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Hadley Tassinari, Michael S. Landy, Todd E. Hudson; Combining priors and noisy visual cues in rapid pointing. Journal of Vision 2005;5(8):126. doi: https://doi.org/10.1167/5.8.126.
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Statistical decision theory suggests that optimal decisions (or actions) combine: (1) prior information (the probability of world states), (2) likelihood of world states given sensory data, and (3) the consequent gains or losses. Previously (Trommershaeuser, Maloney & Landy, JOSA A, 20, 1419–1433, 2003), we asked subjects to rapidly point at visual targets in the presence of neighboring penalty regions, with known payoffs/penalties. Performance was nearly optimal, indicating subjects fully account for (2) and (3). Can subjects optimally integrate likelihood and prior information in a rapid pointing task (assumed, but not tested, by Koerding & Wolpert, Nature, 427, 244–247, 2004)?
Methods: Subjects pointed and were rewarded when a target was hit within 0.7 s. Target location was chosen randomly from a Gaussian prior distribution. The mean location of the prior varied across trials. On each trial, first the prior was displayed as a bright Gaussian blob, with crosshairs at its mean. Next, the blob was replaced by random dots chosen from a distribution centered on the target location. The variance of this target-dot distribution controlled the visual information for the target location (the likelihood (2)), and was varied across trials. The target area was not explicitly displayed; hits on the screen within 7.5 mm of the mean of the target-dot distribution were rewarded.
Results: An optimal movement planner combines the prior and likelihood by aiming at the weighted average of the estimated location of the centroid of the set of target dots and the center of the prior. The weights should be inversely proportional to the respective variances. As predicted, endpoints regressed systematically toward the prior as target uncertainty increased. The data are compared with predictions of the optimal movement planner based on (a) perfect centroid calculation, and (b) a likelihood function determined in separate random-dot-localization experiments.
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