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Another problem of DNA testing that is hinted at in the article is that as more and more people enter the databases the probability of false positives increases

by ajnin 11y ago

Another problem of DNA testing that is hinted at in the article is that as more and more people enter the databases the probability of false positives increases. A 1 in a million chance sounds reasonable when you are testing one person, but with many people tested the probability rises non-intuitively quickly (see: Birthday paradox). For example if you test 100 people the probability of a false positive rises to around 1/200.

mturmon 11y ago
The reason the Birthday Paradox is surprising is that there are N people, but the number of possible matches rises like N^2. The "paradox" occurs because success is defined as any one of the N-choose-2 matches happening. The analog here is there are M people in the database, and N crimes, so the chance of a single failure (mistaken match) is kind of like N*M. But I'm not sure that's the correct metric; I think you really care about the amortized cost of a mistaken match across all N crimes. So you don't see the "paradoxical" quadratic increase. I admit I'm being a bit fussy -- just testing the extent of the analogy. You are of course correct that the database size is growing, and the number of samples that can be collected, even from one crime, also can be made to grow.
- AnthonyMouse 11y ago
  > But I'm not sure that's the correct metric; I think you really care about the amortized cost of a mistaken match across all N crimes. So you don't see the "paradoxical" quadratic increase. It seems to me what we should really care about is the number of people falsely convicted, which is false-positive-rate-per-defendant * number-of-defendants. Since the size of the database (and therefore the false positive rate) is related to the number of defendants, the number of falsely convicted people increases quadratically with the number of people subjected to DNA testing.

by ajnin 11y ago

mturmon 11y ago

The reason the Birthday Paradox is surprising is that there are N people, but the number of possible matches rises like N^2. The "paradox" occurs because success is defined as any one of the N-choose-2 matches happening. The analog here is there are M people in the database, and N crimes, so the chance of a single failure (mistaken match) is kind of like N*M. But I'm not sure that's the correct metric; I think you really care about the amortized cost of a mistaken match across all N crimes. So you don't see the "paradoxical" quadratic increase. I admit I'm being a bit fussy -- just testing the extent of the analogy. You are of course correct that the database size is growing, and the number of samples that can be collected, even from one crime, also can be made to grow.

AnthonyMouse 11y ago
> But I'm not sure that's the correct metric; I think you really care about the amortized cost of a mistaken match across all N crimes. So you don't see the "paradoxical" quadratic increase. It seems to me what we should really care about is the number of people falsely convicted, which is false-positive-rate-per-defendant * number-of-defendants. Since the size of the database (and therefore the false positive rate) is related to the number of defendants, the number of falsely convicted people increases quadratically with the number of people subjected to DNA testing.