Definition and Formula
Bayes' theorem is a formula for updating a prior probability P(A) based on new evidence B to obtain the posterior probability P(A|B). Expressed as P(A|B) = P(B|A) x P(A) / P(B), it was proposed by Thomas Bayes in the 18th century. The core insight is that beliefs should be rationally revised in light of evidence.
Medical Testing Example
Even with a 99% sensitive test, a positive result for a disease with 0.1% prevalence means only about a 9% chance of actually having the disease. When the prior probability (prevalence) is low, false positives dominate even with high test accuracy.
This counterintuitive result exemplifies "base rate neglect," a common cognitive bias that Bayes' theorem helps overcome through precise probability calculation.
Application to Ranking Interpretation
When MyRank shows you in the "top 5%," the reliability of that figure depends on the source data's population size and measurement precision. From a Bayesian perspective, consistently ranking highly across multiple indicators increases the posterior probability that you truly belong in the top tier, while a single indicator provides insufficient evidence.
Tips for Intuitive Understanding
The easiest way to grasp Bayes' theorem intuitively is to think in natural frequencies. Out of 10,000 people, 10 have the disease; of those, 9.9 test positive. Of the 9,990 without it, 99.9 are false positives. Among 109.8 positive results, only 9.9 are true positives, yielding about 9%. Thinking in counts rather than fractions makes the updating process visible.