Convexity of a set of subthreshold stimuli implies a peak detector

It has been shown that for every model of detection (whether single- or multi-channel, with linear or non-linear channels, and whatever decision rule), provided that it predicts a convex set of subthreshold stimuli, there is a psychophysically equivalent peak detector made up of a collection of linear analysers followed by a maximum-output decision rule. In this paper, the equivalent peak detector representations of some widely accepted detection models are calculated. The calculations rest on a general technique for deriving, from a given model, a formula which specifies the analyser most sensitive to any given stimulus.