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Archiver > GENEALOGY-DNA > 2008-03 > 1204592147


From: (John Chandler)
Subject: Re: [DNA] Central Limit Theorem in Action
Date: Mon, 3 Mar 2008 19:55:47 -0500
References: <013801c87d66$d40ce450$6400a8c0@Ken1>
In-Reply-To: <013801c87d66$d40ce450$6400a8c0@Ken1> (knordtvedt@bresnan.net)


Ken wrote:
> For two such markers each with that distribution, the probability
> distribution for the sum s = v(1)+v(2) is the convolution integral

True, but this isn't the problem that James pointed out the other day.
Although the ASD for a combination of two markers is simply the
average of the two ASDs computed for the markers individually, the
combined estimate of TMRCA is not the average of the two
individual-marker estimates. The issue can be seen most clearly by
looking at the probability distribution for the TMRCA of two testees
who match exactly on all markers tested. In this case, the most
likely TMRCA is actually zero, regardless of how many markers are
included in the test, and the shape of the distribution is
approximately an exponential whose mean (expectation) value is the
reciprocal of the sum of the individual mutation rates. Clearly, the
mean value does move closer and closer to zero as more markers are
added, but the distribution never acquires a flat top, or in any other
way becomes more like a gaussian.

John Chandler

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