What's a statistic?

[Martin Taylor 940830 13:40]

Rick Marken (940829.1110)

Martin Taylor (940829 10:40) --

Me:

Have you seen any of this "passive statistical analysis" taking place

Martin:

Of course you can see it, at least some of it, physiologically if not
psychologically. The data flow is reduced by a factor of 100 between the
retinal receptors and the optic nerve

But there is not necessarily anything "statistical" about this reduction.
Statistical analysis implies that some statistical measures of the input data
are being computed -- means, variances, etc. Have you seen any evidence of
this kind of analysis?

What's a statistic? I learned the word as meaning the reduction of a set
of values to one or a few representative values, such as, indeed, means,
variances, etc.

Every PIF computes a statistic of a kind, but I meant a bit more than that
when I talked about "passive statistical analysis" reducing the dimensionality
of the sensory input. A mean is a scaled version of the sum, and any
intensity-level PIF will do that. The question is whether that kind of
operation is done before the sensory data get to the point at which
controllable perceptual signals are computed. The reduction between the
number of retinal receptors and the number of fibres in the optic nerve
is not done by selecting which receptors to connect to an output, but by
computing various relationships among the receptor outputs, and sending
the results of those computations (windowed sums, time-differences,
differences between the average of the middle and the average of a surrounding
ring, and so forth) to the higher levels. These are statistics, and
they seem to be statistics that are of some value in the further development
of controlled perceptions.

One interesting question is just how far the computation of these statistics
reduces the number of degrees of freedom available in the input, because
it is that reduction that determines the magnitude of the alerting problem.

Martin