Signal detection theory in the 2AFC paradigm: attention, channel uncertainty and probability summation

Neural implementation of classical High-Threshold Theory reveals fundamental flaws in its applicability to realistic neural systems and to the two-alternative forced-choice (2AFC) paradigm. For 2AFC, Signal Detection Theory provides a basis for accurate analysis of the observer's attentional strategy and effective degree of probability summation over attended neural channels. The resulting theory provides substantially different predictions from those of previous approximation analyses. In additive noise, attentional probability summation depends on the attentional model assumed. (1) For an ideal attentional strategy in additive noise, summation proceeds at a diminishing rate from an initial level of fourth-root summation for the first few channels. The maximum improvement asymptotes to about a factor of 4 by a million channels. (2) For a fixed attention field in additive noise, detection is highly inefficient at first and approximates fourth-root summation through the summation range. (3) In physiologically plausible root-multiplicative noise, on the other hand, attentional probability summation mimics a linear improvement in sensitivity up to about ten channels, approaching a factor of 1000 by a million channels. (4) Some noise sources, such as noise from eye movements, are fully multiplicative and would prevent threshold determination within their range of effectiveness. Such results may require reappraisal of previous interpretations of detection behavior in the 2AFC paradigm.