Re: Algebraic sum

Scott Ferson (scott@ramas.com)
Wed, 8 Jul 1998 02:37:28 +0200 (MET DST)

WSiler wrote:

> > Sorry to quibble, but this mistake is dangerous enough that it
> > deserves correction every time it appears. Having zero correlation
> > does NOT generally guarantee probabilistic independence.
> I presume that you are referring to the indisputable fact that the
> correlation
> between pairs of values in a sample is only an estimate of the
> correlation in
> the universe from which the sample was drawn. Is this the case? Your
> correction
> is, of course, pefectly accurate.

Well,...no. I just mean that a correlation coefficient is
an incomplete measure of dependence among random
variables. Feller (vol.1, 3rd ed., page 236) explains
that a correlation's being zero isn't sufficient to imply
independence. In fact, it can be zero even if one
variable is a perfect function of the other.

> I am a bit puzzled how to how one can guarantee probabilistic
> independence
> without a perfectly accurate model of the process which generates the
> sample
> values. In real life, especially in Biomathematics, such models are
> (to put it
> mildly) hard to come by. Am I missing something?

That you often don't have perfect knowledge and
therefore can't guarantee independence is exactly
why it is important to have computational tools that
don't require independence assumptions. We work
on methods that give reliable answers *without*
making this or other "fragile" assumptions. See
http://www.ramas.com/Rcal-faq.htm#pbounds.

> By the way - what is Applied Biomathematics? From your phone number,
> it sounds
> like it might be a department at StonyBrook. (I'm a former chairman of
> the
> Biomathematics Department at the University of Alabama at Birmingham.)

Applied Biomathematics is a research firm on Long
Island. Several of us did attend Stony Brook . See
our home page at http://www.ramas.com.

Best regards,
Scott Ferson <scott@ramas.com>
Applied Biomathematics, 516-751-4350, fax -3435

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