It's "My Cousin Vinny" all over again. What's the probability that two pairs of youths could show up at the 'Sack o Suds' at the same time both driving metallic mint green 1964 Buick Skylark convertibles with Michelin model XGV-75R tires? And as we all know, totally violating the laws of probability, Marisa Tomei got an Oscar for it, but she didn't really deserve it. Ah, pop culture...
Back to reality. From the article:"Take the dependent evidence fallacy, which was central to one of the most notorious recent miscarriages of justice in the UK. In November 1999, Sally Clark was convicted of smothering her two children as they slept. A paediatrician, Roy Meadow, testified that the odds of both dying naturally by sudden infant death syndrome (SIDS), or cot death, were 1 in 73 million. He arrived at this figure by multiplying the individual probability of SIDS in a family such as Clark's - 1 in 8500 - by itself, as if the two deaths were independent events.
But why should they be? "There may well be unknown genetic or environmental factors that predispose families to SIDS, so that a second case within the family becomes much more likely," the Royal Statistical Society explained during an appeal.
"Even three eminent judges didn't pick up on the mistake," says Ray Hill of the University of Salford, who worked for the defence team. He estimated that if one sibling dies of SIDS, the chance of another dying is as high as 1 in 60. Bayesian reasoning then produces a probability of a double cot death of around 1 in 130,000. With hundreds of thousands of children born each year in the UK, there's bound to be a double cot death every now and then.
Clark was eventually freed on appeal in 2003. "
That's really astounding. Astounding that the poor calculation wasn't detected earlier. Or was it? Were there people who called out this error at the time?
-FER
Mathematics might seem a logical fit for the courts, then. Judges and juries, though, all too often rely on gut feeling. A startling example was the rape trial in 1996 of a British man, Dennis John Adams. Adams hadn't been identified in a line-up and his girlfriend had provided an alibi. But his DNA was a 1 in 200 million match to semen from the crime scene - evidence seemingly so damning that any jury would be likely to convict him.But what did that figure actually mean? Not, as courts and the press often assume, that there was only a 1 in 200 million chance that the semen belonged to someone other than Adams, making his innocence implausible.It actually means there is a 1 in 200 million chance that the DNA of any random member of the public will match that found at the crime scene (see "The prosecutor's fallacy"). The difference is subtle, but significant. In a population, say, of 10,000 men who could have committed the crime, there would be a 10,000 in 200 million, or 1 in 20,000, chance that someone else is a match too. That still doesn't look good for Adams, but it's not nearly as damning.
The probability that randomly selected judges and juries will understand probability is ... wellllll ... it's vanishingly small.
//>>One side or other will look to exclude jurors who could understand the science/math.<<Remember, it's to be a jury of one's peers.//
I've been called to jury duty five times - excused all times.
Three of the times, there were a half-dozen or so of us who were just excused without any questions (voir dour) - based only upon the questionaires we had filled out. We talked as we left the court house. We all had post-graduate degrees in math, engineering or the physical sciences.
Hmmmmmmm.....
<< Is bad math leading to bad justice? Have a look at this article, and the 5-question test that you can try before reading it: >>
Well bad math led to a bad article!
On the case of the two siblings who died, perhaps of cot (or crib) death, the article is certainly correct that the incidents may not be statistically independent. The possibility of positive correlation is certainly viable. In the quiz question though, they ignore the possibility of anti-correlation, which is also certainly a possibility. Perhaps after one death the parents are alerted to look for the possibility in the other child. (In the article they quote a probability of two siblings both suffering cot death--a number I suspect, though the article doesn't go into details. But that number is not even given in the quiz.) So the quiz author jumps to the conclusion that the probability of two related children dieing of cot death is greater than the odds computed assuming independence. The simple truth is, in the quiz, there is not enough information to decide.
Incidentally, what are the odds of two siblings dieing the same night from cot death? That's the relevant number, in my opinion, if that is what happened in the case they cite.
As for the Baysian arguments, I'm not convinced the author understands what Baysian probability is, or how to apply it here. Bernard made the point that her prose is confusing. I contend, in most cases, the exact odds one comes out with are also irrelevant for a jury. Look at her last example:
"Say you are a juror at an assault trial, and so far you are 60 per cent convinced the defendant is innocent"
What the heck does that mean? Her example starts with some sort of gut feeling. It's not much use to apply rigorous statistics at that point!
Finally, at what probability is a juror allowed to presume guilt in a criminal case, in the American/British courts? It's deliberately not cited as a number. What "Beyond reasonable doubt" is, is left for each juror to decide for themselves. Similarly for civil cases ("preponderance of the evidence). (I was an engineer picked to be on three juries in Los Angeles, and that point was made very clear in the jury briefing in each of them.)
Tom
<< Except...it's worse than that. Juries aren't randomly selected. One side or other will look to exclude jurors who could understand the science/math.They'd exclude you or Bernard or even me, because it's in their interest to be able to flim-flam the jury. >>
Not always true. I have a PhD in electrical engineering, and, when I lived in LA, was called about every other year for jury duty. My record: Served on one civil case, one criminal case, and was alternate on another civil case.
In a case where a cop was accused of beating a piece of scum who probably deserved it, I was not selected, possibly because my grandfather was a police officer (slightly corrupt--though nothing unusual for the standards of the day, and I didn't say so on the questionair), or possibly because I filled out the questionair with the same attitude that I began this paragraph.
<< Remember, it's to be a jury of one's peers<<Yeah, but what does that mean? I certainly don't have a right to a white, middle-aged jury of mailmen with degrees in philosophy. Or one drawn from any of those groups. >>
On any case I'm likely to be hauled in for, I would feel quite comfortable facing a jury of drunken Irish bumpkins. The system was set up for people like me!
It isn't even always true in cases where there is scientific/mathematical evidence that the average plumber might not grasp
The good thing about a carefully deliberative jury of laymen is that a group dynamic is established and correct conclusions can be reached that rival those of a single expert. You may be familiar with the exercise that is trotted out in various management seminars. Individuals are asked to answer questions regarding a scenario in which they have no expertise. As individuals, they fail miserably. Working in groups to answer the questions, they score as high as an expert would in the situation presented. Quite often, the scenario involves actions to be taken in a survival situation, for example a downed aircraft in the wilds of Labrador.
RN
<< The good thing about a carefully deliberative jury of laymen is that a group dynamic is established and correct conclusions can be reached that rival those of a single expert. You may be familiar with the exercise that is trotted out in various management seminars. Individuals are asked to answer questions regarding a scenario in which they have no expertise. As individuals, they fail miserably. Working in groups to answer the questions, they score as high as an expert would in the situation presented. Quite often, the scenario involves actions to be taken in a survival situation, for example a downed aircraft in the wilds of Labrador. >>
I believe that's the very scenario I remember from Air Force Squadron Officers' School some twenty years ago.
And, yes, I saw similar expertise exhibited in the juries I was on.
<< I believe that's the very scenario I remember from Air Force Squadron Officers' School some twenty years ago. >>
I also seem to remember the key to the exercise is to abandon the liquor.
"The Wisdom of Crowds"
"When Santa Cruz officials wanted to get public input on how to deal with their budget crunch, they turned to a Web application named UserVoice. They set up the site in eight days on no budget. The technology lets the public submit ideas and then vote on others’ suggestions. People can add comments to further refine ideas. The technology also shows users whether someone else has already posted a similar idea."
See: http://fcw.com/articles/2009/10/26/tech-crowdsourcing.aspx'
Frank
