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Date:         Mon, 11 Jan 1993 12:40:14 EST
From:         mmt@BEN.DCIEM.DND.CA
Subject: Re: noise in model fitting

[Martin Taylor 9210111 1210]
(Bill Powers 930108.0800) replying to Greg Williams

>>... maybe your model is already "noise"-limited. If so, then
>>adding a noise term should improve prediction of cursor
>>position IN A STATISTICAL SENSE, AVERAGED OVER MANY RUNS.
>
>No, it will make the fit worse. You will never do better with a
>noisy model than with a noiseless one. Noise adds in quadrature.

Here is a transcription (I think it is out of copyright, since C.B.Gibbs
died over 20 years ago) of an article from Nature, May 6 1961, vol 190, p540.

----------------------------
Function of Limb Tremor
C.B.Gibbs

The collaboration of biologists and engineers has led to a hypothesis
concerning the biological function of limb tremor in the frequency range
of 6-15 c./sec.

A target spot of light on a cathode ray tube was moved along a horizontal
line into different positions at 1-sec intervals.  An operator was given
the task of moving a joystick which controlled the movement of a 'follower'
spot of light on the cathode ray tube, in the manner required to bring
the 'follower spot' into line with the target spot as quickly and
accurately as possible.  The manually controlled servo-mechanism was a
high-gain positional system with no delays in time between control and
display movements.

Records of the target and joystick movements were taken on a high-speed
pen recorder.  Backlash in the system set an arbitrary lower limit to the
amplitude of limb movements which were recorded.  Some observations
incidental to the main experiment are reported here.

The records of six experimental subjects were analysed for evidence of a
relationship between the limb tremor recorded in the range of 6-15c./sec. and
three different states of the subject's 'controlling' limb: (a) at rest;
(b) while making gross rapid movements of primary adjusment; (c) while
making the fine movements of secondary adjustment.  It was found that
80 per cent of all tremor, of amplitude exceeding the measurement threshold,
appeared while making the movements of precise secondary adjustment

The finding reported agrees with much previous information (Milsum, J.H.,
Nature 187, 297, 1960); but a new hypothesis has been formulated concerning
the function of the type of tremor described

Mechanical servo-systems have been designed to maintain small oscillations
of medium frequency, that is, the servo 'dither' effect because this 'dither'
takes up backlash in the system and minimizes the breakout forces required
to overcome frictional resistances when movements are initiated.  Peripheral
mechanisms for controlling the movement of body limbs (for example, muscle
spindles, annulo-spiral nerve-endings and associated loops) bear close
analogy to such mechanical servo-systems (Eldred, E., Ganit, R., and
Merton, P.A., J. Physiol., 122, 3, 498, 1953), and it is suggested that
limb tremor provides the same advantages as 'servo dither.'  The fact that
tremor was most marked in the phase of the experiment which necessitated
the greatest precision of movement lends support to the hypothesis presented.

The functional analogies which have been suggested between limb tremor and
servo dither may be applicable to such similar fine tremor of the eyes and
of the head in visual and auditory localization.

-------------------------------------

Two points: (1) I think Gibbs has an important observation, but has the
wrong explanation.  He attributes the tremor to backlash on the output
side, which would be due to static friction, whereas I think that most of
our joints are pretty fluid and reasonably free of that kind of problem
(except in the case of muscular stiffness, which I believe is caused by
the sticking together and tearing apart of muscle fibres).  A more likely
explanation is to be found at the perceptual input, in the general
phenomenon that there is a perceptual dead zone around zero magnitude (the
effect is found in many perceptual dimensions, the reason can be found in
information theory, I think--See Taylor, Forbes and Creelman, J. Acoustical
Soc Amer, 1983, 74, 1367-1374).

(2) If a model did not account for the phase as well as the amplitude
and frequency of this tremor, it would act like noise in the analysis.
But averaging over an integer number of cycles would help the prediction
of a model that ignored the tremor and worked on the basis that the
perceptual function was linear through the zero point.

---------------

I am aware that the standard PCT model does not posit zero as a likely
reference for a perception, and that the actual dead zone of the raw
sensation is not at the level of the perception.  But the effect seems
to be as valid for differences as it is for raw percepts, and I suspect
it speaks to the kind of modified model Bill was talking about before
Xmas, in which expectation models form part of the loop, perhaps being
subtracted from incoming perceptions.  This kind of extended model
seems to be consistent with Gibbs' finding, as well as with all the
things that led to the earlier discussions.

Martin
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU