Does uncertainty amplify history?

A Bayesian observer should lean on the past more when the present is hard to see. Hypothesis H4 tests that by comparing low-contrast, noisy trials with high-contrast ones.

The synthetic cohort used here does not scale its history weight with uncertainty — its stimulus-history gain is 1 in both conditions — so the correct answer for this dataset is “no difference”. The paired within-observer difference is +0.16° (95% CI −0.44 to +0.72, p 0.587), and the median of model M5’s free gain across observers is 0.99× (0.91 to 1.51). A pipeline that reported an uncertainty effect here would be wrong.

One would. The mean of M5’s gain across the same observers is 1.74× (1.24 to 2.55) — a spurious amplification. The gain is a ratio of the high-uncertainty to the low-uncertainty amplitude, and 20% of observers sit at a bound of the parameter (0.05 or 6) because their base amplitude is near zero, which this cohort deliberately contains (between-observer SD 1.2°). A multiplicative gain is not a usable group statistic under that heterogeneity; the median is reported, and the paired difference above is the preregistered test. On a homogeneous observer M5 recovers a generating gain of 1.0 and 2.5 without bias (decision log D-13).

The estimator’s ability to detect a real interaction is tested separately with the variable-uncertainty observer in the model-discrimination study. Note one structural asymmetry: noise is larger in the high-uncertainty condition, so its amplitude is estimated less precisely and the two intervals are not equally wide.