"Mathematician" Coralie Colmez claims that if you do a DNA analysis on an unreliably small piece of evidence and get the same result as the first time, this strengthens the case that the original result is correct and uses some coin-tossing explanation to "prove" her case.
I disagree, her corroborating example repeats the same tests on *different* data whereas doing the DNA test again would be repeating it on the *same* data (and as such, is completely worthless extra information).
I think that she has fundamentally missed the point about the unreliability of the source data here.
Anyone any better ideas than me, what is the right answer here?
(I should really be posting this to ul, but I think the science experts are in this group?)
Well, presumably the first test was on a small sample taken from the knife, and the proposed repeat test would have been on a different sample. And that, I think, would improve the statistics although without knowing the exact methodology it's difficult to be sure.
But it was the scientist suggested a repeat test and I am inclined to think they would have understood the statistics. The journalist's point was that when courts get the science wrong, people suffer. For example the Guilford "bombers", the "cot death" lady, the Dutch nurse...
Before we follow this line of thought, I observe from the BBC report that:
"the DNA sample was tiny, and the appeal judge thought the evidence was unreliable, so he rejected a forensic scientist's suggestion to have it tested again"
which suggests that the "unreliability" of the sample is the subjective opinion of the appeal judge who rejected the views of a forensic scientist.
Are there any reports from the initial trial or the appeal in which the "unreliability" is declared by a scientist (or statistician)? If not, what are you going on? An erroneous decision by that judge?
The coin-tossing example *in itself* is correct. Whether or not the model applies to the DNA analysis of small samples is another question.
In order to answer that question one needs to understand the mechanisms of DNA analysis. I understand that this takes place using a PCR (Polymerase Chain Reaction) to clone any DNA into a large enough sample. My wife is a biologist at the Sanger Institute and does these sorts of things all the time in her research (cancer, malaria, etc).
If the PCR works and the DNA is not contaminated then you get enough DNA to perform an analysis to compare with DNA from the suspect. This is another separate process. I don't know if this can go wrong or not, but I believe there are risks of false positives (the biased coin?)
Erm, presumably the test would be done on another small fragment of the initial small sample on the knife. A PCR would be performed to amplify the material so that it can be compared with the suspect yet again.
Naturally, they would not have used all of the sample in the first test as the risk of it going wrong and the sample therefore being destroyed is too high.
Since the DNA is cloned and therefore "amplified" one does not need a lot of it to start with. A small piece of a small sample ought to suffice.
So, in this case the "biased coin" is rather small and has been chopped up into pieces and tested, with each "piece of coin" behaving as though it were the whole coin. (Unless the blood sample contains drops of blood from more than one person?)
So, the several DNA analyses are indeed equivalent to new tosses of the same coin, with the assessment of the coin being biased being equivalent to the risk of false DNA positive matches?
Ergo, on the face of it, I think I believe Coralie Colmez.
What is the unreliability other being subjectively opined by the appeal judge?
The statistics of DNA analysis resembles Colmez' coin-tossing experiment in some ways, but there are important differences. Whether the coin analogy is appropriate or not depends on exactly what was wrong with the scene-of-crime DNA sample. All we are told is that "the DNA sample was tiny", but that isn't a useful statement.
The way it works is this: An individual's DNA fingerprint consists of a certain number of parameters (loci) each of which can take several different values (alleles). You might think of it a bit like someone's name: for example my name might be expressed as b i g l e s w a d e where the allele at locus number 2 is 'i', the allele at locus 7 is 'w' etc.
So if you find a scene-of-crime DNA sample that is "complete" - i.e. you can read all of the alleles at all of the loci - you can compare it with that of your suspect. If they all match, then it's not looking good for him.
But the trouble with SOC-DNA samples is that they don't always contain a record of all the alleles at all the loci - or if they do contain it, it might be smothered by contamination from another source. The smaller the amount of tissue present at the SOC, the more likely this is to happen.
The equivalent with my personal name analogy is where the police find the corpse with a knife in his stomach, and just before he died he wrote (in blood, on the wall next to him), "I was murdered by big**s**de", where the asterisks are illegible splodges.
Clearly, I might be the murderer. But equally, the victim could have been trying to name Big Al Spode, a well known local gangster. And it doesn't matter how many times you examine this writing, you can't decide whether the real killer is me or Al, simply because that information is not present in the sample. It just isn't there, and you can't use statistics to extract information that isn't there.
I'm not saying that this *is* what was wrong with the Kercher evidence, just that it might be. And if it is, then Colmez' analogy is suspect.
And in fact it's more complicated than that, because certain DNA analysis techniques can sometimes give you a probabilistic result for a certain locus. E.g. in my analogy, that the missing fourth letter has a
90 per cent probability of being an "a", which would rule me out and put Big Al in the frame.
However, such inferences (using what's called low copy number analysis) are still very controversial, and are at the very least a great deal more indirect than those from simple full-length DNA matching. Which itself isn't perfect either, despite what they tell you.
I think the DNA case may be worse than your well described example.
With the splodges on the wall there are all sorts of non-destructive analyses that can be carried out - photographs in UV light, oblique lighting, image enhancement - none of which are destructive so you can repeat them at will.
In the case of a tiny splodge on a knife you have to wipe it off in order to test it, and once you've done your polymerase reactions you don't have it any more.
I'm accepting the position that the judge has primacy here.
The original judge may have been wrong, but I'm evaluating the additional claim from the starting position that they were right.
I agree with you, but the expert wasn't presenting a view on that. They were presenting a strict statistical point, applicable to any scientific test.
The judge in the first trial appears to have ruled that this is amplification is unreliable. The experts view is that the unreliability of a test is lessoned by doing the test twice. Personally I don't see it. You are still testing the same sample and if you can only get a result by amplification, and the judge has ruled that "amplification is unreliable, I can't see that doing it twice (or three times) on that same sample, changes that.
I can't see how that scales to a blood sample (on the basis that you can't split up this coin as you are suggesting)
I suspect that you'll find that the vast majority of experts may be correct. There is, however, a probability that they may be wrong (and that's only when we hear about them in the news).
In the same way judges and juries may be.
Which is presumably why appeals and retrials, and multiple independent expert witnesses are the order of the day!
Rather like tossing that biased coin multiple times, no?
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