Source
Geisler (2011), LIT-1055 (Vision Research 51(7), 771–781), read in NOTE-870 from the NIH author manuscript (PMC3062724). Figures were not seen, and none of the cited primary studies was read, so what they found is the review’s account.
What was actually shown
The definition. “An ideal observer is a hypothetical device that performs a given task at the optimal level possible, given the available information and any specified constraints.” Equation (1): r_opt(Z) = argmax_r Σ_ω γ(r, ω) p(ω | Z), with γ the utility of response r in world state ω. Constraints enter as Z = g(S; θ), “the constraint function that specifies the mapping of the stimulus into a neural representation”; with no constraint, Z is replaced by S. So there is a family of ideals, one for each stage at which the input is taken, each unrestricted in what it computes from its input. With accuracy as the utility in a two-category task, equation (1) is the posterior-maximising rule.
Locating losses. The review’s one explicit statement of the method: studies “evaluated the additional effects on ideal observer performance of biological constraints such as the optics of the eye, the spatial and chromatic sampling by the photoreceptors, photoreceptor noise, and ganglion cell spatial summation”. Human performance “often parallels ideal observer performance qualitatively (and sometimes quantitatively)”, but “the suboptimal performance of human observers implies substantial contributions of central factors.” High external noise is used to swamp early factors and “isolate the effects of some of the central factors”: for the template-matching ideal, squared threshold rises linearly with squared rms noise contrast, human thresholds approximately follow above some noise level, and the intercept gives “an equivalent internal noise”.
The asymmetry of the benchmark. “When human performance approaches ideal performance … all hypotheses (model observers) that cannot approach ideal performance can be rejected. When human performance is far below ideal, there are generally a greater number of models than could explain human performance.”
Examples with numbers, as reported. Ideal colour names on individual cone mosaics correlate with subjects’ names at r = 0.83; a natural-statistics decoder of peripheral samples gives 42% lower mean squared error than linear interpolation over 1000 images; the contour-occlusion ideal predicts “approximately 99%” of the variance in seven subjects’ responses.
What could have come out otherwise. Human performance across conditions could have departed from the retinal-stage ideal’s pattern, which would put the loss somewhere the stage comparison does not reach. The review reports that it often did not. This is the part the record has not checked at source.
What this does not say
- What efficiency is. The review uses the word without a formula. The squared ratio of human to ideal d′ is from Burgess et al. 1981 and Pelli and Farell 1999, which the review cites and the record does not hold.
- That the gap measures a bounded observer’s restriction. A constrained ideal here degrades the input, a garbling that loses information, and stays optimal on what remains. An observer restricted to a class of computations on an intact input is a different object. The two can come apart: a garbling that leaves total variation near one leaves the ideal near perfect, while a restricted class can sit at chance (CLAIM-302). The review’s nearest thing to a restricted class is “degrading the ideal observer with hypothesized neural noise or with hypothesized heuristic computations”, and comparisons with single named suboptimal rules in search, not with the best rule in a class.
- That a gap below the ideal identifies its cause. The review says the opposite: far-below-ideal performance leaves many models standing.
- That every loss is in the input. It names residual losses in the decision rule (spatial or channel uncertainty, which it counts as internal noise, nonlinearities, inefficient pooling), which no input garbling represents.
- Anything about computational indistinguishability. The review does not mention it, or treat computational limits except as noise, heuristics or a biophysical cost it names and does not develop.
Connections
- THEORY-031: the two-category case of equation (1) is the likelihood-ratio rule at a prior-set threshold; consistent, adding nothing formally.
- CLAIM-199 separates what a rendering makes possible for any receiver from what a receiver restricted to a rule class can use. Constrained ideals are the first kind, applied to stages of one system; THEORY-349 is the second kind.
- QUESTION-103: efficiency, so defined, measures the first gap; a measure of the restricted-class gap on real observers is still wanting.