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July 21, 2008

Oh Boy: Statistical Underpinning of DNA Matching Entirely Flawed?

In theory, matching 9 of 13 genetic markers is supposed to result in a nearly positive match -- the odds against another person matching the same 9 of 13 markers are supposed to be 1 in 113 billion.

But we have several instances of these virtually-mathematically-impossible false positives now.

The question is whether the statistical estimate of the unlikelihood of this is flawed, and that it's much easier to accidentally match another person's DNA markers than imagined, or if this is simply, well, expected. The "Law of Truly Large Numbers," as applied as "Littlewood's Law," suggests that, given enough trials, the phenomenally unlikely become downright likely to happen on occasion:

Littlewood defines a miracle is defined as an exceptional event of special significance occurring at a frequency of one in a million; during the hours in which a human is awake and alert, a human will experience one thing per second (for instance, seeing the computer screen, the keyboard, the mouse, the article, etc.); additionally, a human is alert for about eight hours per day; and as a result, a human will, in 35 days, have experienced, under these suppositions, 1,008,000 things. Accepting this definition of a miracle, one can be expected to observe one miraculous occurrence within the passing of every 35 consecutive days -- and therefore, according to this reasoning, seemingly miraculous events are actually commonplace.

His point is well taken, but I think he defines things in a goofy way to get to that "one miracle per month" thing: I don't think I've seen one miracle per month. Even bad "miracles." But that analysis certainly puts things into perspective.

A lot of us shorthand phenomenally unlikely events as "simply impossible." Even if we rationally know one in 113 billion is not, in fact, simply impossible, we (or at least I) tend to categorize it just that way. Oh, sure, I'll admit it's technically possible: But I don't really believe that where it counts, in the gut.

Last week I stumbled across The Black Swan theory, basically one guy's so-obvious-I-never-considered-it theory that almost all the big events in history -- those that shape society for generations -- are incredibly unlikely events ("Black Swans") that, while some here and there conceived as technically possible though ferociously unlikely, were usually considered by most as flatly impossible, the same as "one in 113 billion" gets rounded off to "0 in 113 billion, or impossible." And thus, when the "impossible" happens, it changes all of our mindsets.

Among the most recent of "Black Swans," of course, is 9/11. Looking back it seems so obvious now. In hindsight, it wasn't terribly unlikely at all. But who among us actually considered that a serious and real possibility before the towers came down?

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posted by Ace at 01:59 PM

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