X-Envelope-to: CSG-L@vmd.cso.uiuc.edu
X-VMS-To: @CSG
MIME-version: 1.0
Content-transfer-encoding: 7BIT
Newsgroups: bit.listserv.csg-l
Date:         Mon, 12 Oct 1992 14:35:51 -0600
From:         "William T. Powers" <POWERS_W%FLC@VAXF.COLORADO.EDU>
Subject:      Nonlinear models; modeling

[From Bill Powers (921012.1400)]

Rick Marken (921012.1130) --

Rick, you're giving Martin a pretty hard time for (I think) the wrong
reason.

When you get the unexplained variance as low as it will go using a
linear model, the next thing to try is a nonlinear one. To test a
nonlinear model you have to use more than one value of the reference
signal, because if the perception is nonlinear, the loop gain will
vary with signal amplitude. Martin suggested trying logarithmic
perceptual functions, which isn't a bad idea, considering Weber and
Fechner, and Stevens.

Of course when you get to the point where the residual errors of
prediction are only a few percent, trying to reduce them further can
easily get you into what Runkel calls "fine slicing." Bringing in
nonlinearities introduces more adjustable parameters (a*log(bx))
instead of just bx), which you have to try to estimate from the little
bit of variance that's left, which can make ALL the parameters less
accurately known, and so on to meaningless detail.

I'm satisfied when we get the variance into what I consider a "normal"
range of experimental error; it doesn't seem worthwhile extending
little pseudopods of precision into a forest of imprecision. But when
I sweep a floor I do a raster scan once, while Mary likes to do a bit
here and a bit there. The floor gets swept in either case.

The only serious problem I see with spending a lot of time on one
narrow part of the organization is that when you get the other parts
into better shape, you can easily find that you were pursuing a wrong
idea, so all that effort will be wasted. What if we decide to use the
"new" model in which lower order error signals instead of perceptual
signals go to the higher levels?
------------------------------------------------------------------
Martin Taylor (921012.1500) --

>How does a human START with a model that is correct, rather than
>plausible?

I meant, before we start elaborating on a model, we should be sure
that what we're elaborating on is a solid foundation. But see the
above post to Rick; this is partly a matter of taste. It's my personal
conviction that running ahead of the data too far is usually a waste
of time, but some people are better guessers than others, so ...

I agree: we should start with plausible models and see which accord
better with the data. That's the beginning. Then we should ask why the
best of the models doesn't work any better than it does, and try to
refine it and make it predict new data as closely as possible, up to a
cutoff point where further refinements yield diminishing returns.

>I do hope that your reorganization processes do at some time come
>to alter your thinking about prediction and information.  I take it
>that you have no insurance?

I waste my money on insurance like everyone else. Can't say that I do
much calculation of probabilities when I buy it. I do preventive
maintenance like oil changes, though I don't know how often I really
should do them (probably not as often as I do). I subscribe to
magazines which I expect to show up on time. I lay in wood for the
winter. Let's see, what else? Oh, I drive on highways, assuming other
drivers will stay in their lanes (that is, I ignore them -- not really
a prediction). I vote for people about whom I know almost nothing.
There's not really much more that I actually do any predicting about.
Most of the time I'm just trying to satisfy my goals and whims and
cope with the variance of the environment as it comes along. Control
is very handy, in that you don't have to know what's going to happen
next; you can handle most disturbances when they come up.

Happy Thanksgiving, Canadians.
------------------------------------------------------------------
Best to all,


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