Amanda Knox and bad maths in court

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

by mitmads • 13 years ago

49 40 13 years ago

bbc.co.uk

waterlion• 13 years ago

It will be fascinating to see how this discussion out in a mainly American forum. In very broad terms, the attitude that the Italians seem to have to Knox is similar to the attitude that the Americans had to Woodward, and very much vice versa.

stephencanon• 13 years ago

For anyone who doesn't know what "Woodward" refers to: http://en.wikipedia.org/wiki/Louise_Woodward_case

mikeash3• 13 years ago

Stuff like this terrifies me:

"In the days following the verdict it emerged that the jury had been split about the murder charge, but those who had favoured an acquittal were persuaded to accept a conviction."

I just don't understand it. How can a person serving on a jury, with another person's life in their hands, be "persuaded to accept a conviction" when they don't actually believe the defendant is guilty?

MichaelGG• 13 years ago

Does DNA testing work like that? If so, you'd just build more iterations into the test itself. If they refer to taking another sample, again, for such a critical test, why not take multiple samples? The coin analogy seems misleading as you can flip many times for free, and each flip is (usually) completely independent.

It'd seem a retest would only matter if there's a new test or the previous test was suspected to be improperly done. In any case, you'd need a reason to believe a different outcome is possible.

In this case, a quick search finds[1]. It says evidence and sample procedures were not properly followed, and there wasn't even evidence of blood on the knife.

I'm all for being corrected on statistics, but this doesn't seem like a case of bad math, does it?

1: http://www.westseattleherald.com/2011/06/29/news/update-dna-...

Symmetry4• 13 years ago

More to the point, even if her blood was on the knife would that necessarily be conclusive evidence? I know that I've left a bit of blood on various cooking knives of people I've lived with.

DigitalTurk2• 13 years ago

No offense (maybe a giggle) but that seems highly unusual

e40• 13 years ago

My understanding of the original scene is that the police first on the scene were not very good, so even if the DNA on the knife is hers, one has to think about contamination by the original (postal) police.

http://en.wikipedia.org/wiki/Murder_of_Meredith_Kercher#Disc...

rayiner• 13 years ago

Article on statistics, IDing, and trials from a former professor of mine: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1432516 (free download).

Also very depressing to read his work on forensics. Long story short, everything in CSI besides DNA evidence is an unscientific sham. And even DNA evidence is dominated by lab error (1-2%). See: lst.law.asu.edu/fs09/pdfs/koehler4_3.pdf.

gburt3• 13 years ago

If you know anything about it, how would you/he propose fixing the problem from an institutional perspective?

Section V of that paper suggests that being more precise in language choice (an important problem in statistics) is his main advice there, but perhaps making the data and conclusions open in some "anonymized" form would support this endeavour?

taejo• 13 years ago

And yet the mathematics in the article seems bogus to me, too. Can anyone figure out what calculation Colmez is doing?

I'm not a statistician, but if you toss a fair coin 20 times, there is about 0.1% chance of getting 17 heads, but to figure out the probability that the coin is fair given this data, it seems you need Bayes' theorem, which requires a prior probability on the coin being fair.

mikeash3• 13 years ago

Confusing "the odds of this occurring with a fair coin" with "the odds that the coin is fair" is by far the most frequent statistical error I see, and by far the least often corrected. It's mildly terrifying.

dyno123452• 13 years ago

Is there a formula you can use to convert between the two?

gweinberg• 13 years ago

You are exactly right. Saying "there is only an 8% chance of this happening with a fair coin" is something completely different from saying "there is a 92% chance the coin is biased". The author is utterly clueless when it comes to probability.

raverbashing• 13 years ago

I'm not sure if Bayes theorem is relevant here, (maybe behind the scenes) but you would go probably for http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

hashmymustache2• 13 years ago

Yea, if I flipped a coin 10,000 times and 55% of them were heads then the coin is definitely biased toward heads, not a 55% chance that it's biased.

pcrh• 13 years ago

You are correct. But the reality is even worse.

I don't know the particular DNA test used in this case, but lets assume it gave a certainty of 92% that the DNA isolated was from AK. This means that the particular sequences of DNA identified could have come from another person with a probably of 0.08 (i.e. a one-in-12.5 chance, which is not particularly low in a case like this). It does not mean that the DNA is correctly characterized with a probability of 92%.

For a repeated test to give a different probability, the identity of one or more of the sequences isolated from the sample would have to have been incorrect in one of the assays, i.e. there is a procedural error.

It is not at all like tossing coins. An analogy would be getting someone's eye color as blue the first time and brown the second.

gburt3• 13 years ago

This is how frequentist statistics works. You ask the wrong question ("the chance of the data occurring given the assumption") and use clean, rigorous, impeccable math to get an answer. Bayesian statistics is (usually) the opposite - you ask the correct question ("the chance of the assumption being correct") but find that there is no way without making some big assumptions to get to the answer.

Here's some good (possibly more "fair" than I've been above) discussion if anyone wants to read/think about this more:

http://stats.stackexchange.com/questions/22/bayesian-and-fre...

http://www.quora.com/What-is-the-difference-between-Bayesian...

WildUtah• 13 years ago

A concise explanation of the difference between Bayesian and Frequentist techniques in statistics:

http://xkcd.com/1132/

carbocation• 13 years ago

I don't like that RFLP analysis is still so common. Practitioners of forensics should genotype a few hundred thousand markers and be done with it. I see that Illumina offers tools for this purpose, in fact: http://www.illumina.com/applications/forensics.ilmn?sciid=20...

xrd• 13 years ago

Math is great for winning court cases. I got pulled over 12 years ago, and went into the magistrate hearing with a drawn out model indicating how the cop was either dangerously speeding himself to pull me over or had inaccurately assessed my speed and bumped up the speed he indicated on my ticket. The lawyer took one look at my sheet full of equations and said "Well, just watch your speed next time." He let me off without any fine and dismissed the case. I would always advise high school students who say "I don't need math" to understand that the world is shifting such that people who know math are becoming very powerful. Especially here in America, where no one would ever admit to being "dumb" and will therefore do anything they can to avoid doing math and looking bad. This is a serious weakness, and can easily be exploited if you ever run into a crafty mathematician.

drakaal• 13 years ago

A DNA Test doesn't work like that.

Probability tests do, but not things we label "probability" that aren't. "there is a 25% chance of rain tomorrow" isn't really a 25%. It is a confidence score.

Something people can grasp better than DNA: Let's say you have a partial thumb print in an imaginary murder. You could eliminate suspects who don't have that portion of the thumb print, but you couldn't confirm that the person or people who match did it. Only that the thumbprint is a "Pocked Loop", "Whorl", or "mixed" and so anyone with a "tent Arch" is not the killer.

You can be 100% confident that the print excludes the person with the "Tent Arch" and if you knew there were only 4 people in the room when the victim in our imaginary scenario died you could even go so far as that since only 2 of them have a potential match that you have a 50% confidence in the match. But Running the test 800 times will not get you to a number better than that.

hashmymustache2• 13 years ago

Exactly, that's why it helps to have multiple tests with different sensitivities and specificities for ruling people out and in, respectively. Whorls and a grip circumference of 14cm, say

viveutvivas• 13 years ago

Here is a much better article on the application of probability to the Amanda Knox case: http://lesswrong.com/lw/1j7/the_amanda_knox_test_how_an_hour...

Amanda Knox and bad maths in court

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