4 ms·

“The important fact is that this man’s DNA is the same as the DNA found on Yara,” he said, noting that the odds of anyone else sharing the same genetic prof

by bcoates 12y ago

“The important fact is that this man’s DNA is the same as the DNA found on Yara,” he said, noting that the odds of anyone else sharing the same genetic profile was “one person out of two billion of billions of billions” or practically nonexistent. This fundamental misunderstanding of statistics really doesn't increase confidence in this investigation. When you go on a fishing expedition across 22,000 suspects, the odds of getting a false positive from one cause or another is nearly one.

themartorana 12y ago
Is this true? It feels wrong - that a false positive DNA test is not like picking the right number on a roulette table. Considering the number of bits of information that have to match to be a positive hit in DNA testing, even 22k tests shouldn't hit a false positive. Statistics being what they are, what is the science behind false positives in DNA testing across a fairly large sample set?
- bsder 12y ago
  In addition, I suspect that once they had a match, they could now try to corroborate with other pieces of evidence. I suspect that you could get a DNA match, by itself, thrown out. However, once you use the DNA to narrow down to "these three" you can probably build up the rest of the evidence you need for a solid case.
  - antirez 12y ago
    The suspect cell phone was attached to the tower where the girl was murdered in the same hours of the murdering, even if the suspect does not reside in the exact same area.
    - rwmj 12y ago
      That's not extra evidence, because they were only testing the DNA of people whose cell phones were in the area. Thus the probability that the suspect's cell phone was in the area is always going to be exactly 1.
      - antirez 12y ago
        Actually this is not what happened, the suspect was tested because they found a partial match in the population, reached the dead father, reconstructed with the help of people the possible mother, and then identified the son and tested it. Eventually since the phone was among the ones in the area, they would have reached him, but it was a totally different line of investigation that allowed to reach this specific person, so the fact the cell phone was attached to the tower was an acknowledge.
- e12e 12y ago
  Bear in mind that DNA test != full sequencing. I'm a bit rusty on my combinatorics, but borrowing from wikipedia[1] "if n(p;d) denotes the number of random integers drawn from [1,d] to obtain a probability p that at least two numbers are the same, then:"(...) We have stated above that n=2, p=1/2(10^(39))=1/(2e27), so we have: p ~ 1 - ( (d-1)/d )^(n(n-1)/2)) = 1 - ( (d-1)/d )^(2(2-1)/2)) # -> 2/2 -> 1 = 1 - ( (d-1)/d ) p-1=-(d-1)/d (p-1)d=-d+1 pd-d=1-d pd=1 d=1/p d~2e27 #Yeah, I guess this should have been obvious, in retrospect For n=20k=2e4: p(n=2e4,d=2e27) ~ 1-((d-1)/d)^(n(n-1)/2) Which is so small that in Python I had to use the Decimal module to compute p~1e-19 or so. However, this assumes an even distribution across the possibilities -- and we've approximated the number of combinations based on the statement of collision probability -- not based on actual number of base pairs, or based on some model on how these are likely to be distributed... (eg: if we test for sex, but only sample males -- does that mean we loose a certain number of possibilities? How about caucasian vs other races? It depends on what markers we are testing. Further we know that some markers are likely to match, because there's bound to be some common ansecstors among some members in the sample etc.) Note that the math above might be entirely bogus -- I'm off to bed, so I'd assume I've made some silly mistakes... [edit: On actually reading the article, it could appear that the quote on "two billion billions of billions" are indeed meant to indicate he likelihood of someone sharing the same DNA, rather than the likelihood of two samples testing as similar.] [1] https://en.wikipedia.org/wiki/Birthday_problem#The_generalized_birthday_problem https://en.wikipedia.org/wiki/Birthday_problem#The_generaliz...
  - e12e 12y ago
    For a more relevant discussion, see eg: http://www.councilforresponsiblegenetics.org/GeneWatch/GeneWatchPage.aspx?pageId=57 http://www.councilforresponsiblegenetics.org/GeneWatch/GeneW... Keep in mind that doing 20k tests, there are likely to be mistakes made. In the case of a false positive (or a disputed positive), that shouldn't be too much of a problem -- just run the test again, perhaps using multiple labs to check the results. For a false negative match -- you've just missed/"cleared" the probable perpetrator. Such an error is unlikely to be caught (I'd imagine) -- on the other hand if the error rate is low (say 0.5%?) -- the chance that an error is made when testing that (presumably) one swab that is from the suspect, is pretty low, even with 20k tests.
danmaz74 12y ago
The 22k tests where like screening tests, but for this suspect they were repeated and confirmed many times and using different traces from different parts of the victim's body. Thus, statistical errors in a single test repeated 22k do not count here.
- rasz_pl 12y ago
  You discount 'this is our man, I can feel it, make those inconclusive tests conclusive so the bad man doesnt get away with rape and murder'. This happens very often.

by bcoates 12y ago

themartorana 12y ago

Is this true? It feels wrong - that a false positive DNA test is not like picking the right number on a roulette table. Considering the number of bits of information that have to match to be a positive hit in DNA testing, even 22k tests shouldn't hit a false positive. Statistics being what they are, what is the science behind false positives in DNA testing across a fairly large sample set?

bsder 12y ago
In addition, I suspect that once they had a match, they could now try to corroborate with other pieces of evidence. I suspect that you could get a DNA match, by itself, thrown out. However, once you use the DNA to narrow down to "these three" you can probably build up the rest of the evidence you need for a solid case.
- antirez 12y ago
  The suspect cell phone was attached to the tower where the girl was murdered in the same hours of the murdering, even if the suspect does not reside in the exact same area.
  - rwmj 12y ago
    That's not extra evidence, because they were only testing the DNA of people whose cell phones were in the area. Thus the probability that the suspect's cell phone was in the area is always going to be exactly 1.
    - antirez 12y ago
      Actually this is not what happened, the suspect was tested because they found a partial match in the population, reached the dead father, reconstructed with the help of people the possible mother, and then identified the son and tested it. Eventually since the phone was among the ones in the area, they would have reached him, but it was a totally different line of investigation that allowed to reach this specific person, so the fact the cell phone was attached to the tower was an acknowledge.
e12e 12y ago
Bear in mind that DNA test != full sequencing. I'm a bit rusty on my combinatorics, but borrowing from wikipedia[1] "if n(p;d) denotes the number of random integers drawn from [1,d] to obtain a probability p that at least two numbers are the same, then:"(...) We have stated above that n=2, p=1/2(10^(39))=1/(2e27), so we have: p ~ 1 - ( (d-1)/d )^(n(n-1)/2)) = 1 - ( (d-1)/d )^(2(2-1)/2)) # -> 2/2 -> 1 = 1 - ( (d-1)/d ) p-1=-(d-1)/d (p-1)d=-d+1 pd-d=1-d pd=1 d=1/p d~2e27 #Yeah, I guess this should have been obvious, in retrospect For n=20k=2e4: p(n=2e4,d=2e27) ~ 1-((d-1)/d)^(n(n-1)/2) Which is so small that in Python I had to use the Decimal module to compute p~1e-19 or so. However, this assumes an even distribution across the possibilities -- and we've approximated the number of combinations based on the statement of collision probability -- not based on actual number of base pairs, or based on some model on how these are likely to be distributed... (eg: if we test for sex, but only sample males -- does that mean we loose a certain number of possibilities? How about caucasian vs other races? It depends on what markers we are testing. Further we know that some markers are likely to match, because there's bound to be some common ansecstors among some members in the sample etc.) Note that the math above might be entirely bogus -- I'm off to bed, so I'd assume I've made some silly mistakes... [edit: On actually reading the article, it could appear that the quote on "two billion billions of billions" are indeed meant to indicate he likelihood of someone sharing the same DNA, rather than the likelihood of two samples testing as similar.] [1] https://en.wikipedia.org/wiki/Birthday_problem#The_generalized_birthday_problem https://en.wikipedia.org/wiki/Birthday_problem#The_generaliz...
- e12e 12y ago
  For a more relevant discussion, see eg: http://www.councilforresponsiblegenetics.org/GeneWatch/GeneWatchPage.aspx?pageId=57 http://www.councilforresponsiblegenetics.org/GeneWatch/GeneW... Keep in mind that doing 20k tests, there are likely to be mistakes made. In the case of a false positive (or a disputed positive), that shouldn't be too much of a problem -- just run the test again, perhaps using multiple labs to check the results. For a false negative match -- you've just missed/"cleared" the probable perpetrator. Such an error is unlikely to be caught (I'd imagine) -- on the other hand if the error rate is low (say 0.5%?) -- the chance that an error is made when testing that (presumably) one swab that is from the suspect, is pretty low, even with 20k tests.

danmaz74 12y ago

The 22k tests where like screening tests, but for this suspect they were repeated and confirmed many times and using different traces from different parts of the victim's body. Thus, statistical errors in a single test repeated 22k do not count here.

rasz_pl 12y ago
You discount 'this is our man, I can feel it, make those inconclusive tests conclusive so the bad man doesnt get away with rape and murder'. This happens very often.