Probability✓ Mathematical
◆ The PatternUpdating beliefs with evidence — the foundation of probabilistic ML
Bayes' Theorem tells us how to update a prior belief when we observe new evidence.
P(A|B) = P(B|A) · P(A) / P(B)
P(A|B) = posterior | P(B|A) = likelihood | P(A) = prior | P(B) = evidence
// Medical test — posterior probability after positive result
Prior P(disease) %1.0%
Sensitivity %95%
Posterior—
Base rate fallacy: 1% disease prevalence + 95% accurate test = only ~16% chance you're actually sick after a positive. Low priors dominate!
Pattern bridge: Updating beliefs with evidence is the core of Bayesian statistics. Traders do it intuitively: new data shifts the prior belief — or doesn’t, when confirmation bias blocks the update.