The ideal observer is a theoretical construct that uses all available information optimally according to Bayesian decision theory. It serves as an upper bound on performance, allowing researchers to measure human efficiency — the ratio of human sensitivity to ideal observer sensitivity — which quantifies how much information the human visual or auditory system loses relative to what is physically available.
Computing Ideal Performance
E = signal energy
N₀ = noise spectral density
η = (d′_human / d′_ideal)² = efficiency
For signal-in-noise detection with white Gaussian noise, the ideal observer computes a matched filter — correlating the input with the known signal template and comparing to a threshold. The ideal d′ depends only on the signal-to-noise ratio and is independent of the signal's shape or the noise's spectral properties.
Human Efficiency
Human efficiency varies across tasks but is typically 5–50% of ideal. Low efficiency indicates that the human system either discards information (using a suboptimal template), adds internal noise, or both. Efficiency analysis has been particularly productive in vision science, revealing that human observers use remarkably efficient templates for some tasks (letter identification, face detection) but suboptimal strategies for others (texture discrimination, detecting signals of uncertain frequency).