Statistically optimal integration of biased sensory estimates

Experimental investigations of cue combination typically assume that individual cues provide noisy but unbiased sensory information about world properties. However, in numerous instances, including real-world settings, observers systematically misestimate properties of the world from sensory information. Two such instances are the estimation of shape from stereo and motion cues. Bias in single-cue estimates, therefore poses a problem for cue combination if the visual system is to maintain accuracy with respect to the world, particularly because knowledge about the magnitude of bias in individual cues is typically unknown. Here, we show that observers fail to take account of the magnitude of bias in each cue during combination and instead combine cues in proportion to their reliability so as to increase the precision of the combined-cue estimate. This suggests that observers were unaware of the bias in their sensory estimates. Our analysis of cue combination shows that there is a definable range of circumstances in which combining information from biased cues, rather than vetoing one or other cue, can still be beneficial, by reducing error in the final estimate.