bayesian

What

Bayesian reasoning treats beliefs as probabilities that are updated proportionally as new evidence arrives. The core formula — P(H|E) = P(E|H) × P(H) / P(E) — in plain terms means: posterior = likelihood × prior / normalizer. You start with a prior (what you believed before), observe evidence, and update. Strong evidence produces large updates; weak evidence produces small updates; confirming noise produces tiny updates.

The key insight is that you must have a prior. "I have no opinion" is still a 50/50 prior — state it explicitly. A common error is base rate neglect — ignoring P(H) and overweighting P(E|H). In debugging, ask "what is my prior that this module has a bug vs that module?" and start there. In decision-making, each new data point is an update, not a verdict.

When to Use

Apply Bayesian reasoning whenever you need to update a belief based on new information, assess probabilities under uncertainty, or avoid base rate neglect. Use it in debugging triage, risk assessment, and any situation where evidence quality varies.

How

1. State your prior belief explicitly as a probability.
2. Observe new evidence and assess its strength/likelihood.
3. Update: posterior = (likelihood × prior) / normalizer.
4. Repeat with each new piece of evidence, treating each as an incremental update, not a final verdict.
5. Beware the anti-pattern: treating every piece of new information as equally significant regardless of quality.