The Mixture of Bernoulli Experts: a theory to quantify reliance on cues in dichotomous perceptual decisions.

The appearances of perceptually bistable stimuli can by definition be reported with confidence, so these stimuli may be useful to investigate how visual cues are learned and combined to construct visual appearance. However, interpreting experimental data (percent of trials seen one way or the other) requires a theoretically motivated measure of cue effectiveness. Here we describe a simple Bayesian theory for dichotomous perceptual decisions: the Mixture of Bernoulli Experts or MBE. In this theory, a cue's subjective reliability is the product of a weight and an estimate of the cue's ecological validity. The theory (1) justifies the use of probit analysis to measure the system's reliance on a cue and (2) enables hypothesis testing. To illustrate, we used apparent 3D rotation direction in perceptually ambiguous Necker cube movies to test whether the visual system relied on a newly recruited cue (position of the stimulus within the visual field) to the same extent when a long-trusted cue (binocular disparity) was present or not present in the display. For six trainees, reliance on the newly recruited cue was similar whether or not the long-trusted cue was present, suggesting that the visual system assumed the new cue to be conditionally independent.