Identifying visual gain changes under appearance-criterion drift: an analytic and simulation study

Changes in reported visual appearance can reflect sensory adaptation or a changing judgment criterion. We derive how an effective observer distinguishes these accounts and evaluate fixed-budget sampling by simulation. An unrestricted criterion at each time point removes appearance information about transient gain after nuisance adjustment. Discrimination across external-noise levels retains distinct intercept and slope information under the specified response model. Across 35,160 simulated datasets and 140,640 candidate fits, we compare joint sampling, criterion-drift fitting and gain-targeted discrimination. In the 19,600-dataset extension, transient-shaped criterion drift caused false gain selection in 86.5% of null-gain datasets under a joint linear-criterion procedure and 1.0% under targeted discrimination at 432 responses. At 1728 responses, the rates were 100% and 0.5%. Targeted discrimination increased stable-criterion, coupled-observer transient-gain root-mean-square error (RMSE) from 0.0648 to 0.1866 at 432 responses. Exact coupled-model selection remained weak at 1.5% and 29.5% across the two budgets under drift. Wider fitting bounds preserved the stable-criterion cost and increased joint-model drift error. Interval bias and internal-noise changes exposed further attribution limits. These results identify information about effective gain coefficients within the stipulated observer. They show why more responses can strengthen an incorrect attribution when criterion assumptions fail, without establishing a unique biological mechanism.