On 29/04/2013 21:24, tim...... wrote:
So according to:

http://www.bbc.co.uk/news/magazine-22310186

"Mathematician" Coralie Colmez claims that if you do a DNA analysis on
an unreliably small piece


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?


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.

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?)


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

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.



(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.

What is the unreliability other being subjectively opined by the appeal
judge?


Michael