{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "43e49832-91e1-408b-98ec-9b6e86fefdce",
      "metadata": {
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      },
      "source": [
        "## Computational - 35 points\n",
        "\n",
        "These problems have a coding solution. Code your solutions in Python in the space provided.\n",
        "\n",
        "Use of LLM's such as ChatGPT are not allowed for this computational task, please try not to use such applications as we do check for the same during grading."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c7c5994e-0d69-4b0a-b402-185eda5f4d44",
      "metadata": {
        "id": "c7c5994e-0d69-4b0a-b402-185eda5f4d44"
      },
      "source": [
        "### Problem 1 - Bingo [5 points]\n",
        "\n",
        "You are playing a game of Bingo with 5 balls numbered from 1 to 5. You take 20 balls out of a box, and the following table shows how many times a number was observed.\n",
        "\n",
        "**For background on the Multinomial and its conjugate prior the Dirichlet distribution see https://mcrovella.github.io/DS122-Foundations-of-Data-Science-III/27-Conjugate-Priors.html#lions-and-tigers-and-bears**\n",
        "\n",
        "**Based on these observations we'll determine what the probabilty of drawing ball 3 is.**"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import necessary libraries\n",
        "import pandas as pd  # Utilize this library for data manipulation and analysis.\n",
        "import numpy as np  # This library is for numerical operations.\n",
        "\n",
        "from scipy.stats import dirichlet\n",
        "\n",
        "# Data for bingo ball frequencies. Define a dictionary to represent this information.\n",
        "bingo_data = {\n",
        "    'numbers': [1, 2, 3, 4, 5],  # This key should denote the bingo ball numbers.\n",
        "    'frequency': [4, 5, 2, 6, 3]   # This key corresponds to how often each number has been drawn.\n",
        "}\n",
        "\n",
        "# Create a pandas DataFrame from the data\n",
        "bingo = pd.DataFrame(bingo_data)\n",
        "\n",
        "# Display the DataFrame\n",
        "print(bingo)\n",
        "\n",
        "# Define the prior Dirichlet distribution. Non-informative priors are typically uniform.\n",
        "alpha_prior = np.array([1, 1, 1, 1, 1])  # Specify the Dirichlet prior with equal weight for each outcome.\n",
        "\n",
        "# Update the parameter vector alpha with observed frequencies. The update reflects our belief after seeing the data.\n",
        "alpha_posterior = alpha_prior + bingo['frequency'].values  # Incorporate the observed frequencies into the prior.\n",
        "\n",
        "# Define the posterior Dirichlet distribution. The posterior captures our updated beliefs.\n",
        "posterior = dirichlet(alpha_posterior)\n",
        "\n",
        "# Predict the probability of the next ball being a 3. We use the mean of the posterior distribution.\n",
        "probability_of_3 = posterior.mean()[2]  # Access the mean probability for the third number.\n",
        "\n",
        "# Print the result. The probability is formatted to four decimal places.\n",
        "print(f'Probability of ball 3: {probability_of_3:.4f}')\n",
        "\n",
        "# Visualize the distribution: this part is for plotting the posterior distribution.\n",
        "# To plot, you need to import a specific library designed for creating static, animated, and interactive visualizations.\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Simulate draws from the posterior distribution. The number of simulations can be adjusted for precision, you can try out different numbers.\n",
        "simulations = posterior.rvs(size=10000)\n",
        "plt.hist(simulations[:, 2], bins=50, density=True)  # Extract the simulation data for the third ball.\n",
        "plt.title('Simulated Posterior Distribution for Bingo Ball 3')\n",
        "plt.xlabel('Probability of Ball 3')\n",
        "plt.ylabel('Density')\n",
        "plt.axvline(probability_of_3, color='red', linestyle='dashed', linewidth=2)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 601
        },
        "id": "o830lXL_qxna",
        "outputId": "261fdf67-48d1-4337-b80c-ca0fa2b35cae"
      },
      "id": "o830lXL_qxna",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   numbers  frequency\n",
            "0        1          4\n",
            "1        2          5\n",
            "2        3          2\n",
            "3        4          6\n",
            "4        5          3\n",
            "Probability of ball 3: 0.1200\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1f1a961a-cccd-4a12-8087-6f19484eeb27",
      "metadata": {
        "id": "1f1a961a-cccd-4a12-8087-6f19484eeb27"
      },
      "source": [
        "### Problem 2 - New Beverage Taste Preference [10 points]\n",
        "\n",
        "A beverage company has developed a new flavor and claims that it will be preferred over the current leading brand by 70% of consumers. As a market analyst, you have been tasked with validating this claim. You organize a taste test with 100 participants and find that 65 of them express a preference for the new flavor over the leading brand.\n",
        "\n",
        "Prior to the taste test, you had some reservations about the claim due to the leading brand's strong market presence. Therefore, you choose to use a beta distribution with parameters \\(\\alpha = 50\\) and \\(\\beta = 50\\) as the prior distribution for the probability of preference for the new flavor, indicating a neutral stance with a tendency towards uncertainty due to the balanced alpha and beta parameters.\n",
        "\n",
        "**2.1 Define a beta distribution as your prior using the given alpha and beta values. Plot the prior distribution. [2 points]**"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import necessary libraries\n",
        "import numpy as np  # This library is essential for handling arrays and performing numerical computations.\n",
        "import matplotlib.pyplot as plt  # This library is used for creating static, interactive, and animated visualizations in Python.\n",
        "from scipy.stats import beta  # Import the beta distribution for Bayesian analysis.\n",
        "\n",
        "# Define the prior beta distribution parameters. These parameters represent our prior belief about the probability.\n",
        "alpha_prior = 50  # Represents the number of \"successes\" in our prior knowledge given in the question.\n",
        "beta_prior = 50  # Represents the number of \"failures\" in our prior knowledge given in the question.\n",
        "prior_dist = beta(alpha_prior, beta_prior)\n",
        "\n",
        "# Plotting the prior distribution. The plot represents the density of our prior belief across all possible probabilities.\n",
        "x = np.linspace(0, 1, 1000)  # Generate an array of probability values between 0 and 1.\n",
        "plt.plot(x, prior_dist.pdf(x), label='Prior Distribution')  # Plot the probability density function of the prior.\n",
        "plt.title('Prior Beta Distribution with alpha=50 and beta=50')  # Fill in with the corresponding alpha and beta values.\n",
        "plt.xlabel('Preference Probability')  # Label for the x-axis indicating what it represents.\n",
        "plt.ylabel('Density')  # Label for the y-axis indicating the density of the prior distribution.\n",
        "plt.legend()  # Display a legend to identify the plotted line.\n",
        "plt.show()  # This command will display the plot.\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "mVBEvEzPs7gQ",
        "outputId": "27ec4809-b9b5-49ce-d744-1f273a253e15"
      },
      "id": "mVBEvEzPs7gQ",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ab74b592-227e-4f6c-88ab-427310a4fcb7",
      "metadata": {
        "id": "ab74b592-227e-4f6c-88ab-427310a4fcb7"
      },
      "source": [
        "**2.2 Using the data from the taste test, update your prior to obtain the posterior distribution. Calculate the posterior mean, and plot both the prior and posterior distributions on the same graph for comparison. [5 points]**\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "4a13210d-90ad-407d-acfd-f1e71177032f",
      "metadata": {
        "id": "4a13210d-90ad-407d-acfd-f1e71177032f",
        "outputId": "129712c7-7e93-4676-c7cc-89be444a0ea6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The posterior mean of the new flavor's preference rate is: 0.5750\n"
          ]
        }
      ],
      "source": [
        "# Define the observed data from the taste test\n",
        "preference_count = 65\n",
        "total_participants = 100\n",
        "non_preference_count = total_participants - preference_count # Code the non-preference count from the preference and total participants count\n",
        "\n",
        "# Update the prior with the observed data to form the posterior distribution\n",
        "alpha_posterior = alpha_prior + preference_count # Update the alpha posterier based on the preference count\n",
        "beta_posterior = beta_prior + non_preference_count # Update the beta posterier on the prior\n",
        "posterior_dist = beta(alpha_posterior, beta_posterior)\n",
        "\n",
        "# Calculate the posterior mean\n",
        "posterior_mean = posterior_dist.mean()\n",
        "\n",
        "# Plot the prior and posterior distributions\n",
        "plt.plot(x, prior_dist.pdf(x), label='Prior Distribution')\n",
        "plt.plot(x, posterior_dist.pdf(x), label='Posterior Distribution', color='green')\n",
        "plt.title('Prior vs Posterior Beta Distribution')\n",
        "plt.xlabel('Preference Probability')\n",
        "plt.ylabel('Density')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Print the posterior mean\n",
        "print(f\"The posterior mean of the new flavor's preference rate is: {posterior_mean:.4f}\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f95f4f4b-e62a-428f-bcb1-96fa604e1d45",
      "metadata": {
        "id": "f95f4f4b-e62a-428f-bcb1-96fa604e1d45"
      },
      "source": [
        "\n",
        "In this problem, the prior distribution reflects a neutral yet uncertain stance on the new flavor's potential preference rate. The posterior distribution, updated with the data from the taste test, provides a new estimate that incorporates both the initial skepticism and the actual preference data collected. The posterior mean serves as a Bayesian estimate of the true preference rate, which can then be used to inform the company's marketing strategy."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "263cebbc-7acb-4786-b9b3-b4dc216d76f5",
      "metadata": {
        "id": "263cebbc-7acb-4786-b9b3-b4dc216d76f5"
      },
      "source": [
        "### Problem 3 - Evaluating Rookie Performance [20 points]\n",
        "\n",
        "As a data analyst for Boston University, you've been tasked with evaluating the performance of rookie players. The team is interested in determining which rookies show the most promise based on their batting averages in the minor leagues. You have access to the Baseball data, which includes statistics for rookies.\n",
        "\n",
        "Consider the dataframe `rookie_df` defined below, which contains the number of hits and the total number of at-bats for several rookie players.\n",
        "\n",
        "Adapted from David Robinson"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a0c7a4c6-0d99-4e7b-8da4-14e2124af012",
      "metadata": {
        "id": "a0c7a4c6-0d99-4e7b-8da4-14e2124af012"
      },
      "source": [
        "#### Loading data - 2 Points"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "id": "ac05ba89-58b1-4d7d-9215-21e14b6d91dc",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ac05ba89-58b1-4d7d-9215-21e14b6d91dc",
        "outputId": "22a3fd2b-d211-4a01-a14e-e3413b74cf43"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   success  total\n",
            "0        5     25\n",
            "1       23     75\n",
            "2        2     10\n",
            "3       10     40\n",
            "4       60    150\n"
          ]
        }
      ],
      "source": [
        "# Import necessary libraries\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import beta\n",
        "import numpy as np\n",
        "\n",
        "# Creating the dataframe for the baseball stats\n",
        "rookie_data = {'success': [5, 23, 2, 10, 60],\n",
        "               'total': [25, 75, 10, 40, 150]}\n",
        "\n",
        "rookie_df = pd.DataFrame(rookie_data) # Create a dataframe from the data\n",
        "print(rookie_df)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5481c6ca-3ec1-4874-8e80-c07b1d7d66fe",
      "metadata": {
        "id": "5481c6ca-3ec1-4874-8e80-c07b1d7d66fe"
      },
      "source": [
        "**3.1 Bad approach - Calculate the raw batting average for each player and note the shortcomings of this approach. [3 points]**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "fa4b11fa-42aa-446e-b5a9-b791d174b413",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fa4b11fa-42aa-446e-b5a9-b791d174b413",
        "outputId": "e7aa63ab-4615-44d3-b7d7-39ffd498eaad"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   success  total  batting_average\n",
            "0        5     25         0.200000\n",
            "1       23     75         0.306667\n",
            "2        2     10         0.200000\n",
            "3       10     40         0.250000\n",
            "4       60    150         0.400000\n"
          ]
        }
      ],
      "source": [
        "# Calculating the raw batting average\n",
        "rookie_df['batting_average'] = rookie_df['success'] / rookie_df['total'] # Based on the success and the total\n",
        "print(rookie_df)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "18086f0c-0847-46fc-8cb7-8b89200ea624",
      "metadata": {
        "id": "18086f0c-0847-46fc-8cb7-8b89200ea624"
      },
      "source": [
        "**3.2 Apply empirical Bayes estimation to improve the estimate of each rookie player's batting average. [10 points]**\n",
        "\n",
        "**Loading Batting.csv and Pitching.csv datasets - 2 Points**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "7545b9b2-4905-4a7b-bca4-489e8e4f7c9f",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "id": "7545b9b2-4905-4a7b-bca4-489e8e4f7c9f",
        "outputId": "7d72eada-8ba6-469d-b51d-f91600df6116"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "<IPython.core.display.HTML object>"
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              "      Upload widget is only available when the cell has been executed in the\n",
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              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
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              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving Pitching.csv to Pitching.csv\n",
            "Saving Batting.csv to Batting.csv\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-6-863f93afae1e>:13: FutureWarning: The default value of numeric_only in DataFrameGroupBy.sum is deprecated. In a future version, numeric_only will default to False. Either specify numeric_only or select only columns which should be valid for the function.\n",
            "  batting_df = batting_df.groupby('playerID').sum().reset_index()\n"
          ]
        }
      ],
      "source": [
        "# Google Colab file uploads\n",
        "from google.colab import files\n",
        "uploaded = files.upload()  # Prompt for file upload and store the uploaded file references\n",
        "\n",
        "# Load Batting.csv dataset\n",
        "batting_df = pd.read_csv('Batting.csv')  # Read the Batting CSV into a DataFrame\n",
        "\n",
        "# Load Pitching.csv dataset\n",
        "pitching_df = pd.read_csv('Pitching.csv')  # Read the Pitching CSV into a DataFrame\n",
        "\n",
        "# Proceed with the preprocessing as you have described\n",
        "batting_df = batting_df[batting_df['AB'] > 0]\n",
        "batting_df = batting_df.groupby('playerID').sum().reset_index()\n",
        "batting_df['batting_avg'] = batting_df['H'] / batting_df['AB']\n",
        "\n",
        "pitchers_list = pitching_df['playerID'].unique().tolist()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6d2c343e-2ea9-49df-86a9-1c66e497d54e",
      "metadata": {
        "id": "6d2c343e-2ea9-49df-86a9-1c66e497d54e"
      },
      "source": [
        "**3.2.1 Remove outliers by filtering out all players with fewer than 500 career at-bats from the batting dataset. [2 points]**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "cb008de8-23b8-4dce-9480-4a17e6aa3bb1",
      "metadata": {
        "id": "cb008de8-23b8-4dce-9480-4a17e6aa3bb1"
      },
      "outputs": [],
      "source": [
        "# Filter out players with fewer than 500 career at-bats\n",
        "filtered_batting_df = batting_df[batting_df['AB'] >= 500]"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a4e1a643-f10e-47cd-8865-d4be0b089a3c",
      "metadata": {
        "id": "a4e1a643-f10e-47cd-8865-d4be0b089a3c"
      },
      "source": [
        "**3.2.2 Create a dataframe called `non_pitchers` that excludes players who have pitched. [3 points]**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "90f56dd8-aca5-419e-9d0a-52ade89d74f3",
      "metadata": {
        "id": "90f56dd8-aca5-419e-9d0a-52ade89d74f3"
      },
      "outputs": [],
      "source": [
        "# Exclude players who have also pitched\n",
        "non_pitchers_df = filtered_batting_df[~filtered_batting_df['playerID'].isin(pitchers_list)] # You have to use the Player_ID column and the pitchers_list that you preprocessed"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "48355e48-36d9-4d5c-84a9-a9dc66f7c1c2",
      "metadata": {
        "id": "48355e48-36d9-4d5c-84a9-a9dc66f7c1c2"
      },
      "source": [
        "**3.2.3 Estimate the beta prior using scipy and the non_pitcher data. [3 points]**"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Estimate the beta prior\n",
        "alpha_prior, beta_prior, _, _ = beta.fit(non_pitchers_df['batting_avg'], floc=0, fscale=1)\n",
        "print(f'Alpha prior: {alpha_prior}, Beta prior: {beta_prior}')\n",
        "\n",
        "# Calculate the empirical Bayes estimate for the rookies\n",
        "rookie_df['eb_estimate'] = (rookie_df['success'] + alpha_prior) / (rookie_df['total'] + alpha_prior + beta_prior) # Include the alpha_prior and the success columns in accordance with the formula to calculate the empirical bayes estimate\n",
        "print(rookie_df[['success', 'total', 'batting_average', 'eb_estimate']])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lq7nfWCaoFuW",
        "outputId": "8b97abd3-7b44-4ad8-807c-e20bd6cead84"
      },
      "id": "lq7nfWCaoFuW",
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Alpha prior: 79.43156967970783, Beta prior: 228.0037390687307\n",
            "   success  total  batting_average  eb_estimate\n",
            "0        5     25         0.200000     0.253979\n",
            "1       23     75         0.306667     0.267840\n",
            "2        2     10         0.200000     0.256530\n",
            "3       10     40         0.250000     0.257405\n",
            "4       60    150         0.400000     0.304812\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "79a74f4a-f4ae-4177-841d-ab8d349f1b2a",
      "metadata": {
        "id": "79a74f4a-f4ae-4177-841d-ab8d349f1b2a"
      },
      "source": [
        "**Visualizing the Results [5 Points]**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "e10315be-effe-4a78-8989-68d001ce3091",
      "metadata": {
        "id": "e10315be-effe-4a78-8989-68d001ce3091",
        "outputId": "98165840-5212-4923-d396-3850230f98b8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 725
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x800 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot the empirical Bayes estimates\n",
        "# Hints\n",
        "## You will need to make a scatter plot of the batting average vs eb estimate\n",
        "## Make sure to include correct labels for the x and y axis\n",
        "## You will need to make a diagonal line for reference\n",
        "## Make sure to limit the graph to 0,1 for the axis as shown in the example output\n",
        "## Finally show your output\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "# Seaborn Stuffs\n",
        "sns.set_style(\"whitegrid\")\n",
        "plt.figure(figsize=(10, 8))\n",
        "scatter = plt.scatter(rookie_df['batting_average'], rookie_df['eb_estimate'],\n",
        "                      alpha=0.7, c=rookie_df['total'], cmap='viridis', edgecolor='k')\n",
        "\n",
        "# Labels and title\n",
        "plt.xlabel('Raw Batting Average', fontsize=14)\n",
        "plt.ylabel('Empirical Bayes Estimate', fontsize=14)\n",
        "plt.title('Comparison of Raw Batting Average and Empirical Bayes Estimate', fontsize=16)\n",
        "\n",
        "# Diagonal line\n",
        "plt.plot([0, 1], [0, 1], 'k--', alpha=0.75)\n",
        "\n",
        "# Limit the axes to 0 and 1\n",
        "plt.xlim(0, 1)\n",
        "plt.ylim(0, 1)\n",
        "\n",
        "# Add a color bar\n",
        "plt.colorbar(scatter, label='Total At-Bats')\n",
        "\n",
        "# Show the plot\n",
        "plt.show()\n"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "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": [],
      "gpuType": "T4"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 5
}