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Date:         Thu, 7 Jan 1993 09:54:48 -0700
From:         "William T. Powers" <POWERS_W%FLC@VAXF.COLORADO.EDU>
Subject:      Generative models; prediction; models for mouths

[From Bill Powers (930107.0830)]

Greg Williams (930107) --

>As I've said before, Newton was the Skinner of his day:
>"Hypotheses non fingo!" I think we must admit that he guessed
>right that his trying to make a generative model for gravity --
>and then being able to test it -- would have been fruitless.

But Newton DID propose a generative model. It went "Every bit of
matter in the universe attracts every other bit of matter with a
force proportional to the product of the masses and inversely
proportional to the square of their separation." This was
certainly not what was observed. The observations had to do with
behavior of planets, the moon, and thrown and dropped objects.
Newton proposed an underlying set of entities called "masses"
which had the property stated in his universal law. Beginning
with his generative model, one could do experiments to determine
the model parameters (the universal constant of gravitation), and
then deduce how any collection of bits of matter would behave
gravitationally. So the observations were compared with
deductions from the generative model. Predictions were made by
running the model, by calculation, to generate a specific
behavior, which then could be compared with what actually
happened. They're still testing this model; the most recent test
I know of was intended to see if the spatial exponent was exactly
2.0. It was, to as many decimal places as could be measured.
Pretty good generative model.

Newton fingod plenty of hypotheses. When he said that, he must
have been using the term differently from the way we use it now.

>The question really boils down to whether, at a given time,
>generative models work better FOR THE PURPOSES OF THE
>INVESTIGATORS than do descriptive "models." Even in the long
>run, generative models simply might be too complicated to
>actually make, or you might run into chaos (hair- trigger)
>problems.

Descriptive models work. What they are, basically, are summaries
of observations of how the world has behaved in the past. When
you manipulate A, what has the average effect on B always been?
This is good enough for a lot of purposes -- driving a car, if
not designing an internal-combustion motor. So I agree with you.
If all you want is the level of predictivity you can get with
descriptive models, then they're quite good enough.

>>It's not worthwhile trying to make a model fit every anomaly.

>There goes the PCT standard of "accept nothing less
>99.9999999... correlations."

Curb your gazelle, sir. I have advocated requiring correlations
of at least 0.95 before taking data very seriously. If there are
so many anomalies in a data run that the correlation of model
versus real behavior drops below that level, the anomalies must
be investigated or the model must be improved. You shouldn't put
quotations marks around things I never said.

My reasons for demanding such correlations are not religious.
They have to do with the requirements on scientific facts that
are to be used in deductive arguments that rely on more than just
one or two isolated observations. If your facts have only an 80%
chance of being true, you're limited to arguments in which you
use less than four facts at once, if you want the conclusions to
have even a 50-50 chance of being true. With a 90% chance of
truth, you can use 6 facts. With a 99% truth value you can use 69
facts -- if all you want is a 50-50 chance that the conclusion is
true. If you want a 95% chance that the conclusion is true, and
each fact has an independent  probability of 0.99, you're back
down to only 5 facts.

It's pretty hard to think of any half-way useful scientific
prediction that is made on the basis of only 5 facts that have to
be true at the same time. Most useful predictions, such as the
trajectory of a Mars probe, rest on hundreds of underlying facts,
especially when you consider tracing all derived facts back to
their experimental bases.

So what you said about the usefulness of descriptive models is
true, but you have to think about the implications. Descriptive
models of the kinds we usually find in the behavioral sciences
are made of facts with relatively low truth-values. The most
predictive use of such a fact is to use it alone: If a fact has a
60% chance of being true, then the next time you look the same
fact will still have a 60% chance of being true. But if you try
to combine that fact with another one of the same truth value in
order to draw some more interesting conclusion, your conclusion's
truth value immediately drops to 36% -- it's probably wrong.

The use of low-quality facts is therefore a terrific handicap on
any enterprise that can succeed only to the extent that its
predictions are correct. When low-quality facts are used, there
can be no grand structure of concepts that hangs together as it
does in physics and chemistry. The science of psychology, as long
as it remains satisfied with the degree of predictivity it now
achieves, will always remain simplistic and fragmented. Its
predictions will always remain poor. Only an intensive public-
relations job could have persuaded society to continue supporting
psychology. Selling failure as success has been critical to many
such PR jobs.

>In principle, underlying generative models are more complete
>than descriptions at the level of the phenomena. But in
>practice, the former might not be able to predict better than
>the latter, due to the complexity of the underlying mechanisms
>and/or hair-trigger situations.

I suppose that in some imaginary case that might be true. So far,
however, all the generative models actually developed and tested
under PCT have predicted a lot better than any descriptive models
have done. I'm not going to worry about complexity of underlying
mechanisms and hair-trigger effects until I run into them. Maybe
that's what Newton meant by "hypotheses non fingo." Don't let
your imagination throw up so many difficulties that you never try
anything. I've found that the solution to imagined problems is
always simpler than I thought.

RE: putting model where mouth is.

>I think you better be explicit about what you mean by "real S-R
>model." The kind of model a behaviorist would make is one which
>is a function of observables in the external world; in this
>case, cursor position and velocity, target position, and handle
>position and velocity.

Fine. I'll give you a data record showing the cursor, target, and
handle behavior point by point -- the raw data. I will generate
the disturbance pattern at random, and scout's honor will fit the
control model to the behavior without using any information about
the disturbance or even knowing what disturbance pattern was
created.

You devise an S-R model that will predict the cursor and handle
behavior for a new randomly-generated disturbance pattern,
unknown to either of us in advance, with exactly the same target
behavior. I will predict the new handle and cursor behavior with
the control-system model; you predict them with your S-R model.
We will then compare the results. You can use any definition of S
and R that you please, and any number of integrals or derivatives
that you can get from the data.

>It will save me a lot of trouble if I know in advance that a
>descriptive function which includes a subtraction of cursor
>position from target position won't count for you as a "real"
>descriptive "model."

Any operations you like. But whatever you use, the S-R model must
be expressed as H = f(C,T).

I will be extremely interested to see what you decide to use for
C, without knowing what the disturbance is.
------------------------------------------
>Then you go through a long list of red herrings. What I meant
>to say is that various PCT models such as proportional,
>proportional-integral, and proportional-integral-derivative,
>with various nonlinearities and various parameters, and various
>descriptive "models" with various functions and parameters, ALL
>give about equally high correlations between predicted handle
>positions and actual handle positions, but all do NOT give
>equally high correlations between predicted cursor positions
>and actual cursor positions.

How do you know they all give about equally high correlations?
Isn't all this a conjecture?
------------------------------------------
>I believe that the PCT models used to predict tracking can be
>interpreted also as functional "models" -- the choice of
>interpretation (underlying generative model or function
>"model") depends only on whether one envisions a reference
>signal for target position inside the organism (thus explaining
>why cursor position is subtracted from target position) or one
>simply notes that prediction is good if there is such a
>subtraction in the function relating "input" to "output" at
>each moment and doesn't care about explaining why.

Sure. The canonical mathematical forms are the same whether you
think of the signals as being real or not. If you're incurious
about how the mathematical functions are actually implemented,
you can just leave it there.

To go farther, you can start picking up hints from the nervous
system. I've tried to do that, within my limits.
--------------------------------------------
>As ever,

Damned straight. Gadfly to the CSG.
------------------------------------------------------------
Von Bakanik (930107) --

"Groups", as we use this technical term, means "bunches." I know
that sociologists give a more specialized meaning to this term.
We're talking about using population statistics as a way of
deriving characteristics of individuals, not about group dynamics
and that sort of stuff. Sociologists use statistics more
legitimately than psychologists, because they apply mass measures
to masses, not to individuals.

>Does this imply that sociologists are a lost cause as PCT
>converts?

Gee, I don't know. Ask Chuck Tucker.
----------------------------------------------------------
Best to all,


Bill P.
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU