Many real-world detection tasks involve multiple opportunities to observe the signal — across time (multiple fixations), space (multiple locations), or features (multiple cues). Multiple-observations SDT models how observers combine these separate pieces of evidence into a single detection decision.
Integration Rules
Probability summation: P(detect) = 1 − Π(1 − pᵢ)
Linear summation: evidence = Σ wᵢ × eᵢ
Under optimal integration, the observer combines independent observations by computing their sum (for equal-variance Gaussian channels), yielding d′ that grows as the square root of the number of observations. Probability summation assumes independent decisions at each observation, with overall detection if any single observation exceeds threshold. Linear summation assumes the observer adds the evidence from all observations before applying a single criterion.
Empirical Findings
Human observers typically perform close to optimal integration for simple detection tasks with a small number of observations. However, performance falls below optimal as the number of observations increases, suggesting capacity limitations on the integration process. The distinction between probability summation and genuine neural summation has been important in vision research, with careful signal detection analyses needed to distinguish these mechanisms.