exam_predictor

import pandas as pd
import numpy as np
import pymc as pm
import arviz as az

# Generate dummy data
np.random.seed(1)
data = {
    'Std_No': range(1, 101),
    'HoursStudied': np.random.normal(8, 2, 100), # Mean 8 hrs, SD 2
    'MidtermGrade': np.random.normal(70, 10, 100), # Mean 70, SD 10
    'FinalScore': 0 # Placeholder for target
}
df = pd.DataFrame(data)
# Create a relationship: FinalScore = 20 + 0.8*HoursStudied + 0.5*MidtermGrade + noise
df['FinalScore'] = 20 + 0.8 * df['HoursStudied'] + 0.5 * df['MidtermGrade'] + np.random.normal(0, 5, 100)
df['FinalScore'] = np.clip(df['FinalScore'], 0, 100) # Keep scores in range
print(df.head(10))


# Define the Bayesian Model
with pm.Model() as marks_model:
    # Priors for model parameters
    intercept = pm.Normal('intercept', mu=50, sigma=20) # Intercept (prior belief about average score)
    study_hours = pm.Normal('study_hours', mu=1, sigma=1) # Slope for Hours studied
    midterm_marks = pm.Normal('midterm_marks', mu=0.5, sigma=0.5) # Slope for Midterm grade
    sigma = pm.HalfNormal('sigma', sigma=10) # buffer (standard deviation)

    # Expected value of final score
    mu = intercept + study_hours * df['HoursStudied'] + midterm_marks * df['MidtermGrade']

    # Likelihood
    likelihood = pm.Normal('likelihood', mu=mu, sigma=sigma, observed=df['FinalScore'])

    # Sample from the posterior
    trace = pm.sample(2000, tune=1000, cores=1)
    az.plot_trace(trace) # Visualize posterior distributions

    # Create posterior predictive samples
    posterior_predictive = pm.sample_posterior_predictive(trace, model=marks_model)

# Get mean prediction and credible interval of 95% (let's say)
predicted_score = np.mean(posterior_predictive.posterior_predictive['likelihood'])
ci_lower = np.percentile(posterior_predictive.posterior_predictive['likelihood'], 2.5)
ci_upper = np.percentile(posterior_predictive.posterior_predictive['likelihood'], 97.5)

print(f"\nPredicted Final Score: {predicted_score:.2f}")
print(f"95% Credible Interval: [{ci_lower:.2f}, {ci_upper:.2f}]")

# Or check posterior for specific parameters
az.summary(trace, var_names=['intercept', 'study_hours', 'midterm_marks', 'sigma'])