[From Bill Powers (960221.0930 MST)]

Bruce Abbott (960221.0855 EST) --

Using a steady response rate would be rather uninformative, I

believe. For example, imagine using a steady rate of 1 resp/s,

with dt = 0.1 s. A response will be generated every tenth

iteration. Meanwhile the VI interval timer is decrementing toward

zero; when it reaches zero a reinforcer is set up. It may be that

this coincides with one of those MOD 10 responses, in which case

the reinforcer gets delivered immediately. Or it could happen on

the next iteration, or the next, etc, out to nine iterations.

Since the VI setup is random with respect to the response

generator, the probability that setup will occur on any given

iteration is constant, yielding a rectangular distribution of

delays between setup and collection with a mean of 10/2 iterations

or 0.5 s.

What you do is set up a steady response rate, let the simulation run,

and compute the average reinforcement rate when you have enough data to

get a meaningful result. Then you increment the response rate and do it

again, and so on until you have scanned the entire range of behavior

rates of interest. This will give you a curve showing the mean output

reinforcement rate as a function of input response rate. When I did

this, I got a curve that was closely matchable by a 1 - exp(-kt) curve.

You could also fit your "linear" curve to it (your curve isn't really

linear, is it?).

My interest in assessing how the feedback function changes as a

function of response distribution came about initially ...

If you have a true characterization of the feedback function, it will be

independent of response distribution. Of course with different

distributions of inputs, you will get different distributions of output,

but that does not mean that the feedback function has changed; it means

only that you're presenting the same function with different input

patterns, so naturally you get different output patterns.

If you think about this a bit, you'll realize that the feedback function

has to be independent of the input, since it just represents a piece of

non-adaptive apparatus with fixed characteristics. This physical device

can't vary its physical properties as the input pattern changes. The

same feedback function has to apply as long as you're using the same

schedule.

In engineering, this subject is called "transfer functions." A transfer

function is a way of describing a physical input-output device in a way

that allows calculating its output for ANY pattern of inputs (in the

domain in which inputs and outputs are being measured).

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I will be ordering the rats this week.

Hooray!

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Chris Kitzke 960221.0800 --

Rick Marken 960213.2100 --

While your comments on anger are interesting, Remi Cote used "mad" (I'm

pretty sure) in the sense of "insanity," not "anger."

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Shannon Williams (960221.08:30) --

A thinking creature pauses in one goal to pursue another. A

thinking creature can delay or inhibit the behavior indicated by

'E'. A thinking creature can change his 'R', etc. It seems to me

that the behavior generating mechanism in a thinking creature has

evolved to be quite different from the behavior generating

mechanism in an insect.

Well, I'll leave it up to you. How would you apply hierarchical PCT to

answer these points?

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Gary Cziko (direct post) --

I not only approve of your plans, but am delighted by them!

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Best to all,

Bill P.