How do you use Bayes theorem to weigh up the competing claims about how Raffaele's supposed DNA got onto the bra-clasp? I would be very interested to hear you answer without resorting to any preconceived ideas you may have about what is likely, or not.
That's impossible, by Bayes' theorem (!).
"Preconceived ideas", also known as "previously acquired data", or "prior probabilities",
must be taken into account. There's no way around it; it's a mathematical fact.
So to the extent this is your point, you might as well be arguing against a straw man. It is simply mathematically undeniable; anyone who denies it just needs to look up the proof.
The only reason you could have for bringing this up and emphasizing it is in order to argue that the preconceived ideas in question here are
wrong. But you haven't done that yet (except by implication) as far as I can tell.
I wasn't originaly arguing with Kevin and it seems to me that Kevin doesn't actually want to defend the point that I originally commented on, that one cannot remove our personal and individual beliefs, experiences, preconceptions (and so on) about the world from our arguments. I don't think this necessarily undermines anybodies argument to any great extent since as far as I'm concerned it's inevitable.
Then why are we talking about it? Presumably, we're not here to dwell on banal facts that everyone agrees on.
That really wasn't what I was trying to argue. I do think that of course (to be honest I wonder the same think about the strong guilt people), but that is outside the scope of my response to the original post in this digression.
I suggest that we abandon the digression and return to the (more interesting) main topic.
I know you don't. Equally the evil guilters don't believe the white knights of the Amanda-is-innocent group's opinions are worth anything either. Somehow it seems important to people to point at polls and say "the tide is turning in our favour" based on the number of people who post on the comments sections of web forums.
Regarding "evil guilters" versus "white knights", I do have to say that I am amused by the contrast between the color schemes of PMF and IIP, which is a helpful reminder of which side in this battle is the Dark Side and which is the Light Side.
Polls should be of little epistemic importance to those who know the facts of the case, unless perhaps the results are extremely skewed against one's own opinion (in a poll whose sample isn't selected to produce that result).
OK. Please argue without reference to any preconceived notion that you may have about what is and isn't likely
Again, this is impossible. "Preconceived notions about what is and isn't likely" are an integral part of Bayesian inference; it's literally
in the equation.
that the DNA on the bra-clasp got their due to contamination unconnected with the crime. Not that it could, not that it is theoretically possible, but with a level of confidence that makes it a useful part of your argument.
(1) Contamination sometimes happens -- often enough for us to hear about it and for investigative agencies to have rules and policies mandating specific precautions against it.
(2) When such precautions are not taken or not properly implemented, the risk of contamination becomes significant.
(3) In the absence of contamination or other error on the part of investigators, the presence of Sollecito's DNA on the bra clasp would be strong evidence of his guilt.
(4) By (3), since Sollecito's guilt is a priori unlikely, the presence of his DNA on the clasp via means other than contamination is a priori unlikely. (See my Less Wrong post
Inherited Improbabilities for the mathematical details of this kind of deduction.)
(5) Proper precautionary procedures were not followed in collecting the bra clasp evidence.
(6) By (2), (4), and (5), contamination (etc.) is a more likely explanation for the bra clasp result than anything implying Sollecito's guilt.
I'll gladly assign probabilities if you allow me error bars that are wide enough to make the exercise pointless.
That would mean error bars so wide that disagreement with me couldn't be detected. Since you apparently do admit to disagreeing with me, your error bars can't be that wide.
).
