GENEALOGY-DNA-L Archives

Archiver > GENEALOGY-DNA > 2003-07 > 1057258655


From: "John F. Chandler" <>
Subject: Re: [DNA] Ancestry test - a must-read article URL
Date: Thu, 3 Jul 2003 14:37 EST
In-Reply-To: Circles54@webtv.net message <5080-3F021415-5953@storefull-2175.public.lawson.webtv.net> of Tue, 1 Jul 2003 17:06:54 -0600


Ray wrote:
> When I said:
>
> "In most cases, there are so many points which plot 'below' 0% that one
> of those points is MORE LIKELY to be your true percentage than your
> MLE!"
>
> I meant that if you have six "estimates" plotted at 0%, on your 1/5
> contour, it is more likely that your true value is somewhere among those
> six "estimates" than that it is where your MLE is plotted. No?

It's a question of semantics. When you focus on one particular point,
as you did in the original statement, the others are out of the picure.
You phrased it as a one-on-one comparison betweeen the MLE and some
selected point elsewhere. By definition, the MLE is more likely than
any selected point elsewhere, so you need to rephrase it to get a
statement that is both instructive and true. Words like "collectively"
and "all told" would help. Also, bear in mind that the probability
distribution seems to be pretty symmetric on all these plots, so any
straight line through the MLE is a median divider. A line parallel
to one of the sides of the triangle is a contour of constant ethnic
fraction for the group mentioned at the opposite corner. In other
words, if your report says you have 13% Amerindian, the chances are
50-50 as to whether you have more than 13% or less than 13%. (Needless
to say, the probability of having EXACTLY 13.000000000000% is 0!)

John Chandler

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