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