Statistical decision theory as a framework for cognition and action.

Laurence Maloney
New York University

In executing any speeded movement, there is uncertainty about the outcome due to motor variability. I’ll present a statistical decision theoretic (SDT) model of ideal movement planning that takes into account a subject’s own spatial and temporal motor uncertainty. I’ll then describe recent experiments in which subjects carried out speeded motor tasks. The outcome of each movement earned an explicit monetary reward or penalty. In one game, for example, subjects attempted to reach out and touch briefly presented reward disks while avoiding nearby, overlapping penalty disks. The task for the subject was to trade off the risk of missing the reward disk against the risk of hitting the penalty disk. The optimum tradeoff depended on the magnitudes of penalty and reward and the subject’s own motor error. For each subject, in each game, we could estimate the ideal movement strategy and maximum expected gain possible using the SDT model. We compared subjects’ movements and winnings to this ideal. In many of these experiments, subjects consistently chose movements that were close to optimal.
This outcome is surprising: these motor tasks are formally equivalent to decision making under risk and subjects making decisions under risk typically do not maximize expected gain. I’ll describe very recent work in which we set out to translate classical decision making experiments (concerning the independence axiom of expected utility theory) into motor form and compare decision making under risk to movement planning under risk in the same subjects.

Support: NIH EY08266.


Hudson, T. E., Maloney, L. T. & Landy, M. S. (2007), Optimal movement timing with temporally asymmetric penalties and rewards. Journal of Neuroscience, under review, 12/2006.

Hudson, T. E., Maloney, L. T. & Landy, M. S. (2007), Planning movements toward probabilistic mixtures of possible targets, Journal of Neurophysiology, under review, 11/2006.

Dean, M., Wu, S.-W. & Maloney, L. T. (2007), Trading off speed and accuracy in rapid, goal directed movements, Journal of Vision, accepted pending revisions, 1/2007.

Maloney, L. T., Trommershäuser, J. & Landy, M. S. (2007), Questions without words: A comparison between decision making under risk and movement planning under risk. In Gray, W. (Ed), Integrated Models of Cognitive Systems. New York, NY: Oxford University Press, pp. 297-315.

Trommershäuser, J., Landy, M. S. & Maloney, L. T. (2006), Humans rapidly estimate expected gain in movement planning. Psychological Science, 17, 981-988.

Trommershäuser, J., Mattis, J., Landy, M. S. & Maloney, L. T. (2006), Limits to human movement planning with delayed and unpredictable onset of needed information. Experimental Brain Research, 175, 276-284.

Wu, S.-W., Trommershäuser, J., Maloney, L. T. & Landy, M. S. (2006), Limits to human movement planning in tasks with asymmetric gain landscapes. Journal of Vision, 6, 53-63.

Trommershäuser, J., Gepshtein, S., Maloney, L. T., Landy, M. S. & Banks, M. S. (2005), Compensation for changes in effective movement variability. Journal of Neuroscience, 25, 7169-7178.
Trommershäuser, J., Maloney, L. T. & Landy, M. S. (2003), Statistical decision theory and rapid, goal-directed movements. Journal of the Optical Society A, 20, 1419-1433.

Trommershäuser, J., Maloney, L. T. & Landy, M. S. (2003), Statistical decision theory and tradeoffs in motor response. Spatial Vision, 16, 255-275.

Presentation (PDF File)

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