/python3.7/site-packages/ipykernel_launcher.py:1: InitialParamWarning: Parameter beta is floating but does not have initial step size. Assume 1.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n",
      "/usr/lib/python3.7/site-packages/ipykernel_launcher.py:1: InitialParamWarning: errordef is not given. Default to 1.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "minimizer = Minuit(target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td title=\"Minimum value of function\">FCN = 2596.7825517871224</td>\n",
       "        <td title=\"Total number of call to FCN so far\">TOTAL NCALL = 42</td>\n",
       "        <td title=\"Number of call in last migrad\">NCALLS = 42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td title=\"Estimated distance to minimum\">EDM = 3.946446998385696e-06</td>\n",
       "        <td title=\"Maximum EDM definition of convergence\">GOAL EDM = 1e-05</td>\n",
       "        <td title=\"Error def. Amount of increase in FCN to be defined as 1 standard deviation\">\n",
       "        UP = 1.0</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table>\n",
       "    <tr>\n",
       "        <td align=\"center\" title=\"Validity of the migrad call\">Valid</td>\n",
       "        <td align=\"center\" title=\"Validity of parameters\">Valid Param</td>\n",
       "        <td align=\"center\" title=\"Is Covariance matrix accurate?\">Accurate Covar</td>\n",
       "        <td align=\"center\" title=\"Positive definiteness of covariance matrix\">PosDef</td>\n",
       "        <td align=\"center\" title=\"Was covariance matrix made posdef by adding diagonal element\">Made PosDef</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td align=\"center\" title=\"Was last hesse call fail?\">Hesse Fail</td>\n",
       "        <td align=\"center\" title=\"Validity of covariance\">HasCov</td>\n",
       "        <td align=\"center\" title=\"Is EDM above goal EDM?\">Above EDM</td>\n",
       "        <td align=\"center\"></td>\n",
       "        <td align=\"center\" title=\"Did last migrad call reach max call limit?\">Reach calllim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">True</td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "        <td align=\"center\"></td>\n",
       "        <td align=\"center\" style=\"background-color:#92CCA6\">False</td>\n",
       "    </tr>\n",
       "</table>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td><a href=\"#\" onclick=\"$('#ggPgmgiWVv').toggle()\">+</a></td>\n",
       "        <td title=\"Variable name\">Name</td>\n",
       "        <td title=\"Value of parameter\">Value</td>\n",
       "        <td title=\"Hesse error\">Hesse Error</td>\n",
       "        <td title=\"Minos lower error\">Minos Error-</td>\n",
       "        <td title=\"Minos upper error\">Minos Error+</td>\n",
       "        <td title=\"Lower limit of the parameter\">Limit-</td>\n",
       "        <td title=\"Upper limit of the parameter\">Limit+</td>\n",
       "        <td title=\"Is the parameter fixed in the fit\">Fixed?</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>0</td>\n",
       "        <td>alpha</td>\n",
       "        <td>0.564506</td>\n",
       "        <td>0.0520685</td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>1</td>\n",
       "        <td>beta</td>\n",
       "        <td>0.533814</td>\n",
       "        <td>0.103877</td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td>No</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<pre id=\"ggPgmgiWVv\" style=\"display:none;\">\n",
       "<textarea rows=\"10\" cols=\"50\" onclick=\"this.select()\" readonly>\n",
       "\\begin{tabular}{|c|r|r|r|r|r|r|r|c|}\n",
       "\\hline\n",
       " & Name & Value & Hesse Error & Minos Error- & Minos Error+ & Limit- & Limit+ & Fixed?\\\\\n",
       "\\hline\n",
       "0 & $\\alpha$ & 0.564506 & 0.0520685 &  &  &  &  & No\\\\\n",
       "\\hline\n",
       "1 & $\\beta$ & 0.533814 & 0.103877 &  &  &  &  & No\\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "</textarea>\n",
       "</pre>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<hr>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "({'fval': 2596.7825517871224,\n",
       "  'edm': 3.946446998385696e-06,\n",
       "  'nfcn': 42,\n",
       "  'up': 1.0,\n",
       "  'is_valid': True,\n",
       "  'has_valid_parameters': True,\n",
       "  'has_accurate_covar': True,\n",
       "  'has_posdef_covar': True,\n",
       "  'has_made_posdef_covar': False,\n",
       "  'hesse_failed': False,\n",
       "  'has_covariance': True,\n",
       "  'is_above_max_edm': False,\n",
       "  'has_reached_call_limit': False},\n",
       " [{'number': 0,\n",
       "   'name': 'alpha',\n",
       "   'value': 0.5645058564291071,\n",
       "   'error': 0.052068472299683415,\n",
       "   'is_const': False,\n",
       "   'is_fixed': False,\n",
       "   'has_limits': False,\n",
       "   'has_lower_limit': False,\n",
       "   'has_upper_limit': False,\n",
       "   'lower_limit': None,\n",
       "   'upper_limit': None},\n",
       "  {'number': 1,\n",
       "   'name': 'beta',\n",
       "   'value': 0.533814452696201,\n",
       "   'error': 0.10387652244722304,\n",
       "   'is_const': False,\n",
       "   'is_fixed': False,\n",
       "   'has_limits': False,\n",
       "   'has_lower_limit': False,\n",
       "   'has_upper_limit': False,\n",
       "   'lower_limit': None,\n",
       "   'upper_limit': None}])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimizer.migrad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<ValueView of Minuit at 5567744698c8>\n",
      "  alpha: 0.5645058564291071\n",
      "  beta: 0.533814452696201\n"
     ]
    }
   ],
   "source": [
    "print(minimizer.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the maximum likelihood:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum likelihood LLH = -1298.4\n"
     ]
    }
   ],
   "source": [
    "maxllh = -1/2 * minimizer.fval\n",
    "print('Maximum likelihood LLH = {:.1f}'.format(maxllh))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the parabolic error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td><a href=\"#\" onclick=\"$('#EiGwgkgtyo').toggle()\">+</a></td>\n",
       "        <td title=\"Variable name\">Name</td>\n",
       "        <td title=\"Value of parameter\">Value</td>\n",
       "        <td title=\"Hesse error\">Hesse Error</td>\n",
       "        <td title=\"Minos lower error\">Minos Error-</td>\n",
       "        <td title=\"Minos upper error\">Minos Error+</td>\n",
       "        <td title=\"Lower limit of the parameter\">Limit-</td>\n",
       "        <td title=\"Upper limit of the parameter\">Limit+</td>\n",
       "        <td title=\"Is the parameter fixed in the fit\">Fixed?</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>0</td>\n",
       "        <td>alpha</td>\n",
       "        <td>0.564506</td>\n",
       "        <td>0.0520683</td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>1</td>\n",
       "        <td>beta</td>\n",
       "        <td>0.533814</td>\n",
       "        <td>0.103876</td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td></td>\n",
       "        <td>No</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<pre id=\"EiGwgkgtyo\" style=\"display:none;\">\n",
       "<textarea rows=\"10\" cols=\"50\" onclick=\"this.select()\" readonly>\n",
       "\\begin{tabular}{|c|r|r|r|r|r|r|r|c|}\n",
       "\\hline\n",
       " & Name & Value & Hesse Error & Minos Error- & Minos Error+ & Limit- & Limit+ & Fixed?\\\\\n",
       "\\hline\n",
       "0 & $\\alpha$ & 0.564506 & 0.0520683 &  &  &  &  & No\\\\\n",
       "\\hline\n",
       "1 & $\\beta$ & 0.533814 & 0.103876 &  &  &  &  & No\\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "</textarea>\n",
       "</pre>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td><a onclick=\"$('#SzJHwiBITI').toggle()\" href=\"#\">+</a></td> <td>alpha</td> <td>beta</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>alpha</td> <td style=\"background-color:rgb(255,117,117)\">1.00</td> <td style=\"background-color:rgb(208,188,153)\">0.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td>beta</td> <td style=\"background-color:rgb(208,188,153)\">0.48</td> <td style=\"background-color:rgb(255,117,117)\">1.00</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<pre id=\"SzJHwiBITI\" style=\"display:none;\">\n",
       "<textarea rows=\"13\" cols=\"50\" onclick=\"this.select()\" readonly>\n",
       "%\\usepackage[table]{xcolor} % include this for color\n",
       "%\\usepackage{rotating} % include this for rotate header\n",
       "%\\documentclass[xcolor=table]{beamer} % for beamer\n",
       "\\begin{tabular}{|c|c|c|}\n",
       "\\hline\n",
       "\\rotatebox{90}{} & \\rotatebox{90}{$\\alpha$} & \\rotatebox{90}{$\\beta$}\\\\\n",
       "\\hline\n",
       "$\\alpha$ & \\cellcolor[RGB]{255,117,117} 1.00 & \\cellcolor[RGB]{208,188,153} 0.48\\\\\n",
       "\\hline\n",
       "$\\beta$ & \\cellcolor[RGB]{208,188,153} 0.48 & \\cellcolor[RGB]{255,117,117} 1.00\\\\\n",
       "\\hline\n",
       "\\end{tabular}\n",
       "</textarea>\n",
       "</pre>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[{'number': 0,\n",
       "  'name': 'alpha',\n",
       "  'value': 0.5645058564291071,\n",
       "  'error': 0.052068327674719854,\n",
       "  'is_const': False,\n",
       "  'is_fixed': False,\n",
       "  'has_limits': False,\n",
       "  'has_lower_limit': False,\n",
       "  'has_upper_limit': False,\n",
       "  'lower_limit': None,\n",
       "  'upper_limit': None},\n",
       " {'number': 1,\n",
       "  'name': 'beta',\n",
       "  'value': 0.533814452696201,\n",
       "  'error': 0.10387619711317195,\n",
       "  'is_const': False,\n",
       "  'is_fixed': False,\n",
       "  'has_limits': False,\n",
       "  'has_lower_limit': False,\n",
       "  'has_upper_limit': False,\n",
       "  'lower_limit': None,\n",
       "  'upper_limit': None}]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minimizer.hesse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<ErrorView of Minuit at 5567744698c8>\n",
      "  alpha: 0.052068327674719854\n",
      "  beta: 0.10387619711317195\n"
     ]
    }
   ],
   "source": [
    "print(minimizer.errors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Likelihood landscape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_range = np.linspace(-0.2, 1, num=100)\n",
    "beta_range  = np.linspace(   0, 1, num=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "aa, bb = np.meshgrid(alpha_range, beta_range, indexing='ij')\n",
    "aaa = aa[np.newaxis,:,:]\n",
    "bbb = bb[np.newaxis,:,:]\n",
    "xxx = data[:,np.newaxis,np.newaxis]\n",
    "ttt = make_target(xxx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "target_landscape = ttt(aa, bb)\n",
    "llh_landscape = -1/2 * target_landscape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fe94d876710>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 386,
       "width": 489
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dllh = 1/2 * np.sort(np.array([-1, -4, -9]))\n",
    "fig_landscape, ax_landscape = plt.subplots(figsize=(8,6))\n",
    "plot_landscape = ax_landscape.pcolormesh(aa, bb, llh_landscape, label='LLH')\n",
    "mval = minimizer.values\n",
    "ax_landscape.scatter([mval['alpha']], [mval['beta']], label='Minuit')\n",
    "ax_landscape.scatter([true_alpha], [true_beta], label='Truth')\n",
    "iso = maxllh + dllh\n",
    "# Hack to get black contours: create a uniform, black colormap.\n",
    "black_cmap = matplotlib.colors.ListedColormap(['black'])\n",
    "cs = ax_landscape.contour(aa, bb, llh_landscape, levels=iso, cmap=black_cmap)\n",
    "def fmt(llh):\n",
    "    return 'ΔLLH={:}'.format(llh-maxllh)\n",
    "ax_landscape.clabel(cs, cs.levels, inline=True, fmt=fmt, colors='k')\n",
    "ax_landscape.set_xlabel(r'$\\alpha$')\n",
    "ax_landscape.set_ylabel(r'$\\beta$')\n",
    "cbar_landscape = fig_landscape.colorbar(plot_landscape)\n",
    "cbar_landscape.ax.set_title('LLH')\n",
    "ax_landscape.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does the LLH landscape change when varying the true parameters $\\alpha$ and $\\beta$ or the number of points?"
   ]
  }
 ],
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