The latency between the appearance of a visual target and the start of the saccadic eye movement made to look at it varies from trial to trial to an extent that is inexplicable in terms of ordinary 'physiological' processes such as synaptic delays and conduction velocities. An alternative interpretation is that it represents the time needed to decide whether a target is in fact present: decision processes are necessarily stochastic, because they depend on extracting information from noisy sensory signals. In one such model, the presence of a target causes a signal in a decision unit to rise linearly at a rate r from its initial value s0 until it reaches a fixed threshold theta, when a saccade is initiated. One can regard this decision signal as a neural estimate of the log likelihood of the hypothesis that the target is present, the threshold being the significance criterion or likelihood level at which the target is presumed to be present. Experiments manipulating the prior probability of the target's appearing confirm this notion: the latency distribution then changes in the way expected if s0 simply reflects the prior log likelihood of the stimulus.