{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "963b7001-be41-4c01-9242-975ceaf152ca",
   "metadata": {},
   "source": [
    "## Computational\n",
    "\n",
    "The solutions to problems in this section should be in the form of code. You might be required to state your observations, in which case, an empty markdown cell will be provided."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a96b100-064e-4a6a-af6d-12fd2dd625eb",
   "metadata": {},
   "source": [
    "## The Problem: Weights of Elephants 35 Points (5 Points Bonus)\n",
    "\n",
    "Suppose we choose two elephants from a population; let's call them elephant A and elephant B. If we see that A weighs more than B, what is the weight of A?\n",
    "\n",
    "### Approaching the Problem\n",
    "\n",
    "1: Establish a prior for A's weight: we can use background information about the weight of elephants.\n",
    "\n",
    "2: Construct a joint prior distribution of weight for A and B.\n",
    "\n",
    "3: Update the prior with the information that A is heavier.\n",
    "\n",
    "4: From the joint posterior distribution extract the posterior distribution of weight for A.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86583a7-da47-4f42-b6f3-15323f65f741",
   "metadata": {},
   "source": [
    "The Prior\n",
    "\n",
    "The average weight of an adult African elephant is about 6000 kg, and the standard deviation is roughly 500 kg, and is approximately normal.\n",
    "\n",
    "We can use that as the prior distribution for the weights of both elephant A and B."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028e0afb-0487-4564-ab30-0996173f00cc",
   "metadata": {},
   "source": [
    "Start by importing the necessary libraries. We will need `pandas` for data manipulation, `numpy` for numerical operations, and `scipy.matplotlib` for visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2943cd49-9092-4e06-b7b4-96224d32fb39",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# Add any additional libraries you think you'll need below this line.\n",
    "# __________ # <-- Fill in the blank with the library name"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d65e0d-6468-46ad-877a-8378297a34e8",
   "metadata": {},
   "source": [
    "# Prior Plotting - 5 Points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4adcd9e4-01da-47db-8072-9dc675ff65fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the prior distribution\n",
    "plt.figure()\n",
    "x = np.linspace(______, ______, ______)  # Fill in the start, end, and number of points for the x-axis.\n",
    "plt.plot(x, norm.pdf(x, ______, ______),'b-', lw = 5, alpha = 0.6)  # Fill in the mean and standard deviation for the prior.\n",
    "plt.title('Prior Distribution', size=14)\n",
    "plt.xlabel('Weight in kg', size=14)\n",
    "plt.ylabel('PDF', size=14)\n",
    "\n",
    "# Normal prior\n",
    "p_dist = pd.DataFrame(index = np.linspace(______, ______, ______))  # Repeat the start, end, and number of points for the x-axis.\n",
    "p_dist['probs'] = [norm.pdf(x, ______, ______) for x in p_dist.index]  # Repeat the mean and\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9143599-2fb6-4bf8-8e73-1a40861b3a4f",
   "metadata": {},
   "source": [
    "# Joint Priors - 10 Points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "50b63781-c299-4050-a5a4-16adc5f1e70f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# multiplies prbabilities from two distributions\n",
    "def make_joint(____, ____):\n",
    "    \"\"\"\n",
    "    Compute the outer product of two PMFs to create a joint distribution.\n",
    "\n",
    "    Parameters:\n",
    "    ____: DataFrame representing the first PMF with probabilities.\n",
    "    ____: DataFrame representing the second PMF with probabilities.\n",
    "\n",
    "    Returns:\n",
    "    A DataFrame representing the joint distribution of the two PMFs.\n",
    "    \"\"\"\n",
    "    # Create a meshgrid which will represent all possible pairs of probabilities from ____ and ____\n",
    "    X, Y = np.meshgrid(____['probs'], ____['probs'])\n",
    "    \n",
    "    # Compute the outer product to get the joint probabilities\n",
    "    # The resulting matrix will have probabilities where rows correspond to ____ and columns to ____\n",
    "    joint_pmf = pd.DataFrame(X * Y, columns=____.index, index=____.index)\n",
    "    \n",
    "    return joint_pmf\n",
    "\n",
    "# Usage example with blanks filled in:\n",
    "# joint_distribution = make_joint(pmf1, pmf2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "43f5ef7d-2d37-4653-855f-c033be07161f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Joint prior distribution of weight for A and B')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define a normal distribution for the prior with mean and standard deviation\n",
    "# Replace '____' with appropriate values for mean and standard deviation\n",
    "p_dist = pd.DataFrame(index=np.linspace(140, 220, 161))\n",
    "p_dist['probs'] = [norm.pdf(x, ____, ____) for x in p_dist.index]\n",
    "p_dist['probs'] = p_dist['probs'] / sum(p_dist['probs'])\n",
    "\n",
    "# Create a joint prior distribution using the function 'make_joint'\n",
    "# 'make_joint' needs to be defined earlier in the code or imported if it's from a library\n",
    "joint = make_joint(p_dist, p_dist)\n",
    "\n",
    "# Plotting the joint prior distribution\n",
    "plt.figure()\n",
    "plt.pcolormesh(joint.columns, joint.index, joint, cmap='Blues')\n",
    "plt.colorbar()\n",
    "plt.xlabel('Weight of A in kg', size=14) # Modify label to match the context of the data\n",
    "plt.ylabel('Weight of B in kg', size=14) # Modify label to match the context of the data\n",
    "plt.title('Joint prior distribution of weight for A and B', size=14) # Modify title to match the context\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84c8a60f-3257-48d2-a9e8-9fbd0086959b",
   "metadata": {},
   "source": [
    "Joint Likelihood\n",
    "\n",
    "Now that we have a joint prior distribution, we can update it with the data, which is that elephant A is heavier than B."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "efced181-954e-4a9e-aeed-4c87fa74d0b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Likelihood A > B')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a grid of weights for A and B\n",
    "A, B = np.meshgrid(joint._______, joint._______)  # Q1: Fill in the attribute for penguin A's weight range, Q2: Fill in the attribute for penguin B's weight range.\n",
    "\n",
    "# Check if A is heavier than B (and add 0 to make it numeric)\n",
    "A_heavier = (A ____ B) + 0  # Q3: Fill in the comparison operator to check if A's weight is greater than B's weight.\n",
    "\n",
    "# Create a DataFrame with the likelihood of A being heavier than B\n",
    "likelihood = pd.DataFrame(A_heavier, index=joint._______, columns=joint._______)  # Q4 & Q5: Fill in the attributes for the index and columns from `joint`.\n",
    "\n",
    "plt.figure()\n",
    "plt.pcolormesh(likelihood._______, likelihood._______, likelihood, cmap='_______')  # Q6: Use `likelihood.columns` and `likelihood.index`, Q7: Fill in the colormap name.\n",
    "plt.colorbar()\n",
    "plt.xlabel('_______', size=_____)  # Q8: Fill in the label for x-axis and the text size.\n",
    "plt.ylabel('_______', size=_____)  # Q9: Fill in the label for y-axis and the text size.\n",
    "plt.title('_______', size=_____)  # Q10: Fill in the title of the plot and the text size.\n",
    "\n",
    "# Remember to fill in the blanks based on the instructions in the comments.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fda05643-2e3d-42e9-99aa-7635014d3960",
   "metadata": {},
   "source": [
    "# The Update - 10 Points\n",
    "\n",
    "Update the posterior, which is the joint prior times the joint likelihood."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a493dae9-a201-4c02-aaa7-88b980e34f8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Joint posterior distribution of weight for A and B')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Update the posterior by multiplying the joint prior with the likelihood\n",
    "posterior = joint * likelihood\n",
    "\n",
    "# Calculate the probability of the data by summing all the probabilities in the posterior\n",
    "prob_data = posterior._______().sum()  # <-- Fill in the method to convert the DataFrame to a numpy array\n",
    "\n",
    "# Normalize the posterior by dividing by the probability of the data\n",
    "posterior = posterior / prob_data\n",
    "\n",
    "# Plotting the joint posterior distribution\n",
    "plt.figure()\n",
    "plt.pcolormesh(posterior._______, posterior._______, posterior, cmap='_______')  # Q1: Fill in posterior column attribute, Q2: Fill in posterior index attribute, Q3: Fill in the colormap name\n",
    "plt.colorbar()\n",
    "plt.xlabel('Weight of A in kg', size=_____)  # Q4: Fill in the text size\n",
    "plt.ylabel('Weight of B in kg', size=_____)  # Q5: Fill in the text size\n",
    "plt.title('Joint posterior distribution of weight for A and B', size=_____)  # Q6: Fill in the text size\n",
    "\n",
    "# Remember to replace the blanks with the correct code based on the comments provided.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9912eb11-4aa1-467c-a82b-b72d6b6bf576",
   "metadata": {},
   "source": [
    "# Marginal Distribution\n",
    "\n",
    "Compute the posterior distribution of weights for elephant A."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c734f578-56ca-437f-906c-f8885f998152",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PDF')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sum over the rows of the joint posterior to get the marginal for A\n",
    "marginal_A = posterior.sum(axis=0)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "p_dist.plot(ax=ax, style='--')\n",
    "marginal_A.plot(ax=ax)\n",
    "ax.legend(['Prior', 'Posterior for A'], fontsize=14, loc='best')\n",
    "plt.title('Prior and Posterior Distribution', size=14)\n",
    "plt.xlabel('Weight in kg', size=14)\n",
    "plt.ylabel('PDF', size=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ad70d997-e731-4d01-b5f7-43757da2c7ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the MMSE weight for A.\n",
    "mmse_weight_A = sum(marginal_A.index * marginal_A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51d51229-bcd6-4ac8-998e-2af4d4e840ab",
   "metadata": {},
   "source": [
    "# Elephant B Computation - 10 Points\n",
    "\n",
    "#### Following the example for the posterior distribution of weights for elephant A, now calculate and plot the posterior distribution of weights for elephant B and calculate it's MMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3776a075-dc14-42fc-9e85-07d288a87fe6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your code here"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a03267d-aad3-412c-8f48-e57c5444317f",
   "metadata": {},
   "source": [
    "# Conditional Posteriors - 5 Points (Bonus)\n",
    "\n",
    "Suppose we now measure A and find that it weighs 6500 kg. What does that tell us about the weight of B?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b551c85-6047-4848-bdd2-eb9c909eb6ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the column index closest to the given weight\n",
    "# Q1: Replace 6500 with the desired weight to find the closest column.\n",
    "closest_weight = min(posterior.columns, key=lambda x: abs(x-______))  # <-- Fill in the desired weight\n",
    "\n",
    "# Extract the column for the closest weight\n",
    "# Q2: Replace 'closest_weight' with the variable holding the closest weight.\n",
    "column_closest_weight = posterior[______]  # <-- Fill in the variable holding the closest weight\n",
    "# Normalize the extracted column to get a valid probability distribution\n",
    "column_closest_weight = column_closest_weight / sum(column_closest_weight)\n",
    "\n",
    "# Prepare a figure and axis for plotting with subplots\n",
    "fig, ax = plt.subplots()\n",
    "# Plot the prior distribution on the axis created\n",
    "# Q3: Replace 'p_dist' with the prior distribution DataFrame.\n",
    "p_dist.plot(ax=ax, style='--')  # <-- Fill in the DataFrame containing the prior distribution\n",
    "# Plot the conditional posterior distribution on the same axis\n",
    "# Q4: Replace 'column_closest_weight' with the normalized posterior column.\n",
    "column_closest_weight.plot(ax=ax)  # <-- Fill in the normalized posterior column\n",
    "# Set the legend for the plot with font size 14 and the best location\n",
    "ax.legend(['Prior', 'Conditional Posterior for B'], fontsize=14, loc='best')\n",
    "# Set the title for the plot\n",
    "# Q5: Replace 'size=14' with the desired title font size.\n",
    "plt.title('Prior and Posterior Distribution for Weight Closest to 6500 kg', size=_____)  # <-- Fill in the title font size\n",
    "# Set the x-label with the desired font size\n",
    "# Q6: Replace 'size=14' with the desired label font size.\n",
    "plt.xlabel('Weight in kg', size=_____)  # <-- Fill in the label font size\n",
    "# Set the y-label with the desired font size\n",
    "# Q7: Replace 'size=14' with the desired label font size.\n",
    "plt.ylabel('PDF', size=_____)  # <-- Fill in the label font size\n",
    "# Display the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3119cb5-e41c-495f-aa29-5e309b43620d",
   "metadata": {},
   "source": [
    "# Classifying Birds - 30 Points (Bonus: 5 Points)\n",
    "\n",
    "Using a dataset of measurements of three types of birds, we’ll learn to classify a penguin as one one of those three types: Robin, Eagle and Sparrow.\n",
    "\n",
    "We’ll consider a dataset with three measurements:\n",
    "\n",
    "- Wing Length\n",
    "\n",
    "- Beak Length\n",
    "\n",
    "- Body Mass\n",
    "\n",
    "And we’ll begin to approach the problem in our typical way:\n",
    "\n",
    "Define a prior distribution for how likely we think our unknown example is to belong to each of the three possible species\n",
    "\n",
    "- Compute the likelihood of the data for each species\n",
    "\n",
    "- Compute the posterior probability of each hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "459c63d4-127a-4900-958f-c28fa6f07f8b",
   "metadata": {},
   "source": [
    "Start by importing the necessary libraries. We will need `pandas` for data manipulation, `numpy` for numerical operations, and `scipy.stats` for statistical functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6a8a6b0f-8ef1-4bef-9d07-8819da4fe5c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "\n",
    "# Add any additional libraries you think you'll need below this line.\n",
    "# __________ # <-- Fill in the blank with the library name"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "397d43d5-2568-4db8-b06c-d1a5a0b58cc7",
   "metadata": {},
   "source": [
    "# Defining the Priors - 5 Points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a68b4da-1a84-486c-8d2b-4be1895cf4b3",
   "metadata": {},
   "source": [
    "Load the dataset from a CSV file into a Pandas DataFrame. Replace the `file_path` with the actual path to your CSV file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "167854ad-873e-4c7e-a51f-e96a85a20c5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>wing_length</th>\n",
       "      <th>beak_length</th>\n",
       "      <th>body_mass</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>179.919021</td>\n",
       "      <td>22.297573</td>\n",
       "      <td>46.901258</td>\n",
       "      <td>Robin</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>218.835690</td>\n",
       "      <td>28.937718</td>\n",
       "      <td>99.936140</td>\n",
       "      <td>Eagle</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>155.907941</td>\n",
       "      <td>10.710851</td>\n",
       "      <td>36.686616</td>\n",
       "      <td>Sparrow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>161.175754</td>\n",
       "      <td>14.245663</td>\n",
       "      <td>24.597168</td>\n",
       "      <td>Sparrow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>161.904417</td>\n",
       "      <td>20.438017</td>\n",
       "      <td>51.000078</td>\n",
       "      <td>Robin</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   wing_length  beak_length  body_mass  species\n",
       "0   179.919021    22.297573  46.901258    Robin\n",
       "1   218.835690    28.937718  99.936140    Eagle\n",
       "2   155.907941    10.710851  36.686616  Sparrow\n",
       "3   161.175754    14.245663  24.597168  Sparrow\n",
       "4   161.904417    20.438017  51.000078    Robin"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the dataset\n",
    "df = pd.read_csv('______')  # <-- Fill in the blank with the file path\n",
    "\n",
    "# Take a quick look at the data\n",
    "df._____"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0fd628b-80bc-41d9-bff6-993724b5c6af",
   "metadata": {},
   "source": [
    "Define a prior distribution for the likelihood that an example belongs to each species in the dataset. The prior should be uniform across all species if you have no prior knowledge about the likelihood of each species.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3f6ff675-70a8-4d85-8e4d-46d4abba5466",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a uniform prior for the species\n",
    "# In the blank after 'species', fill in the column name that contains species information\n",
    "species = np.sort(df['species'].______) # <-- Replace with the column name from your DataFrame that contains species names to get only unique values.\n",
    "\n",
    "# In the DataFrame constructor, fill in the variable that holds the sorted species names\n",
    "p_dist = pd.DataFrame(______, columns=['species']) # <-- Replace with the variable you defined above.\n",
    "\n",
    "# For the prior probabilities column, fill in the name of the column you want to create for storing probabilities\n",
    "p_dist['______'] = 1 / len(species) # <-- Replace with the name of the new column (probabilities column)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5af607d7-9e69-4e47-8753-3907c031ab30",
   "metadata": {},
   "source": [
    "# Computing Likelihood - 10 Points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d402c085-d148-4ef6-8dee-217dda170ab1",
   "metadata": {},
   "source": [
    "Compute the likelihood of the observed data for each species based on the provided features. Replace `feature_names` with the actual names of the features you are using from your dataset.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a56f970c-3bcf-472d-82a3-a003dacafdda",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function to compute likelihoods\n",
    "def compute_likelihoods(df, feature_names):\n",
    "    # Initialize a dictionary to hold the likelihoods\n",
    "    likelihoods = {}\n",
    "    # Loop through each species and calculate its likelihood\n",
    "    for species in df['______'].unique(): # <-- Fill in the column name that contains species information.\n",
    "        # Subset the dataframe for the current species\n",
    "        subset = df[df['______'] == species] # <-- Replace with the column name that contains species information.\n",
    "        # Calculate the mean and covariance of the features for this species\n",
    "        mean = subset[______].mean() # <-- Fill in the 'feature_names' variable.\n",
    "        cov = subset[______].cov() # <-- Fill in the 'feature_names' variable.\n",
    "        # Create a multivariate normal distribution\n",
    "        rv = multivariate_normal(______, ______) # <-- Fill in 'mean' and 'cov' respectively.\n",
    "        # Store the distribution in the likelihoods dictionary\n",
    "        likelihoods[species] = rv\n",
    "    return likelihoods\n",
    "\n",
    "# Use the function to compute likelihoods\n",
    "# Fill in the feature names you're using to calculate the likelihoods\n",
    "feature_names = ['______', '______', '______'] # <-- Fill in the actual feature names you want to include.\n",
    "likelihoods = compute_likelihoods(df, feature_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5518d95-2a1f-473a-9134-4c2bbbf5cf45",
   "metadata": {},
   "source": [
    "# Updating Posterior Probabilities - 10 Points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ef1ec6f-ea44-4c55-831a-dece6ea30eb4",
   "metadata": {},
   "source": [
    "Once we have our likelihoods and prior, we can update the posterior probabilities. This involves multiplying the prior probabilities by the likelihoods and normalizing.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "de5181aa-55cc-4185-9e39-5e660e9c39ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the update function\n",
    "def update(p_dist, likelihoods, observed_data):\n",
    "    # Multiply the prior by the likelihoods\n",
    "    p_dist['probs'] *= [likelihoods[species].pdf(observed_data) for species in p_dist['______']]  # <-- Fill in the column name for species.\n",
    "    # Normalize the probabilities\n",
    "    p_dist['probs'] /= p_dist['probs'].______()  # <-- Fill in the method to sum the probabilities.\n",
    "    return p_dist\n",
    "\n",
    "# Apply the update\n",
    "# For the blank below, input the observed data point\n",
    "observed_data = [160, 18, 35]  # <-- Fill in the blanks with observed feature values.\n",
    "posterior = update(p_dist, likelihoods, observed_data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4111528b-bed2-49ea-aa3d-4459f63c9464",
   "metadata": {},
   "source": [
    "Display the updated posterior probabilities to see the most likely species given the observed data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64bf9a99-0933-441d-bced-d79f6d80453f",
   "metadata": {},
   "source": [
    "# Printing Probabilities and Reasoning - 10 Points (Reasoning - 5 Points bonus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7e459cd8-efbd-44cb-9d60-77a1c163d266",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   species         probs\n",
      "0    Eagle  1.975966e-13\n",
      "1    Robin  1.968779e-02\n",
      "2  Sparrow  9.803122e-01\n"
     ]
    }
   ],
   "source": [
    "# Display the posterior probabilities\n",
    "print(______)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "eab4ac49-aa05-4291-857d-cb18689d3f3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write your reflection below and what was the final prediction. Explain in words how using 2 features rather than 3 could have changed the outcome"
   ]
  }
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