Gura_QNC_Frequentist Vs Bayesian Approaches.ipynb

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        "<a href=\"https://colab.research.google.com/github/hansgura/NGG6050/blob/main/Gura_QNC_Frequentist%20Vs%20Bayesian%20Approaches.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "import scipy.stats as st\n",
        "import numpy as np\n"
      ]
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        "N = 10000\n",
        "false_positive_rate = 0.05\n",
        "false_negative_rate = 0\n",
        "\n",
        "print(f'The probability of obtaining the data under the Null Hypothesis = {false_positive_rate}')\n",
        "\n",
        "is_infected = st.binom.rvs(1, 0.5, size=N)\n",
        "\n",
        "num_infected = is_infected.sum()\n",
        "\n",
        "is_positive = np.copy(is_infected)\n",
        "\n",
        "is_positive[is_infected==0] = st.binom.rvs(1, false_positive_rate, size=N-num_infected)\n",
        "\n",
        "p_is_infected_given_is_positive = (np.logical_and(is_infected==1, is_positive==1).sum())/is_positive.sum()\n",
        "print(f'Probaility infected given a positive test = {p_is_infected_given_is_positive:.4f}')\n",
        "\n",
        "infected_proportions = np.arange(0.0, 1.1, 0.1)\n",
        "for idx, val in enumerate(infected_proportions):\n",
        "\n",
        "\n",
        "   is_infected = st.binom.rvs(1, val, size=N)\n",
        "\n",
        "   num_infected = is_infected.sum()\n",
        "\n",
        "   is_positive = np.copy(is_infected)\n",
        "\n",
        "   is_positive[is_infected==0] = st.binom.rvs(1, false_positive_rate, size=N-num_infected)\n",
        "\n",
        "   p_is_infected_given_is_positive = (np.logical_and(is_infected==1, is_positive==1).sum())/is_positive.sum()\n",
        "\n",
        "   p_data_given_hypothesis = 1 - false_negative_rate\n",
        "   p_hypothesis = val\n",
        "   p_data = is_positive.sum()/is_positive.size\n",
        "   p_hypothesis_given_data = (p_data_given_hypothesis * p_hypothesis) / p_data\n",
        "\n",
        "   print(f'Infection rate={val:.1f}, proportion infected given a positive test={p_is_infected_given_is_positive:.3f}, Posterior={p_hypothesis_given_data:.3f}')\n"
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          "text": [
            "The probability of obtaining the data under the Null Hypothesis = 0.05\n",
            "Probaility infected given a positive test = 0.9538\n",
            "Infection rate=0.0, proportion infected given a positive test=0.000, Posterior=0.000\n",
            "Infection rate=0.1, proportion infected given a positive test=0.673, Posterior=0.680\n",
            "Infection rate=0.2, proportion infected given a positive test=0.829, Posterior=0.823\n",
            "Infection rate=0.3, proportion infected given a positive test=0.905, Posterior=0.894\n",
            "Infection rate=0.4, proportion infected given a positive test=0.932, Posterior=0.920\n",
            "Infection rate=0.5, proportion infected given a positive test=0.955, Posterior=0.941\n",
            "Infection rate=0.6, proportion infected given a positive test=0.969, Posterior=0.967\n",
            "Infection rate=0.7, proportion infected given a positive test=0.980, Posterior=0.976\n",
            "Infection rate=0.8, proportion infected given a positive test=0.988, Posterior=0.986\n",
            "Infection rate=0.9, proportion infected given a positive test=0.993, Posterior=0.989\n",
            "Infection rate=1.0, proportion infected given a positive test=1.000, Posterior=1.000\n"
          ]
        }
      ]
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