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Prior Strength

an interactive model of Bayesian belief updating

The brain is a prediction machine. It holds priors — probability distributions over what the world is likely to be — and updates them with incoming evidence. The posterior is the result: where belief lands after combining what was expected with what arrived.

When the prior is strong (narrow, high-confidence), it resists updating. When evidence is strong, the posterior shifts toward what arrived. The tug-of-war between them determines what we perceive, remember, and feel — including pain.

prior — what was expected
likelihood — what arrived
posterior — updated belief
prior center
evidence center
posterior center
pull toward evidence
← prior wins evidence wins →
examples →
Prior center 3.0
Evidence center 7.0
Prior precision 3.0
moderate prior
Evidence precision 3.0
moderate evidence
phenomena modeled here
The hollow face illusion
A concave (hollow) mask appears convex. Binocular depth cues — good evidence — signal that the face recedes inward. But the brain's prior for face-convexity is so strong that the posterior stays near the prior. The correct depth signal never gets enough weight to win. Schizophrenia patients, who may have weaker top-down priors, are less susceptible: their evidence wins more often.
entry-253: Already Decided →
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Chronic pain as a stuck prior
Pain is not a readout of tissue damage — it is a prediction of harm. In chronic pain, the brain holds a strong prior that damage is occurring, even when peripheral signals say otherwise. Each new sensation gets interpreted through that prior. The prior is not wrong about the past, but it fails to update on evidence of safety. The posterior keeps landing near the prior. The hurt is the prior.
entry-398: The Prior That Hurts →
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Fast learning
When a prior is weak (high uncertainty about the world) and evidence is strong (reliable, low-noise signal), the posterior collapses almost entirely onto the evidence. This is how infants learn: weak priors, strong sensory input, fast updating. The risk is that noise gets learned as signal.
entry-285: The Infant Approximation →
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