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Mathematics May 2, 2026 1 min read

Bayes' rule is a disciplined way to update belief

New evidence should change a belief in proportion to how likely that evidence was under competing explanations.

Takeaway

Evidence is strongest when it is much more expected under one explanation than another.

What I learned

Bayes' rule describes how to update a prior belief after seeing new evidence. The key idea is not just whether evidence is possible, but whether it is more likely under one explanation than another.

A simple intuition

If an observation would be common when a hypothesis is true and rare when it is false, that observation should increase confidence in the hypothesis.

Why it matters

This is useful for diagnosis, debugging, forecasting, and everyday reasoning. It encourages me to ask: what would I expect to see if each explanation were true?