I am curious about the actual false positive rate and how they compound. To use your hypothetical number, if the false positive rate is one in a million per test, if law enforcement tests your DNA sample against 700,000 samples from crime scenes, there is a 50% chance at least one of them will be a match due to false positive [1]. That is much scarier than what one in a million suggests.

[1] (1 - 1e-6) ^ 700,000 = 49.6 % chance of no false positive match

Or you now have 299,999,700 probable negatives, and 300 possible positives to review for motive, method, and opportunity before you start looking at/for alibis.

Oh yeah, lots of American police want to work this hard; there's probably five or six of them at least. What most police will do instead is arrest the first name on the list. When she or he documents an alibi, they'll arrest the second name on the list. Eventually, some poor bastard who lives in the same state will have gone hiking alone the day of the crime, or stayed home and slept after a week of overtime, or whatever. Unless there is a statistician on the jury, that person is going to prison.

Statisticians probably get excluded in jury selection, along with anybody else whose profession indicates they have a clue.

https://www.quora.com/Are-engineers-usually-excused-from-jur...

Unless you've got a cold case, that seems like more potential suspects than a general person may reasonably have.

That's like saying police shouldn't be allowed to use Google's "similar image" search because there could be false positives among the similar images.

These genetic databases are tools used for investigation to identify suspects. Once the suspect is identified, the investigators still have to build a case against them, including obtaining their DNA directly for testing against the crime scene DNA. Since all the cases I've read about the police got the suspect's DNA samples from the garbage, it doesn't seem like the genetic research itself is even enough to get a warrant for the suspect's DNA.

The hypothesis of this example is that the unfortunate suspect's DNA "matches" the crime scene DNA. Of course it's going to "match" when they test it again. The point is that when the original match is against a huge population, you're going to find a bunch of matches, most or all of whom are innocent. Picking one out of that set and then confirming that one is really in that set doesn't prove anything.

I'm not an expert, but I would guess it would be possible to have an exact match on the genetic fingerprinting, but then do a full genome sequencing to confirm that the two samples are from different people.

The funny thing is that although I have often heard about the police finding an exact DNA match with someone who was provably not at the crime scene, I've never heard about anyone doing a different DNA test afterwards to investigate what happened: did a fragment of skin get carried in the wind from one city to another, did samples get mixed up in a laboratory, or was the match a false one, akin to a hash collision?

These DNA tests do not use full genome sequencing, they use SNPs.

https://en.wikipedia.org/wiki/SNP_genotyping

I agree with your conclusion in general, but you add in some very basic secondary checks and you won't get that many false positives... do they live anywhere near the crime? Do they have any motive or opportunity to commit the crime? Were they in the area at the time?

So now you are fishing with a net with smaller holes. You're going to catch suspects that look bad because you've selected for that but that still may not have anything to do with the crime you are investigating.

God forbid any of them are minorities and the victim a white person, you're 95% on the road to a conviction.

But if you're testing 300Mi most of those are probably not even in you jurisdiction or have no ties to the case