Using simulation to disambiguate transducer and noise.

The relationship between perceived stimulus magnitude and physical stimulus intensity has traditionally been probed through two largely separate experimental traditions: near-threshold measures of sensitivity and suprathreshold measures of appearance. Reconciling both approaches has proven difficult because they rely on different theoretical assumptions and involve different experimental techniques. Here we argue that the empirical relationship between sensitivity and appearance cannot be resolved by experiment alone and propose a simulation-based approach, which requires explicitly specifying the transducer, the noise model, and the observer's decision rule. Within this framework, we evaluate whether maximum likelihood difference scaling (MLDS) can recover a known transducer from simulated data, especially for the critical cases in which different transducer and noise combinations produce identical discrimination performance. We simulate MLDS experiments for logarithmic and power-law transducers combined with additive and multiplicative noise at magnitudes representative of psychophysical data. MLDS recovers compressive, linear, and moderately expansive transducers accurately for both noise types. Systematic bias appears for strongly expansive transducers under large multiplicative noise, a case not often encountered in low-level vision. These results indicate that, for the transducer and noise models simulated here, MLDS recovers transducer shape. Our results illustrate how simulation can be used to evaluate and compare psychophysical methods by making their assumptions explicit.