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) × 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 test that is 99% sensitive and 99% specific, 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.
The result feels counterintuitive because we tend to judge by test accuracy alone while ignoring prevalence (the base rate). This error is a typical example of the cognitive bias known as base rate neglect, and Bayes' theorem lets you calculate the probability with the base rate built in.
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 on the same indicator across different data sources or years increases the posterior probability that you truly belong in the top tier, while a single statistic means the update has happened only once.
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.