Tom Bourbon [940831.1456]

[From Rick Marken (940830.1420)] who wrote in reply to:

Martin Taylor (940830 13:40) who had earlier written about passive

statistical analyses by nervous systems. Here, Martin was replying to Rick's

question:

Martin:

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.

Rick:

Actually, a _statistic_ is a measure of some characteristic of a sample (such

as the mean or variance of the sample values) that is used as an _estimate_

of the corresponding characteristic of the population from which the sample

was taken. The corresponding characteristic of the population is called a

_parameter_. Sample statistics are used to estimate ppoulation parameters.

The sample mean is used as an estimate of he population mean. Remember?

And so far as we know, _all_ of the sampling and calculations necessary to

produce these estimates are performed (more or less) knowingly by an entire

human being, or by a surrogate for a human being. Discussions of statistical

computations by small parts of human beings are metaphorical, in much the

same way that discussions in which nervous systems are said to transmit,

receive, or process information are metaphorical. Individual sensory

neurons do not sample selected parameters of the environment and then

calculate descriptive statistics (most-representative scores, ranges,

correlations, etc) or perform inferential statistical procedures (tests for

differences and their levels of significance, etc), or do they?

So, when you say that the perceptual input function computes a statistic I

hear you saying that perceptions are _estimates_ of what is really out

there.

To me, that is the _direct_ implication of the popular metaphor in which

sensory neurons perform statistical analyses on "features" of the

environment. If the metaphor is intended to be strict, then those

statistical procedures would be performed upon, and their results would then

comprise estimates of, something "real" in the environment. To determine the

adequacy of the statistical analyses, a person would compare the original

environmental parameters with the statistical estimates of those parameters.

When the metaphor is applied to nervous systems, all of these analyses and

comparisons are said to occur within individual neurons, but in fact they

require an entire person with access to all of the required data. The

limits on the plausibility of the statistical metaphor are similar to those

when the information metaphor is applied, as Rick also said:

Of course, this is exactly the information theory view of perception;

the senses transmit information to the brain about what is actually out

there. The brain is a statistician using perceptual statistics to estimate

real world parameters. This is quite a different picture of perception

than that given by PCT.

Nice understatement, Rick.

In PCT, perception is a functional analog of an

aspect of the external world that is defined by the perceptual function. The

perceptual function could compute the mean or variance of its inputs; so the

perceptual signal's value could represent variations in the mean or variance

of the inputs to the perceptual function. But this perceptual signal is not

an _estimate_ of anything (the mean or variance it represents if not computed

as a statistic); it is simply a perceptual variable.

Yes. A perceptual signal is a perceptual signal is an analog of

-- something? Speaking strictly, a perceptual signal _is_; it is not

"about."

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.What is an "alerting problem"? How do you "alert" a control system?

Interesting questions. Martin?

Later,

Tom