Why High Accuracy ≠ High Reliability in Rare Event Detection

📚In my role as a data scientist, I've learned that probability isn’t just an abstract concept. It deeply impacts decision making in high-stakes, low-frequency events like medical diagnoses, fraud detection, and risk assessment.

One frequently overlooked fundamental is that precision collapses when events are rare, even if a model is very accurate.

This classic probability problem demonstrates why intuition often fails us when evaluating test results for infrequent events. If you test positive for a rare disease, what’s the actual chance you have it? The answer is more surprising than you’d expect! To demonstrate, let's say I have a medical test for Disease X with the following stats:

✅ It correctly detects Disease X 90% of the time.

❌ It incorrectly flags healthy people 5% of the time.

🏥 Disease X affects 0.2% of the population.

If a patient were to get a positive test, what's the probability that they actually have Disease X?

There's more than one way to think about this problem, but after a quick plug in to Bayes' Theorem we find that the precision of this test is only 3.5%, meaning there's less than a 4% chance a patient truly has Disease X if they test positive.

🔎 So what does this mean?

Even though a model can seem highly accurate, its real-world usefulness depends on how it’s applied. In rare event detection, false positives can far outnumber true positives, making confirmatory testing or additional safeguards essential. Some examples:

• Medical tests require confirmatory testing before diagnosis.

• Fraud detection models can’t rely on raw scores alone, thresholds and secondary checks are critical.

• Security alerts from AI-driven systems must be carefully tuned to avoid overwhelming analysts with false positives.

🚀 The lesson? When dealing with rare events, accuracy alone isn’t enough—you need to carefully consider precision and base rates, or risk making bad decisions based on misleading probabilities.