Earnings_expectation.ipynb

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      "source": [
        "# Predicting earnings expectations with sparse data"
      ],
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        "# Import the relevant Python libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Fix the random seed so numbers can be reproduced\n",
        "rng = np.random.default_rng(seed=11)"
      ]
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        "# Create 9 grid points for the model parameter, from 0.1 to 0.9 spaced 0.1 apart\n",
        "p = np.arange(0.1, 1, 0.1)\n",
        "\n",
        "# Since all parameters are uniformly distributed and equally likely, the probability for each parameter = 1/n = 1/9\n",
        "prior = 1/len(p)\n",
        "\n",
        "# Create a Pandas dataframe with the relevant columns to store individual calculations\n",
        "earnings_beat = pd.DataFrame(columns = ['parameter', 'prior', 'likelihood', 'posterior*', 'posterior'])\n",
        "\n",
        "# Store each parameter value\n",
        "earnings_beat['parameter'] = p\n",
        "\n",
        "# Loop computes the unnormalized posterior probability distribution for each value of the parameter\n",
        "for i in range(0,len(p)):\n",
        "  earnings_beat.iloc[i,1] = prior\n",
        "  #Since our training data has three earnings beats in a row, each having a probability of p\n",
        "  earnings_beat.iloc[i,2] = p[i]**3\n",
        "  #Use the unnormalized inverse probability rule\n",
        "  earnings_beat.iloc[i,3] = prior * (p[i]**3)\n",
        "\n",
        "# Normalize the probability distribution so that all values add up to 1\n",
        "earnings_beat['posterior'] = earnings_beat['posterior*']/sum(earnings_beat['posterior*'])\n",
        "\n",
        "# Display the data frame to show each calculation\n",
        "earnings_beat"
      ],
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              "   parameter     prior likelihood posterior* posterior\n",
              "0        0.1  0.111111      0.001   0.000111  0.000494\n",
              "1        0.2  0.111111      0.008   0.000889  0.003951\n",
              "2        0.3  0.111111      0.027      0.003  0.013333\n",
              "3        0.4  0.111111      0.064   0.007111  0.031605\n",
              "4        0.5  0.111111      0.125   0.013889  0.061728\n",
              "5        0.6  0.111111      0.216      0.024  0.106667\n",
              "6        0.7  0.111111      0.343   0.038111  0.169383\n",
              "7        0.8  0.111111      0.512   0.056889   0.25284\n",
              "8        0.9  0.111111      0.729      0.081      0.36"
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              "      <th></th>\n",
              "      <th>parameter</th>\n",
              "      <th>prior</th>\n",
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              "      <th>posterior</th>\n",
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              "      <td>0.024</td>\n",
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              "      <th>6</th>\n",
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              "      <td>0.111111</td>\n",
              "      <td>0.343</td>\n",
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              "      <th>7</th>\n",
              "      <td>0.8</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>0.512</td>\n",
              "      <td>0.056889</td>\n",
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              "      <td>0.111111</td>\n",
              "      <td>0.729</td>\n",
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        "# Plot the prior and posterior probability distribution for the model parameter\n",
        "plt.figure(figsize=(16,6)), plt.subplot(1,2,1), plt.ylim([0,0.5])\n",
        "plt.stem(earnings_beat['parameter'],earnings_beat['prior'])\n",
        "plt.xlabel('Model parameter p'), plt.ylabel('Probability of parameter P(p)'), plt.title('Prior distribution of our model parameter')\n",
        "\n",
        "plt.subplot(1,2,2), plt.ylim([0,0.5])\n",
        "plt.stem(earnings_beat['parameter'],earnings_beat['posterior'])\n",
        "plt.xlabel('Model parameter p'), plt.ylabel('Probability of parameter P(p)'), plt.title('Posterior distribution of our model parameter')\n",
        "plt.show();"
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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Since P(yi=1|pi) = pi, we compute the probability weighted average of observing y=1 using our prior probabilities as the weights\n",
        "# This probability weighted average gives us the prior predictive probability of observing y=1 before observing any data\n",
        "prior_predictive_1 = sum(earnings_beat['parameter'] * earnings_beat['prior'])\n",
        "\n",
        "# The prior predictive probability of observing outcome y=0 is the complement of P(y=1) calculated above\n",
        "prior_predictive_0 = 1 - prior_predictive_1\n",
        "\n",
        "# Since we have picked a uniform distribution for our parameter, our model predicts that both outcomes are equally likely prior to observing any data\n",
        "prior_predictive_0, prior_predictive_1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MNz-EAE5SPZg",
        "outputId": "3ad7a5cb-4ff8-467d-f3de-d6883749a25e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.5, 0.5)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Since P(yi=1|pi) = pi, we compute the probability weighted average of observing y=1 but now we use the posterior probabilities as the weights\n",
        "# This probability weighted average gives us the posterior predictive probability of observing y=1 after observing in-sample data D={y1=1, y2=1, y3=1}\n",
        "posterior_predictive_1 = sum(earnings_beat['parameter'] * earnings_beat['posterior'])\n",
        "\n",
        "# The posterior predictive probability of observing outcome y=0 is the complement of P(y=1|D) calculated above\n",
        "posterior_predictive_0 = 1- posterior_predictive_1\n",
        "\n",
        "# After observing data D, our model predicts that observing y=1 is about 3 times more likely than observing y=0\n",
        "round(posterior_predictive_0,3), round(posterior_predictive_1,3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mt8mpOX9Ubgg",
        "outputId": "7e0d1f7b-4de9-413c-e655-57e28f6bd4d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.243, 0.757)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot the prior and posterior predictive probability distribution for the event outcomes\n",
        "plt.figure(figsize=(17,6)), plt.subplot(1,2,1), plt.ylim([0,1])\n",
        "plt.stem([0,1],[prior_predictive_0, prior_predictive_1])\n",
        "plt.xlabel('Binary outcome for variable y'), plt.ylabel('Probability P(y)'), plt.title('Distribution of prior predictive mean of an earnings beat')\n",
        "\n",
        "plt.subplot(1,2,2), plt.ylim([0,1])\n",
        "plt.stem([0,1],[posterior_predictive_0, posterior_predictive_1])\n",
        "plt.xlabel('Binary outcome for variable y'), plt.ylabel('Probability P(y)'), plt.title('Posterior predictive distribution of an earnings beat')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 562
        },
        "id": "rZa6vOvCZp-w",
        "outputId": "42e18ca0-16a8-48b2-ca0e-c559e837b765"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1700x600 with 2 Axes>"
            ],
            "image/png": 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    }
  ]
}