23 May 2009

Human sensorimotor cognition is Bayesian!

In tasks involving hand-eye coordination (for example, returning a serve in tennis), the brain has to estimate a quantity u based on an observation v. Bayes' rule tells us that the optimal estimate of u's distribution depends on both the prior distribution of u as well as on the evidence v:

P(u | v) ∝ P(u) P(v | u)

Intuitively we know that anytime we make an decision based on evidence, the decision critically depends on the uncertainty associated with the evidence (how "trustworthy" the evidence is). This is actually encoded in the equation above. If the observation contains little information about the actual value, then we put more weight on the prior. In the extreme case, if the distribution P(v | u) is independent of (i.e. contains no information about) u then the estimate is exactly the prior:

P(u | v) ∝ P(u)

But if the evidence tells us a lot, then we put less weight on the prior. In the extreme case, if P(v | u) = δ(v, u), we can actually ignore the prior:

P(u | v) = δ(v, u)

So, we have to integrate the two pieces of information— the prior and the evidence— to make an estimate, while accounting for the reliability of the evidence.

Now, if this sounds complicated, you can take some consolation in the fact that you actually already know all this stuff. In a paper published in Nature, Körding and Wolpert (1994) described an experimental setup in which they asked volunteers to complete a hand-eye coordination task. The subjects' task performance indicates that the human brain maintains estimates of the prior distribution and the evidence uncertainty, and combines them in a way that is consistent with the Bayesian estimate above (and inconsistent with a couple of alternative models of cognition).

That's right: we appear to be hard-wired for Bayes' rule. This is pretty amazing, if you ask me.

Konrad P. Körding and Daniel M. Wolpert, Bayesian integration in sensorimotor learning. Nature vol. 427, pp. 244-247 (15 January 2004)

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