{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 7:  Confidence Intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### In the exercises of this sheet we consider a measured sample of events after applying quality cuts to separate signal from background events. The total number of observed events follows a Poisson distribution:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "  P(n_0|\\nu_t) = \\frac{\\nu_t^{n_0} e^{-\\nu_t}}{n_0!},\n",
    "\\end{equation}\n",
    "$n_0$ is the number of observed events after the quality cuts, and $\\nu_t=\\nu_{t,S}+\\nu_{t,B}$ is the true number of events expected to pass the cuts, where $\\nu_{t,S}$ is the contribution from true signal events and $\\nu_{t,B}$ the background remaining after the cuts.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "from scipy.stats import poisson, norm\n",
    "from scipy.interpolate import interp1d as scipy_interp1d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 7.1: Significance (voluntary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### For a specific experiment, the background is expected to be $\\nu_{t,B}=1$ while the measurement is $n_0=3$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### a) How often do you expect to measure $n_0$ or more events if you expect only background?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### b)  What is the corresponding significance?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### c)  Is the measurement compatible with a statistical fluctuation of the background, or is there an evidence (defined as significance $\\ge 3\\,\\sigma$ )or a discovery of the signal ($\\ge 5\\,\\sigma$)?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### d) How many events would have to be observed to reach the evidence and discovery thresholds?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function to calculate the probability to observe n_0 or more events, if the expected number is mu\n",
    "# Hint: Have a look at the methods of scipy.stats.poisson and in particular the method poisson.cdf.\n",
    "\n",
    "def pPoisson(n_0, mu):\n",
    "    # TODO: Calculate the probability to observe n_0 or more events\n",
    "    #       and also determine the necessary number of observed events for a discovery / evidence.\n",
    "    # Hint: Take a look at the method scipy.stats.norm.ppf to calculate the significances in terms of standard deviations.\n",
    "    pass\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def exercise7_1():\n",
    "    # TODO: Implement your solution to this exercise\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 7.2: Confidence intervals (obligatory)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) Frequentist approach (Neyman construction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This classical approach can be used to determine a confidence interval or lower/upper limit, respectively, at a given confidence level (CL).\n",
    "\n",
    "First, let us assume that the background is negligible: $\\nu_{t,B}=0$. Using the frequentist approach, we will compute a $90\\%$ CL upper \n",
    "limit on $\\nu_t=\\nu_{t,S}$ if the measured number of event is $n_0 = 3$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Determine the $90\\,\\%$ CL upper limit $\\nu_{UL}$ such that:\n",
    "  \\begin{eqnarray}\n",
    "    \\label{eqs}\n",
    "    \\sum_{n=0}^{n_0} P(n|\\nu_{UL}) & = & 0.10.\n",
    "  \\end{eqnarray}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Now, consider the realistic case with background, i.e., $\\nu_{t,B} > 0$:\n",
    "   \n",
    "   * Compute the $90\\%$ CL upper limits on $\\nu_{t,S}$ as function of $\\nu_{t,B}$.\n",
    "     By convention, the upper limit on $\\nu_{t,S}$ is the limit which would be obtained for $\\nu_{t,S}$ without background minus the number of expected background events,\n",
    "     i.e., $\\nu_{t,B}$, ($CL_{SB}$-limit).\n",
    "     This is done automatically when calling the function `get_upper_poisson_limit` (defined below) with $\\nu_{t,B} > 0$.\n",
    "     $CL_{SB}$ is the confidence level with respect to the signal-plus-background hypothesis and a measure for the compatibility of the experiment with this hypothesis.\n",
    "     **What makes this procedure inconvenient?**\n",
    "  \n",
    "   * Make a plot of the $CL_{SB}$-limit on $\\nu_{t,S}$ as a function of $\\nu_{t,B}$ varying $n_0$ from 0 to 5 (draw all six curves in the same plot).\n",
    "     \n",
    "   * Utilizing the function `get_upper_poisson_limit_normalized` (also defined below) the limit is calculated using the  $CL_{S}$-method:\n",
    "     $CL_{S} = CL_{SB}/CL_{B}$. $CL_{B}$ is a measure for the compatibility with the background-only hypothesis.\n",
    "     The $CL_{S}$-method provides a useful limit, even if the number of observed events is much smaller than the expected background.\n",
    "    \n",
    "   * Create also a plot of the $CL_{S}$-limit on $\\nu_{t,S}$ as a function of $\\nu_{t,B}$ varying $n_0$ from 0 to 5 (draw all six curves in the same plot).\n",
    "   \n",
    "   \n",
    "**HINT:** Read and understand the functions defined below. Use them to solve the following tasks! They use the following definitions:\n",
    "  \n",
    "\\begin{eqnarray}\n",
    "  CL_{SB} & = & \\sum_{n=0}^{n_0} P(n|\\nu_{t,S}+\\nu_{t,B}), \\\\\n",
    "  CL_{B} & = & \\sum_{n=0}^{n_0} P(n|\\nu_{t,B}), \\\\\n",
    "  CL_{S} & = & CL_{SB}\\, /\\, CL_{B}.\n",
    "\\end{eqnarray}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_x(f, y0, x_min, x_max, kw_params=None, n_int=1000):\n",
    "    \"\"\"\n",
    "    Returns an approximation of the x value of the function f for a given y value (y0).\n",
    "    The paremeter params is a dictionary of keyword-value pairs, which are passed on to the function f.\n",
    "    Requires f beeing invertible (monotonic, ...) on the given invervall.\n",
    "    \"\"\"\n",
    "    \n",
    "    x = np.linspace(x_min, x_max, n_int)\n",
    "\n",
    "    if kw_params is None:\n",
    "        y = np.array([f(x_i) for x_i in x])\n",
    "    else:\n",
    "        y = np.array([f(x_i, **kw_params) for x_i in x])\n",
    "    \n",
    "    f_inv = scipy_interp1d(y, x, fill_value=\"extrapolate\")\n",
    "    \n",
    "    return f_inv(y0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $90\\,\\%$ CL Upper Limit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(6.68078975)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Die 0.9000004165502344-Obergrenze ist bei nu_t=6.680789748072546\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import minimize\n",
    "from scipy.special import factorial\n",
    "\n",
    "def exercise7_2a_90cl_upper_limit(method=0):\n",
    "    n0 = 3\n",
    "    def P(n, nu):\n",
    "        return nu**n*np.exp(-nu)/factorial(n)\n",
    "    m = get_x(lambda nu_ul: np.sum(P(np.arange(4),nu_ul)), 0.1, 0, 10)\n",
    "    display(m)\n",
    "    print(f\"Die {1-np.sum(P(np.arange(4), m))}-Obergrenze ist bei nu_t={m}\")\n",
    "\n",
    "exercise7_2a_90cl_upper_limit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $CL_{SB}$ Limit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_poisson_probability(nu_t_s, nu_t_b, n0):\n",
    "    \"\"\"\n",
    "    Calculates the probability to observe n0 or less signal events for given expected signal and expected background\n",
    "    @param nu_t_s: expected signal\n",
    "    @param nu_t_b: number of expected background events\n",
    "    @param n0: number of observed events\n",
    "    \"\"\"\n",
    "    return poisson.cdf(k=n0, mu=nu_t_s + nu_t_b, loc=0)\n",
    "\n",
    "def get_upper_poisson_limit(n0, nu_t_b, cl):\n",
    "    \"\"\"\n",
    "    returns the upper poisson limit (classical)\n",
    "    @param n0: number of observed events\n",
    "    @param nu_t_b: expected background\n",
    "    @param cl: confidence level\n",
    "    \"\"\"\n",
    "    \n",
    "    # targeted pvalue\n",
    "    p_val = 1 - cl\n",
    "    \n",
    "    # probability to observe n0 or less events\n",
    "    \n",
    "    # interpolation limits\n",
    "    x_min = -1\n",
    "    x_max = 10 * (n0 + 1)\n",
    "    \n",
    "    limit = get_x(\n",
    "        f=get_poisson_probability,\n",
    "        y0=p_val,\n",
    "        x_min=x_min,\n",
    "        x_max=x_max,\n",
    "        kw_params={\"nu_t_b\": nu_t_b, \"n0\": n0},\n",
    "    )\n",
    "    return limit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def exercise7_2a_Csb():\n",
    "    nu_t_b_space = np.linspace(0,8,100)\n",
    "\n",
    "    for n0 in range(6):\n",
    "        plt.plot(nu_t_b_space, [get_upper_poisson_limit(n0, nu_t_b, 0.9) for nu_t_b in nu_t_b_space])\n",
    "    plt.show()\n",
    "    \n",
    "    # TODO: Use the predefined funcitons above to solve the exercise.\n",
    "    # TODO: Create plots for 100 points varying the background from 0 to 8\n",
    "exercise7_2a_Csb()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $CL_{S}$ Limit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_normalized_probability(nu_t_s, nu_t_b, n0):\n",
    "    \"\"\"\n",
    "    Calculates the probability, to observe n0 or less signal events for given expected signal and expected background\n",
    "    @param nu_t_s: expected signal\n",
    "    @param nu_t_b: number of expected background events\n",
    "    @param n0: number of observed events\n",
    "    \"\"\"\n",
    "    \n",
    "    # p_value for signal+background hypothesis\n",
    "    p1 = poisson.cdf(k=n0, mu=nu_t_b + nu_t_s, loc=0)\n",
    "    \n",
    "    # p_value for background only hypothesis\n",
    "    p2 = poisson.cdf(k=n0, mu=nu_t_b)\n",
    "    \n",
    "    return p1 / p2\n",
    "\n",
    "def get_upper_poisson_limit_normalized(n0, nu_t_b, cl):\n",
    "    \"\"\"\n",
    "    Returns the normalized upper poisson limit (classical)\n",
    "    @param n0: number of observed events\n",
    "    @param nu_t_b: expected background\n",
    "    @param cl: confidence level\n",
    "    \"\"\"\n",
    "    \n",
    "    # targeted pvalue\n",
    "    p_val = 1 - cl\n",
    "    \n",
    "    # interpolation limits\n",
    "    x_min = -1\n",
    "    x_max = 10 * (n0 + 1)\n",
    "    \n",
    "    limit = get_x(\n",
    "        f=get_normalized_probability,\n",
    "        y0=p_val,\n",
    "        x_min=x_min,\n",
    "        x_max=x_max,\n",
    "        kw_params={\"nu_t_b\": nu_t_b, \"n0\": n0},\n",
    "    )\n",
    "    \n",
    "    return limit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def exercise7_2a_Cs():\n",
    "    # TODO: Use the predefined funcitons above to solve the exercise.\n",
    "    # TODO: Create plots for 100 points varying the background from 0 to 8\n",
    "    nu_t_b_space = np.linspace(0,8,100)\n",
    "\n",
    "    for n0 in range(6):\n",
    "        plt.plot(nu_t_b_space, [get_upper_poisson_limit_normalized(n0, nu_t_b, 0.9) for nu_t_b in nu_t_b_space])\n",
    "    plt.show()\n",
    "    \n",
    "exercise7_2a_Cs()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Likelihood approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood function for a Poisson process for one single measurement is:\n",
    "\n",
    "  $ L(n_0|\\nu_t) = \\frac{\\nu_t^{n_0} e^{-\\nu_t}}{n_0!}. $\n",
    "\n",
    "where $n_0=3$ is the number of measured events.\n",
    "\n",
    "- Draw the curve $-2\\ln L$ as function of $\\nu_t$, performing a scan \n",
    "over a meaningful range of values. Where is the minimum, $-2\\ln L_{min}$, of this curve?\n",
    "- Calculate the boundaries of the confidence interval at $68\\%$ CL. These are the points for which $2\\cdot \\Delta \\ln L = 1$, where $\\Delta \\ln L$ is defined as $\\ln L_{min} - \\ln L$.\n",
    "- Determine the $90\\%$ CL upper limit, i.e. the point with $\\nu_t>n_0$ for which $2\\cdot \\Delta \\ln L = (1.28)^{2}$.\n",
    "- Plot the likelihood function and the convidence intervals of interest.\n",
    "\n",
    "\n",
    "**Note:** To translate a CL into the proper $\\Delta \\ln L$ cut for a **one-sided** interval, you can use the equation\n",
    "\n",
    "$ 2 \\cdot \\Delta \\ln L = (\\sqrt{2} \\cdot \\texttt{erfinv}(2 \\cdot CL - 1))^2 $,\n",
    "\n",
    "where `erfinv` is the inverse of the error function as provided for instance by `scipy` as `scipy.special.erfinv`.\n",
    "\n",
    "The term which is passed on as argument to the `erfinv` function is equal to $1 - 2 \\cdot{} (1 - CL) = 2 \\cdot{} CL - 1$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import erfinv\n",
    "from scipy.optimize import minimize, root_scalar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hint:** You can use the `root_scalar` function provided by `scipy.optimize.root_scalar` to find the intersects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 * DeltaL = (\\sqrt(2) * erfinv(0.68...))^2 = (1.0000000000060216)^2\n"
     ]
    }
   ],
   "source": [
    "print(f\"2 * DeltaL = (\\sqrt(2) * erfinv(0.68...))^2 = ({np.sqrt(2) * erfinv(0.68268949214)})^2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 * DeltaL = (\\sqrt(2) * erfinv(2 * 0.9 - 1))^2 = (1.2815515655446006)^2\n"
     ]
    }
   ],
   "source": [
    "print(f\"2 * DeltaL = (\\sqrt(2) * erfinv(2 * 0.9 - 1))^2 = ({np.sqrt(2) * erfinv(2 * 0.90 -1)})^2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def negative_log_likelihood(nu_t, n0):\n",
    "    \"\"\"\n",
    "    Returns 2 * negative log likelihood for poisson pdf\n",
    "    @param nu_t: number of expected events\n",
    "    @param n0: number of observed events\n",
    "    @return: NNL\n",
    "    \"\"\"\n",
    "    \n",
    "    return -2. * poisson.logpmf(k=n0, mu=nu_t, loc=0)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  message: Optimization terminated successfully.\n",
      "  success: True\n",
      "   status: 0\n",
      "      fun: 2.9918452064474517\n",
      "        x: [ 3.000e+00]\n",
      "      nit: 0\n",
      "      jac: [ 0.000e+00]\n",
      " hess_inv: [[1]]\n",
      "     nfev: 2\n",
      "     njev: 1\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "68% confidence in [1.5794271066892471;5.090180265806246]\n",
      "90% confidence in [0,5.80210060243859]\n"
     ]
    }
   ],
   "source": [
    "def exercise7_2b():\n",
    "    minimum = minimize(lambda nu_t: negative_log_likelihood(nu_t, 3), x0=(3,))\n",
    "    print(minimum)\n",
    "\n",
    "    t = np.linspace(0,10,200)\n",
    "    plt.plot(t, negative_log_likelihood(t, 3))\n",
    "    plt.plot(t, np.full(t.shape, minimum.x[0]),\"--\")\n",
    "    plt.plot(t, np.full(t.shape, minimum.x[0]+1),\"--\")\n",
    "    plt.plot(t, np.full(t.shape, minimum.x[0]+(1.28)**2),\"--\")\n",
    "    plt.show()\n",
    "\n",
    "    a1 = minimize(lambda nu_t: np.abs(negative_log_likelihood(nu_t, 3)-minimum.x[0]-1), x0=(2,)).x[0]\n",
    "    b1 = minimize(lambda nu_t: np.abs(negative_log_likelihood(nu_t, 3)-minimum.x[0]-1), x0=(6,)).x[0]\n",
    "    print(f\"68% confidence in [{a1};{b1}]\")\n",
    "\n",
    "    a1 = minimize(lambda nu_t: np.abs(negative_log_likelihood(nu_t, 3)-minimum.x[0]-1.28**2), x0=(2,)).x[0]\n",
    "    b1 = minimize(lambda nu_t: np.abs(negative_log_likelihood(nu_t, 3)-minimum.x[0]-1.28**2), x0=(6,)).x[0]\n",
    "    print(f\"90% confidence in [0,{b1}]\")\n",
    "\n",
    "    # TODO: Implement your solution:\n",
    "    #       - Get the minimum of the likelihood\n",
    "    #       - Get the 68% confidence level interval (points where the the likelihood is by 1 higher than its minimum value\n",
    "    #       - Get the 90% confidence level upper limit\n",
    "    #       - Plot the likelihood function\n",
    "\n",
    "exercise7_2b()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Bayesian approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Bayesian posterior probability $P(\\nu_t|n_0)$ is given by the Bayes theorem:\n",
    "\n",
    "$$P(\\nu_t|n_0)=\\frac{L(n_0|\\nu_t)\\ \\Pi(\\nu_t)}{\\int_{\\mathrm{all}\\,\\, \\nu_t} L(n_0|\\nu_t)\\ \\Pi(\\nu_t) d\\nu_t}.$$\n",
    "\n",
    "$\\Pi(\\nu_t)$ is called the prior probability on $\\nu_t$ and describes our prior belief about the distribution of this parameter.\n",
    "\n",
    "Try two different priors and compare the results:\n",
    "\n",
    "   i) $\\Pi(\\nu_t) = const.$ for $\\nu_t>0$ and $0$ otherwise,\n",
    "   \n",
    "   ii) $\\Pi(\\nu_t)$ proportional to $1/\\nu_t$ for $\\nu_t>0$ and $0$ otherwise.\n",
    "\n",
    "\n",
    "\n",
    "- Compute and draw the posterior probability for $n_0=3$ and $\\nu_{t,B}=0$.\n",
    "- What are the $90\\%$ credibility upper limits?\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import quad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood_pdf(nu_t,  n0):\n",
    "    \"\"\"\n",
    "    Returns likelihood for poisson pdf\n",
    "    @param nu_t: number of expected events\n",
    "    @param n0: number of observed events\n",
    "    @return: NNL\n",
    "    \"\"\"\n",
    "    \n",
    "    return poisson.pmf(k=n0, mu=nu_t, loc=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prior_flat_function(nu_t):\n",
    "    return nu_t > 0\n",
    "\n",
    "    \n",
    "def prior_inverse_function(nu_t):\n",
    "    return (1/nu_t) * (nu_t > 0) \n",
    "\n",
    "\n",
    "def posterior_function_with_flat_prior(nu_t_list, n0):\n",
    "    return np.array([likelihood_pdf(nu_t,  n0)*prior_flat_function(nu_t)/(quad(lambda tx :likelihood_pdf(tx,  n0)*prior_flat_function(tx), 0,np.inf)[0]) for nu_t in nu_t_list])\n",
    " \n",
    "  \n",
    "def posterior_function_with_inverse_prior(nu_t_list, n0):\n",
    "    return np.array([likelihood_pdf(nu_t,  n0)*prior_inverse_function(nu_t)/(quad(lambda tx :likelihood_pdf(tx,  n0)*prior_inverse_function(tx), 0,np.inf)[0]) for nu_t in nu_t_list])\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Die 0.8999999996988178-Obergrenze ist bei nu_t=6.680783063426109\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33333333333333687\n",
      "Die 0.8999999994848809-Obergrenze ist bei nu_t=5.322320330383766\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def exercise7_2c():\n",
    "    t = np.linspace(0,10,30)\n",
    "    plt.plot(t,posterior_function_with_flat_prior(t,3))\n",
    "    div = quad(lambda tx :likelihood_pdf(tx,  3)*prior_flat_function(tx), 0, np.inf)[0]\n",
    "    percentage = lambda x: quad(lambda tx :likelihood_pdf(tx,  3)*prior_flat_function(tx), 0, x)[0] / div\n",
    "    m = minimize(lambda x: np.abs(percentage(x)-0.9), x0=(4,) )\n",
    "    print(f\"Die {percentage(m.x[0])}-Obergrenze ist bei nu_t={m.x[0]}\")\n",
    "    plt.axvline(m.x[0])\n",
    "    plt.show()\n",
    "\n",
    "    t = np.linspace(0.1,10,30)\n",
    "    plt.plot(t,posterior_function_with_inverse_prior(t,3))\n",
    "    div = quad(lambda tx :likelihood_pdf(tx,  3)*prior_inverse_function(tx), 0, np.inf)[0]\n",
    "    print(div)\n",
    "    percentage = lambda x: quad(lambda tx :likelihood_pdf(tx,  3)*prior_inverse_function(tx), 0, x)[0] / div\n",
    "    m = minimize(lambda x: np.abs(percentage(x)-0.9), x0=(4,) )\n",
    "    print(f\"Die {percentage(m.x[0])}-Obergrenze ist bei nu_t={m.x[0]}\")\n",
    "    plt.axvline(m.x[0])\n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "\n",
    "    # TODO: Implement your solution:\n",
    "    #       - Calculate the posterior probabilities\n",
    "    #       - Draw the posterior probabilities\n",
    "    #       - Determine the 90 % credibility upper limits\n",
    "\n",
    "\n",
    "exercise7_2c()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Finally, compare the upper limits of the methods a), b), c) for $n_0=3$ and $\\nu_{t,B}=0$**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "nu_t_a  = 6.680789748072546\n",
    "nu_t_b  = 5.80210060243859\n",
    "nu_t_c1 = 6.680783063426109\n",
    "nu_t_c2 = 5.322320330383766"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Obergrenze bei inversem Prior ist minimal."
   ]
  }
 ],
 "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": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}