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.