Dear Alastair:

An clarification of my analysis of your -1 to + 10 example:


That is your model and it is one dimensional [call it x] that is it has one 
venue.
Now add a dimension call it y that is infinite and perpendicular to your 
example's x.  This is an infinite number of venues.  Add the y boundaries 
at x = -1 and x = +10.  Now randomly sample on this bounded xy plane.  The 
area of the plane below zero on the x dimension is the same as the area 
above zero on the x dimension i.e. infinite = no bias as to sign mix of the 
resulting random sample of reals on x.

{near the end of my post a further clarification}

What you seem to be saying re my approach using the above analysis of your 
example is that either of the boundaries of the above plane in the y 
dimension may meander between x = -1 and x = + 1. With this I agree. 
Actually its essential. So what?  The areas above and below the x = 0 line 
are still equal i.e. infinite so a random sample in the xy plane over this 
structure still produces no bias as to sign mix of the resulting random 
sample of reals on x.

Hal



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