bayes regression using kde

bayes_regression.py

# Since we don't have internet access in this environment, I'll replicate a similar workflow.
# Let's assume the 'data' is a pandas DataFrame obtained from the CSV file.

# For the example, let's create a simulated 'Poverty' column with random data

data_ = pd.read_csv("https://raw.githubusercontent.com/thistleknot/Python-Stock/master/data/raw/states.csv?token=GHSAT0AAAAAACIYSECGQETPAPO6K4QYIFV6ZKDCJIQ").set_index('States')
for c in data_.columns:
    print(c)
    data = data_[[c]]
    
    # Step 1: Estimate the distribution
    distribution = stats.norm.fit(data[c])
    
    # Or for nonparametric
    kde = KernelDensity(kernel='gaussian', bandwidth=0.5).fit(data[[c]])
    
    # Step 2: Validate the estimated distribution (visual and statistical)
    x = np.linspace(data[c].min(), data[c].max(), 1000)
    pdf = stats.norm.pdf(x, *distribution)
    
    # For nonparametric, get the log-probability and convert to pdf
    logprob = kde.score_samples(x[:, np.newaxis])
    kde_pdf = np.exp(logprob)
    
    # Plot for visual inspection
    plt.figure(figsize=(12, 7))
    plt.hist(data[c], bins=30, density=True, alpha=0.5, color='g', label='Data Histogram')
    plt.plot(x, pdf, label='Parametric fit', color='blue')
    plt.plot(x, kde_pdf, label='KDE fit', color='red')
    plt.legend()
    plt.show()
    
    # Step 3: Use the distribution in a model
    # For example, in a simulation
    simulated_data = stats.norm.rvs(*distribution, size=1000)



# Specify the target and predictors
target = 'Poverty'  # Replace with actual target column name
predictors = [col for col in data_.columns if col != target]

# Using KDE to estimate the distribution and generate new samples
kde_models = {}
kde_samples = {}
for c in data_.columns:
    # Fit KDE to the data
    kde = KernelDensity(kernel='gaussian', bandwidth=0.5).fit(data_[[c]].values)
    kde_models[c] = kde
    
    # Generate new samples from the KDE
    new_samples = kde.sample(1000)  # Adjust the number of samples as needed
    kde_samples[c] = new_samples.flatten()

# Define the likelihood function for the data given the predictors
def likelihood_function(data, coefficients):
    predicted = np.dot(data[predictors], coefficients)
    return stats.norm.pdf(data[target], loc=predicted, scale=1)

# Find the MAP estimate for the coefficients
def map_estimate(data, kde_samples):
    A = np.zeros((len(predictors), len(predictors)))
    b = np.zeros(len(predictors))
    
    for i, pred_i in enumerate(predictors):
        for j, pred_j in enumerate(predictors):
            A[i, j] += (data[pred_i] * data[pred_j]).sum()
        b[i] = (data[pred_i] * data[target]).sum()
    
    # Integrate the KDE samples into the MAP estimation
    # This is a placeholder for the integration process
    # In practice, you would use a Bayesian updating method such as MCMC
    
    coefficients = inv(A).dot(b)
    return coefficients
# Assuming that 'Poverty' is the target variable, replace 'Poverty' with the actual target column name

# Compute the MAP estimate for coefficients
coefficients_map = map_estimate(data_, kde_samples)

# Display the estimated coefficients
print(coefficients_map)