{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "f039bb78-5200-4bce-bdd3-f04f68fe344e",
      "metadata": {
        "id": "f039bb78-5200-4bce-bdd3-f04f68fe344e"
      },
      "source": [
        "## Computational - 10 points\n",
        "\n",
        "- Add your answers in the same cell as the code or add another cell by copy pasting the existing cell\n",
        "- Outputs from the answer key have been left as they are for your reference. My personal suggestion would be to create a new cell with the same code copied and make sure that the output coming is the same."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "77f7a13b-b904-4087-9301-2153c549c4d6",
      "metadata": {
        "id": "77f7a13b-b904-4087-9301-2153c549c4d6"
      },
      "outputs": [],
      "source": [
        "# Import the required libraries\n",
        "\n",
        "# TODO: import numpy below\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize\n",
        "from sklearn.datasets import load_breast_cancer\n",
        "import seaborn as sns"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "17cddbaf-9083-491d-986b-a32e4b0fd298",
      "metadata": {
        "id": "17cddbaf-9083-491d-986b-a32e4b0fd298"
      },
      "outputs": [],
      "source": [
        "# Load the breast cancer dataset from sklearn.datasets, read the documentation to see how to do the same\n",
        "data = load_breast_cancer()\n",
        "\n",
        "y = data.target  # Extracting the binary target variable"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "1b79fd98-c435-4997-a0ba-13d2f84ac353",
      "metadata": {
        "id": "1b79fd98-c435-4997-a0ba-13d2f84ac353"
      },
      "outputs": [],
      "source": [
        "# TODO: define the log likelihood function with the above given formula\n",
        "\n",
        "def log_likelihood(p, k):\n",
        "    return np.sum(y * np.log(p) + (1 - y) * np.log(1 - p))\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "8648ef50-fb17-483a-b18e-6d8e7a8daef7",
      "metadata": {
        "id": "8648ef50-fb17-483a-b18e-6d8e7a8daef7"
      },
      "outputs": [],
      "source": [
        "# Plot the log-likelihood function\n",
        "p_values = np.linspace(0.01, 0.99, 100)\n",
        "ll_values = [log_likelihood(p, y) for p in p_values]\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(p_values, ll_values, label='Log-Likelihood Curve')\n",
        "plt.xlabel('p')\n",
        "plt.ylabel('Log-Likelihood')\n",
        "plt.title('Log-Likelihood for Bernoulli Distribution')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "wLeWR07xOMPg",
        "outputId": "8b3a92ef-6f28-482c-a0ac-0e3c3edeebdd"
      },
      "id": "wLeWR07xOMPg",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Find its maximum using scipy\n",
        "result = minimize(lambda p: -log_likelihood(p, y), 0.5, bounds=[(0.01, 0.99)])\n",
        "print(f\"The maximum log-likelihood is at p = {result.x[0]:.2f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KRhJvqEMOTcv",
        "outputId": "239ab3d9-cb70-4091-fa88-ba3affeb0424"
      },
      "id": "KRhJvqEMOTcv",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The maximum log-likelihood is at p = 0.63\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8f9ea698-6198-49f3-b6ad-7bf18c8e03e8",
      "metadata": {
        "id": "8f9ea698-6198-49f3-b6ad-7bf18c8e03e8"
      },
      "source": [
        "# Data Cleaning and likelihood estimation - 10 points\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "3feb171f-6914-499b-be67-d9415f5145cb",
      "metadata": {
        "id": "3feb171f-6914-499b-be67-d9415f5145cb"
      },
      "outputs": [],
      "source": [
        "# Load the titanic dataset\n",
        "titanic = sns.load_dataset('titanic')\n",
        "\n",
        "# Drop rows where 'survived' is missing and 'age' is missing as we do not want information of people without an age\n",
        "titanic_cleaned = titanic.dropna(subset=['survived'])\n",
        "titanic_cleaned = titanic_cleaned.dropna(subset=['age'])\n",
        "num_survived = titanic_cleaned['survived'].sum()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "890c153c-506b-4bd9-98fb-ec573895521e",
      "metadata": {
        "id": "890c153c-506b-4bd9-98fb-ec573895521e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ea412865-a2ed-463d-dc6d-99f350f68f68"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The MLE for the probability of survival is: 0.41\n"
          ]
        }
      ],
      "source": [
        "total_passengers = len(titanic_cleaned)\n",
        "p_MLE = num_survived / total_passengers\n",
        "\n",
        "print(f\"The MLE for the probability of survival is: {p_MLE:.2f}\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Load the titanic dataset\n",
        "titanic = sns.load_dataset('titanic')\n",
        "\n",
        "print(f\"Count of Titanic dataset before cleaning: {len(titanic)}\")\n",
        "\n",
        "# Drop rows where 'survived' and 'age' is missing below\n",
        "\n",
        "num_survived = titanic_cleaned['survived'].sum()\n",
        "\n",
        "print(f\"Count of Titanic dataset after cleanin: {len(titanic_cleaned)}\")\n",
        "\n",
        "total_passengers = len(titanic_cleaned) # Get the total passengers\n",
        "p_MLE = num_survived / total_passengers # Get the p_MLE for the passengers\n",
        "\n",
        "print(f\"The MLE for the probability of survival is {p_MLE:.2f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1DUuwn-6QLsA",
        "outputId": "b3d13a9a-04ba-4380-9727-8a4e3312e76b"
      },
      "id": "1DUuwn-6QLsA",
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Count of Titanic dataset before cleaning: 891\n",
            "Count of Titanic dataset after cleanin: 714\n",
            "The MLE for the probability of survival is 0.41\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "466b3f36-708c-4992-bf1d-ee3ddde81548",
      "metadata": {
        "id": "466b3f36-708c-4992-bf1d-ee3ddde81548"
      },
      "source": [
        "**Code the likelihood function - 4 points**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "56f598d6-0842-4ab5-8144-2f131eac7bcb",
      "metadata": {
        "id": "56f598d6-0842-4ab5-8144-2f131eac7bcb"
      },
      "outputs": [],
      "source": [
        "# Create a range of possible p values (from 0 to 1 in increments of 0.01)\n",
        "p_values = np.linspace(0, 1, 101)\n",
        "\n",
        "# Define the likelihood function\n",
        "def likelihood(p, n, k):\n",
        "    return (p**k) * ((1-p)**(n-k))\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "25edfa15-b657-4989-8aea-d3c0acb9d256",
      "metadata": {
        "id": "25edfa15-b657-4989-8aea-d3c0acb9d256",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "outputId": "8a45fe19-efc9-4e0f-c90c-97039817b6e8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Compute likelihood values for each p\n",
        "L_values = [likelihood(p, total_passengers, num_survived) for p in p_values]\n",
        "\n",
        "# Plot\n",
        "plt.figure(figsize=(8, 6))\n",
        "plt.plot(p_values, L_values, label='Likelihood Function', color='blue')\n",
        "plt.axvline(x=p_MLE, color='red', linestyle='--', label=f'MLE at p = {p_MLE:.2f}')\n",
        "plt.xlabel('p (Probability of Survival)')\n",
        "plt.ylabel('Likelihood')\n",
        "plt.title('Likelihood Function of Survival Probability')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ]
    }
  ],
  "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": "3.9.13"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}