Naive Bayes

# BAYES' THEOREM IN ACTION

import numpy as np

def bayes_theorem(prior, likelihood, false_positive_rate):
    """
    Calculate posterior probability using Bayes' theorem
    
    P(Disease|Positive) = P(Positive|Disease) * P(Disease) / P(Positive)
    
    P(Positive) = P(Positive|Disease)*P(Disease) + P(Positive|NoDisease)*P(NoDisease)
    """
    # P(Positive)
    p_positive = (likelihood * prior) + (false_positive_rate * (1 - prior))
    
    # P(Disease|Positive)
    posterior = (likelihood * prior) / p_positive
    
    return posterior

# Example: Dengue test in India
prior_dengue = 0.01           # 1% of population has dengue
test_sensitivity = 0.99       # Test correctly identifies 99% of cases
false_positive_rate = 0.05    # 5% false positive rate

probability = bayes_theorem(prior_dengue, test_sensitivity, false_positive_rate)

print("🏥 Medical Diagnosis Example: Dengue Test")
print("="*50)
print(f"Prior probability (having dengue): {prior_dengue:.1%}")
print(f"Test sensitivity: {test_sensitivity:.1%}")
print(f"False positive rate: {false_positive_rate:.1%}")
print()
print(f"If test is POSITIVE:")
print(f"Probability of actually having dengue: {probability:.1%}")
print()
print("💡 Insight: Even with 99% accurate test, low prior")
print("   means many positives are false positives!")

# Multiple tests example
print("\n" + "="*50)
print("If we do a SECOND TEST and it's also positive:")
# Now the prior becomes the posterior from first test
second_test_prob = bayes_theorem(probability, test_sensitivity, false_positive_rate)
print(f"Probability after 2 positive tests: {second_test_prob:.1%}")