The Bactra Review Spikes
What the homunculus wants to know is <s|T>, the expected stimulus given a
particular spike-train, and for this it needs Pr(s|T), the probability of a
stimulus given the spike-train. What we as experimenters can easily find are
<T|s> and Pr(T|s), the corresponding quantities for the spike-train given
the stimulus. To invert the conditional probability distributions, we employ
Bayes's rule: Pr(s|T) = Pr(T|s) Pr(s)/Pr(T), which is a direct consequence of
the definition of conditional probabilities. To make use of it, we need to
know Pr(T), the probability of a particular spike-train (all else being equal)
and Pr(s), the probability of a particular stimulus, again all else being
equal. Now, there is a whole sect of statistical thought whose attitude to
Bayes's rule is simply idolatrous, venerating it as the font and form of all
legitimate inference, and place nearly as much weight on Pr(s) and its
equivalents, the so-called ``prior probabilities,'' or just ``priors.'' The
follies of this school shall not, on this occasion, detain us (see rather the
review of Mayo's Error and the Growth of Experimental
Knowledge), since, in the laboratory or the field, Pr(s) is in
principle a perfectly well-defined set of frequencies, as our authors stress.
I do take issue, though, with their repeated statements that the homunculus
and/or the neurons must employ Bayes's rule, and so have something like a
prior: this seems a classical instance of William James's ``psychologist's
fallacy,'' only here it would be the neurobiologist's fallacy. The
homunculus, much less the actual cells, don't know Pr(T|s), so Bayes's rule,
prior or no prior, would be of no use to them in estimating Pr(s|T) and (more
importantly) <s|T>. The only thing which might, so to speak, see both
Pr(T|s) and Pr(s) is natural selection, which would act to tune both the
encoding and decoding processes, conceivably implementing rules like
``Sensations of flying are almost certainly wrong'' in elephants or ``small
moving black dots are probably edible bugs'' in frogs; but at this point we
begin to cross the border from the neural code to the structure of the nervous
system.