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How Statistics Can Foul the Meaning of DNA Evidence
azoblue writes with a piece in New Scientist that might make you rethink the concept of "statistical certainty." As the article puts it, "even when analysts agree that someone could be a match for a piece of DNA evidence, the statistical weight assigned to that match can vary enormously, even by orders of magnitude." Azoblue writes: "For instance, in one man's trial the DNA evidence statistic ranged from 1/95,000 to 1/13, depending on the different weighing methods used by the defense and the prosecution."
I speak from personal experience. I use them al the time and still don't really understand them. Not how they apply in criminal investigations anyway.
Let's say you have evidence that matches 1 in a thousand people. You search through your database of all 1000 suspects and you get a single match. Did he do it? Logically you'd expect this to mean you can be 99.9% sure. You then search through the database of a million random people. You get 1000 matches. Does this mean there's only a 0.1% chance that your original suspect was guilty? Well, maybe there's some other compelling evidence that makes it most likely that one of those 1000 people were the culprits. But you have 10000 outliers. They're each a tenth as likely to have committed the crime. You get 10 matches. So, once again we're at the 50% probability of guilt, or something in that ballpark.
I'm sure this is a somewhat different example than that given in the article but that's not the point. The point is that is there a 99.9% probability, a 0.1% probability, a 50% probability or some other probability of guilt? Or am I just trying to confuse you by throwing numbers at you?
In this case, however, there were many people present at the discovery of the object from which the DNA was taken for analysis. As it happens, several of these people were relatives (brother, mother) of the person the prosecution were trying to persuade us was the person that possessed (in legal terms) the object.
The question that I kept hoping the defense attorney would ask was "what are the probabilities of an erroneous match if the people are relatives, not just two random people off the street"? Unfortunately, he didn't.
As it happened, there were so many other peculiarities in this case as well as some pretty bizarre testimony from prosecution witnesses that we voted to acquit without making much of the DNA evidence.
udin
...we couldn't rule out the possibility that the cops got the wrong guy, so we found him not guilty. If I had to take a bet, I'd say he did it, but I wouldn't bet his life on it.
I'm glad you think the way that you do. Too many people would call him guilty if they figured there was a 55% chance of it being him. Hmm, someday someone will have to draw a line in the sand as to what odds constitute reasonable doubt. If a trial could be conducted in a completely unbiased, Bayesian way and a probability of guilt were established, what number would be needed to convict?