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.
"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?
Have you ever sat on a jury? Unless all 12 people start in unanimous agreement, then some people are probably going to have to be persuaded to change their mind. This is intentionally part of the process; it's how the system is supposed to work.
Maybe I'm reading it wrong, but the way it's worded makes me think that they never changed their mind about the innocence of the defendant, but were simply persuaded to vote against what they believed to be true.
I'm perfectly fine with someone starting out thinking the defendant is innocent and then later changing their minds to thinking the defendant is guilty. I'm very much against anyone thinking the defendant is innocent but voting to convict due to peer pressure or whatever.
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?
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.
Anyone that isn't a professional chef is probably going to leave a little blood on a knife by cutting themselves with it.
There's a difference between a knife drenched in blood and a tiny bit of blood from a cut, certainly, but as far as forensics goes that may not matter - they may want to find any evidence of blood, like some blood caught in the space between the handle and the blade, on the assumption that a killer may have tried to clean blood off a weapon.
> Anyone that isn't a professional chef is probably going to leave a little blood on a knife by cutting themselves with it.
That's a strong claim.
I'm not a professional chef but I like to use a chef's knife, and I cut rather fast. Yet I don't remember ever cutting myself to the point of bleeding. I only remember scraping off nails and skin.
> like some blood caught in the space between the handle and the blade
I reckon that if it gets stuck between the handle and the blade then we're talking about more than a little blood.
I've cut my fingers deeply with a kitchen knife more than once, and bled profusely.
I rarely cook, but I work on cars a lot. Cutting my hands and fingers is part of the routine. Oddly, such cuts have never gotten infected, even when the dirt gets embedded below the skin. I think car grease is an effective bacteriacide!
(I find wearing gloves while working on a car uncomfortable, though I'll do it when cracking a rusted nut loose - when it finally gives way you'll always bang your hand against something.)
That same grease make my cuts all red and inflamed. What gets me is that its rarely jobs that you know will be hard that result in cuts. It's the small simple ones. Switch a ram stick on this beige box, change a set of windscreen wipers. Adjust the temp on the hot water cylinder. Do anything maintenance related to a washing machine.
I don't cut fast and have cut myself a few times to the point of bleeding. Maybe the fact that you cut fast indicates that you are reasonably skilled at this and therefore less likely than others to make yourself bleed, rather than speed indicating that mistakes are more likely.
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.
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.
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?
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.
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.
Reading some other comments in this thread, I feel that I really ought to have included some more stuff here. There isn't actually such a thing as "the odds that the coin is fair." Either it's fair or it's not. What we can talk about is what probability we should ascribe to it being fair given what we know. Even a single coin flip will have a single result, uniquely determined by the way in which it is launched into the air and caught. Probabilities only exist in the presence of our ignorance of the actual facts, and some people consider probabilities to be themselves a measure of our ignorance of the world.
A normal significance test tells you P(observation|H0). [Though I'm not sure about P(observation|!H0)]. To apply Bayes' Rule you need P(H0), where P(H0)=???
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.
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.
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:
You know, I didn't understand that comic when it was posted (despite feeling like I have an understanding of Bayesian vs. frequentist statistics) and I still don't. So, I looked it up and apparently I'm not the only one.
It seems to me, and the commenters on stats.stackexchange [1] that this comic both misinterprets frequentist statistics and misrepresents Bayesian statistics. I realize that XKCD is a nerdy comic meant to be entertaining - I just wanted to leave this discussion here in case anyone else is confused; I think this is an important distinction and one most people interested in statistics should spend some time thinking about.
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...
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.
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.
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
What's the probability of fucken time travel? ROFLMAO 'Terry is innocent. Seys Bible."
God says...
11:21 And at that time came Joshua, and cut off the Anakims from the
mountains, from Hebron, from Debir, from Anab, and from all the
mountains of Judah, and from all the mountains of Israel: Joshua
destroyed them utterly with their cities.
11:22 There was none of the Anakims left in the land of the children
of Israel: only in Gaza, in Gath, and in Ashdod, there remained.
11:23 So Joshua took the whole land, according to all that the LORD
said unto Moses; and Joshua gave it for an inheritance unto Israel
according to their divisions by their tribes. And the land rested from
war.
12:1 Now these are the kings of the land, which the children of Israel
smote, and possessed their land on the other side Jordan toward the
rising of the sun, from the river Arnon unto mount Hermon, and all the
plain on the east: 12:2 Sihon king of the Amorites, who dwelt in
Heshbon, and ruled from Aroer, which is upon the bank of the river
Arnon, and from the middle of the river, and from half Gilead, even
unto the river Jabbok, which is the border of the children of Ammon;
12:3 And from the plain to the sea of Chinneroth on the east, and unto
the sea of the plain, even the salt sea on the east, the way to
Bethjeshimoth; and from the south, under Ashdothpisgah: 12:4 And the
coast of Og king of Bashan, which was of the remnant of the giants,
that dwelt at Ashtaroth and at Edrei, 12:5 And reigned in mount
Hermon, and in Salcah, and in all Bashan, unto the border of the
Geshurites and the Maachathites, and half Gilead, the border of Sihon
king of Heshbon.
answered me (as he could) "that the force of chance, diffused
throughout the whole order of things, brought this about. For if
when a man by haphazard opens the pages of some poet, who sang and
thought of something wholly different, a verse oftentimes fell out,
wondrously agreeable to the present business: it were not to be
wondered at, if out of the soul of man, unconscious what takes place
in it, by some higher instinct an answer should be given, by hap,
not by art, corresponding to the business and actions of the
demander."
be heard in the land; a rumour shall both come one year, and after
that in another year shall come a rumour, and violence in the land,
ruler against ruler.
51:47 Therefore, behold, the days come, that I will do judgment upon
the graven images of Babylon: and her whole land shall be confounded,
and all her slain shall fall in the midst of her.
51:48 Then the heaven and the earth, and all that is therein, shall
sing for Babylon: for the spoilers shall come unto her from the north,
saith the LORD.
51:49 As Babylon hath caused the slain of Israel to fall, so at
Babylon shall fall the slain of all the earth.
51:50 Ye that have escaped the sword, go away, stand not still:
remember the LORD afar off, and let Jerusalem come into your mind.
----
God says...
turn distribute Sudden embarrassments hers if_and_only_if
dissolution aghast minutest confiding joking story unbelieving
sighing willest gliding hurting diddest ordinarily correspondence
flashedst nature shepherd's material locking true Could
showed rejection replacing minds deceivingness Enlightener
scourges Too all-sufficient Especially brethren Shine
mislike energy high greedily judgeth betters refresh affirm
never audaciously containeth mounting hunger loathed unchain
aghast fraud esteeming unpunished thanks chastity carnal
unwilling additional refute benediction Humans righteousness
curiously overthrow nation I_donno Etexts Other prey containest
3296 dwelling-place unsearchable don't_mention_it Ignorant
glowing severer continued obeys king fanned forging speedily
beholding year's furnish urgently abideth contented reverse_engineer
forefathers this assail Wales named whereby journeyed
idols prevails follow accusing pale foretelling feareth
naked privately troublesome Pontitianus shall pervious
medicines etext02 where Narrow Sovereign exacted same
conversations passible owes PURPOSE you_don't_say might
plenteousness stooping retard -nor pervious Togo agents
sides Passing trifles don't_push_it ornamenting servant's
position daemon-worshippers conveyedst natures absurd
teachings Descend aloft listing harlotries racked becoming
Entrust guarded definitely Moon neglecteth
42 comments
[ 3.7 ms ] story [ 74.3 ms ] thread"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?
I'm perfectly fine with someone starting out thinking the defendant is innocent and then later changing their minds to thinking the defendant is guilty. I'm very much against anyone thinking the defendant is innocent but voting to convict due to peer pressure or whatever.
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-...
There's a difference between a knife drenched in blood and a tiny bit of blood from a cut, certainly, but as far as forensics goes that may not matter - they may want to find any evidence of blood, like some blood caught in the space between the handle and the blade, on the assumption that a killer may have tried to clean blood off a weapon.
That's a strong claim.
I'm not a professional chef but I like to use a chef's knife, and I cut rather fast. Yet I don't remember ever cutting myself to the point of bleeding. I only remember scraping off nails and skin.
> like some blood caught in the space between the handle and the blade
I reckon that if it gets stuck between the handle and the blade then we're talking about more than a little blood.
I rarely cook, but I work on cars a lot. Cutting my hands and fingers is part of the routine. Oddly, such cuts have never gotten infected, even when the dirt gets embedded below the skin. I think car grease is an effective bacteriacide!
(I find wearing gloves while working on a car uncomfortable, though I'll do it when cracking a rusted nut loose - when it finally gives way you'll always bang your hand against something.)
Surely cleaning blood off the knife makes just as much sense if it was a cooking accident as if you've killed someone with it?
http://en.wikipedia.org/wiki/Murder_of_Meredith_Kercher#Disc...
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.
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?
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.
http://en.wikipedia.org/wiki/Bayes%27_theorem
P(H0|observation) = P(observation|H0) * P(H0) / P(observation)
P(observation) = P(observation|H0) * P(H0) + P(observation|!H0) * P(!H0)
A normal significance test tells you P(observation|H0). [Though I'm not sure about P(observation|!H0)]. To apply Bayes' Rule you need P(H0), where P(H0)=???
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.
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...
http://xkcd.com/1132/
It seems to me, and the commenters on stats.stackexchange [1] that this comic both misinterprets frequentist statistics and misrepresents Bayesian statistics. I realize that XKCD is a nerdy comic meant to be entertaining - I just wanted to leave this discussion here in case anyone else is confused; I think this is an important distinction and one most people interested in statistics should spend some time thinking about.
[1] http://stats.stackexchange.com/questions/43339/whats-wrong-w...
Edit: I can't edit my first comment now, but gweinberg's post (sibling to the grandparent of this) words the problem perfectly.
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.
God says...
11:21 And at that time came Joshua, and cut off the Anakims from the mountains, from Hebron, from Debir, from Anab, and from all the mountains of Judah, and from all the mountains of Israel: Joshua destroyed them utterly with their cities.
11:22 There was none of the Anakims left in the land of the children of Israel: only in Gaza, in Gath, and in Ashdod, there remained.
11:23 So Joshua took the whole land, according to all that the LORD said unto Moses; and Joshua gave it for an inheritance unto Israel according to their divisions by their tribes. And the land rested from war.
12:1 Now these are the kings of the land, which the children of Israel smote, and possessed their land on the other side Jordan toward the rising of the sun, from the river Arnon unto mount Hermon, and all the plain on the east: 12:2 Sihon king of the Amorites, who dwelt in Heshbon, and ruled from Aroer, which is upon the bank of the river Arnon, and from the middle of the river, and from half Gilead, even unto the river Jabbok, which is the border of the children of Ammon; 12:3 And from the plain to the sea of Chinneroth on the east, and unto the sea of the plain, even the salt sea on the east, the way to Bethjeshimoth; and from the south, under Ashdothpisgah: 12:4 And the coast of Og king of Bashan, which was of the remnant of the giants, that dwelt at Ashtaroth and at Edrei, 12:5 And reigned in mount Hermon, and in Salcah, and in all Bashan, unto the border of the Geshurites and the Maachathites, and half Gilead, the border of Sihon king of Heshbon.
----
Anakin Skywalker
answered me (as he could) "that the force of chance, diffused throughout the whole order of things, brought this about. For if when a man by haphazard opens the pages of some poet, who sang and thought of something wholly different, a verse oftentimes fell out, wondrously agreeable to the present business: it were not to be wondered at, if out of the soul of man, unconscious what takes place in it, by some higher instinct an answer should be given, by hap, not by art, corresponding to the business and actions of the demander."
-----
http://www.templeos.org/Wb/Apps/HolySpirit/HSNotes.html
----
God says...
be heard in the land; a rumour shall both come one year, and after that in another year shall come a rumour, and violence in the land, ruler against ruler.
51:47 Therefore, behold, the days come, that I will do judgment upon the graven images of Babylon: and her whole land shall be confounded, and all her slain shall fall in the midst of her.
51:48 Then the heaven and the earth, and all that is therein, shall sing for Babylon: for the spoilers shall come unto her from the north, saith the LORD.
51:49 As Babylon hath caused the slain of Israel to fall, so at Babylon shall fall the slain of all the earth.
51:50 Ye that have escaped the sword, go away, stand not still: remember the LORD afar off, and let Jerusalem come into your mind.
----
God says... turn distribute Sudden embarrassments hers if_and_only_if dissolution aghast minutest confiding joking story unbelieving sighing willest gliding hurting diddest ordinarily correspondence flashedst nature shepherd's material locking true Could showed rejection replacing minds deceivingness Enlightener scourges Too all-sufficient Especially brethren Shine mislike energy high greedily judgeth betters refresh affirm never audaciously containeth mounting hunger loathed unchain aghast fraud esteeming unpunished thanks chastity carnal unwilling additional refute benediction Humans righteousness curiously overthrow nation I_donno Etexts Other prey containest 3296 dwelling-place unsearchable don't_mention_it Ignorant glowing severer continued obeys king fanned forging speedily beholding year's furnish urgently abideth contented reverse_engineer forefathers this assail Wales named whereby journeyed idols prevails follow accusing pale foretelling feareth naked privately troublesome Pontitianus shall pervious medicines etext02 where Narrow Sovereign exacted same conversations passible owes PURPOSE you_don't_say might plenteousness stooping retard -nor pervious Togo agents sides Passing trifles don't_push_it ornamenting servant's position daemon-worshippers conveyedst natures absurd teachings Descend aloft listing harlotries racked becoming Entrust guarded definitely Moon neglecteth