# Inference by Signal Strength

This graph plots how much subjects over- or underinfer from signals as a function of the true signal strength.

Subjects start with a prior of 1/2, and are given binary symmetric signals of different strengths. The x-axis measures what a Bayesian's posterior would be. The y-axis measures how much weight subjects put on the signal, relative to a Bayesian. Values greater than 1 indicate overinference; values less than 1 indicate underinference.

The figure shows overinference from weak signals and underinference from strong signals. A 2-parameter model of cognitive imprecision (Khaw et al., 2020) about signal strength fits the data well, and is shown in dark red.