── ── Decision-making · Update beliefs with evidence
Bayesian Reasoning
Bayesian reasoning updates belief in proportion to how diagnostic new evidence is: your posterior odds equal your prior odds multiplied by the likelihood ratio. What you believe after seeing evidence depends not only on the evidence but on how probable the claim was beforehand—the base rate you started from.
How it works
Begin with a prior: how likely the hypothesis is before the new evidence, grounded in the base rate. Then weigh the evidence by its likelihood ratio—how much more probable that evidence is if the hypothesis is true than if it is false. Multiply, and you have your updated belief.
The discipline lives in two places people skip: anchoring on the real base rate instead of the vivid story, and asking how often the same evidence would appear even when the hypothesis is false. Strong-feeling evidence with a weak likelihood ratio should barely move you.
When to use it
- Reading an early metric or A/B result and deciding how much to update your roadmap
- Evaluating a rare-event claim ('this user is fraud,' 'this is the breakout channel') against its base rate
- Reacting to a single dramatic data point that could easily be noise
- Updating conviction on a hypothesis as evidence arrives piece by piece rather than overreacting to each
When not to use it
When you have no reasonable prior and no way to estimate likelihoods—forcing precise-looking numbers onto pure guesses produces false confidence dressed as math.
Worked example
The Sally Clark Case, 1999
Sally Clark was convicted of murdering her two infants after an expert testified that two cot deaths in one family had a roughly 1-in-73-million chance. The figure ignored the prior question—how rare double murder of infants is by comparison—and treated the events as independent. Weighing the evidence against the correct base rates, the prosecution's case was far weaker than the number implied; the conviction was a notorious miscarriage of justice.
Why it matters for founders
Founders live on noisy signals—one churned customer, one viral post, one investor's offhand comment—and the temptation is to overhaul strategy on each fresh data point. Bayesian reasoning keeps you anchored to the base rate and updating in proportion to how diagnostic the evidence actually is, so you neither ignore real signal nor whipsaw on noise. deciqAI's agents update on evidence rather than the most recent or most vivid input.
Install this skill (free, MIT)
npx skills add deciqAI/knowledge-skillsFAQ
What is the base rate fallacy in Bayesian terms?
It's neglecting your prior—judging a hypothesis only on how striking the new evidence looks while ignoring how rare or common the hypothesis was to begin with. Even very strong evidence can leave a rare claim improbable.
Do I need actual numbers to think like a Bayesian?
No. The core habit is qualitative: start from how likely something was beforehand, then ask how much this evidence really discriminates between the hypothesis being true or false, and update proportionally.