William Chambers asked an interesting question to which I havent seen any
responses yet - perhaps they were off line. For my part I think that this
may not be thought of as a problem for simulators since the real world
systems they are often trying to simulate show exactly the tendency to
normalisation that you describe. We carry out simulations with  a series of
apparently independent uniform 'causes' and find stability emerging and
count this as success because it seems lifelike. Any views?

Alan

>     Dear List Members:   I am developing a family of statistical methods
>that allows us to infer causation from continuous linear variables: 
>http://www.wynja.com/chambers/regression.html     I have applied the
>methods of corresponding correlations and corresponding  regressions to
>real data but most of my work is based on simulations,  I  have some
>general questions about how experts conduct simulations.   The methods I
>am using assume that the causes  are uniformly distributed.  If we create
>a series of such causes, the  subsequent causes become progressively
>normally distributed. Consider the following model:   y1=x1+x2, where x1
>and x2 are uniformly  distributed,   y2=y1+x3 y3=y2+x4   Notice that half
>of the causes (yn) tend to be  progressively more normally distributed. As
>the model progresses, the  distributions become thinner in the extremes, 
>This gives more weight to  midrange variables, because they are more
>frequently instantiated,      The problem is worse when we create the
>dependent variables directly from series of normally distributed causes, 
>  The dependent variable that is generated from  normally distributed
>causes tends to be determined in the extremes by either one  cause or the
>other (disjunctive causation),  The combination of two extreme  values of
>x1 and x2 (conjunctive cause) is very rare when the causes are normal
>because extremes of x1 or x2 are rare, even on their own. Their
>combination is  even more rare. The upshot is that as we go from uniform
>to normal  distributions, the causal model in the extremes of y(n) becomes
>progressively  disjunctive while that in the mid range of y(n) stays
>conjunctive,       Have any of you dealt with this problem  before?  How
>do you keep causal (x) distributions uniform in  sequences?   Thanks,  
>William Chambers


________________________________________________________
Alan Penn, Reader in Architectural and Urban Computing
Director, VR Centre for the Built Environment
The Bartlett School of Architecture and Planning
1-19 Torrington Place  (Room 335)
University College London, Gower Street, London WC1E 6BT
tel. (+44) 020 7504 5919   fax. (+44) 020 7916 1887
mobile. (+44) 0411 696875
email. [log in to unmask]
www.   http://www.vr.ucl.ac.uk/
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