Bayesian thinking

1. Three words are enough

Concept	The question	Everyday phrasing
Prior	Before this evidence, how likely was it?	"Is this sort of thing common?"
Likelihood	If it were true, how probable is this evidence?	"How well does the evidence fit?"
Posterior	Putting it together, how likely is it now?	"The updated judgement"

In one line: posterior ∝ prior × likelihood. Skip the formula, keep the order.

2. A worked example

A colleague has not replied for half a day. Two explanations appear:

• A: he is busy today;
• B: he is annoyed with you and is deliberately ignoring you.

Prior: with no other information, "a colleague is busy" is far more common than "a colleague is targeting you". So A starts much higher.

Evidence: a new clue arrives — he replied to someone else instantly, and skipped only you.

Update: that evidence is more likely under B, so B rises and A falls. But note: even if the evidence favours B, if B started extremely low it may still be low after updating. That is why you do not skip the prior.

The typical error is asking only "how much does this evidence look like B", never "how rare is B in the first place".

3. Why it beats intuition

• It resists vivid stories — the more cinematic the explanation, the more it tends to be overrated. Bayesian thinking puts the prior back on the table.
• Evidence accumulates — each new clue updates the previous judgement rather than starting over.
• The output is a range, not a verdict — admitting uncertainty is what stops one bad call from locking you in.

4. Three common misuses

Confusing resemblance with probability. "This explanation sounds right" is a statement about likelihood, not about the posterior — the prior still matters.

Concluding from a single clue. One piece of evidence usually shifts probability a little. When evidence is weak, the posterior should stay close to the prior.

Ignoring the reliability of the evidence. "Someone said" or "I caught a glimpse" has a much lower likelihood than "it reproduced three times in a row".

5. Putting it to work

When something is uncertain, ask in this order:

1. How common is this in reality? (prior)
2. How probable is my evidence under "true" versus "false"? (likelihood)
3. After updating, how many options are still worth considering?
4. Which one do I test, and what do I observe next?

That is the loop Ockham runs — see the method. Related: base-rate fallacy, correlation vs causation, Occam\'s razor.