Continuation Part 2 - Discussion of the Amanda Knox case

[Kevin_Lowe]

First, I'd like to thank Kevin_Lowe for his insightful OP. One of the reasons I enjoy hanging out here is that there are so many people whose view of the world I can find common ground with. I think Randi deserves enormous credit for allowing the community to find itself. So thank you Randi.

I have had an interest in the Amanda Knox case that predated finding the threads here, but my interest has never been strong enough to justify spending much effort in forming an opinion for myself based on research and a detailed understanding of the case.

So, I would check in on the threads every now and then to see which way my fellow JREF posters were leaning but alas, I couldn't discern a clear cut pattern so I have pretty much remained without a strong opinion with regards to the case.

One thing I would note about the threads that I looked at was that it seemed like both sides had taken their eye off the ball a bit. This wasn't something where certainty was likely. The only reasonable goal was to come up with an estimate of how likely a particular view was to be correct and yet the proponents of both sides seemed to be arguing that they had found enough evidence that their view was correct with a high degree of certainty. Why did they think this? From the outside it seemed unlikely that this could be so. Two groups of JREF posters had seen the same evidence and analysis and they were not forming a consensus. This is the same group of JREF posters that have shown amazing insights, and knowledge over a wide range of topics. If this was a situation where practical certainty was possible did the group of JREF posters on the wrong side of the issue suddenly go nuts, or stupid?

What I was looking for was to see some dedicated discussion on the issue of the level of confidence possible in this case. Did the level of confidence that she was guilty satisfy a beyond-a-reasonable-doubt criteria? Were there some posters that thought she was probably guilty but the confidence level was insufficient for a guilty verdict? Were there moderates in the debate or was everybody for her or agin her?

Thanks for the kind reply davefoc, and what I can say over here but can't say over there is that the pro-innocence side have solved the case, but the incredibly rapid flow of the thread means that the proof gets swept away almost instantly and people peering in over the wall see no proof at all, just two sides disagreeing with each other. It's really unfortunate but I don't know what to do about it.

Okay, the proof that the prosecution case did not meet the level of reasonable doubt hinges on a little bit of forensic science. We've hashed all the details out thoroughly so I'll skip the citations (searching for them is a pain, and it's been a long day cleaning up flood damage) for now and get them for you if people want them.

There's a term called t(lag), which is the time it takes for food you have swallowed to start moving from the stomach to the duodenum. It's distinct from t(1/2) which is the time for half the food in a meal to get out of the stomach into the duodenum. T(lag) distribution is a normal distribution on the right hand side of the graph, and depending on the meal and the person it can be as short as minutes or as long as three or just maybe even four hours.

No reliable source whatsoever will state that t(lag) in a normal, healthy young woman who ate a small to moderate sized meal with no alcohol, stress or other known confounding factors can exceed four hours, and a t(lag) of four hours is really, incredibly unlikely. Three hours is incredibly unlikely, and some sources say it's the plausible upper limit, but it's not quite as bad as four.

Meredith Kercher, a normal, healthy young woman ate a meal of pizza followed by apple crumble no later than 18:30. All of that meal was still in her stomach when she was murdered. The prosecution case was that she was murdered at 23:30. If you do the math, that's just not possible.

How the court settled on 23:30 as the time of death is a long story, but the short version is that they picked that time because if Meredith died any earlier Knox and Sollecito couldn't possibly have done it. Computer evidence or prosecution witnesses that the case simply couldn't do without either had them somewhere else at every other time, or there were unimpeachable witnesses outside the murder house who testified that the house was dark and silent when they were there.

It was an impassable logical pickle. They wanted to convict Knox and Sollecito. The prosecution's own evidence and witnesses ruled out the possibility that they murdered Meredith at any time before 23:30. The autopsy evidence proved that Meredith died before 21:30. So they just cut the Gordian knot by ignoring the autopsy evidence and convicted them of doing it at 23:30 anyway.

There are multiple sub-controversies I haven't gone in to, like the spurious reasoning the court used to discard the coroner's opinion that Meredith died around 21:30 in favour of the totally made-up 23:30 time, the fact that the only witness who contradicted their alibi was a homeless heroin dealer the police had the dirt on, who just so happened to have also been a prosecution witness in two previous murder trials, who came forth long after the events in question with an incredibly detailed statement accurate to the minute, and whose testimony has other serious inconsistencies with the known facts, and the fact that when Raffaele Sollecito handed his computer over to the police so they could verify from the time stamps that he had been at home all night they overwrote all the relevant time stamps and then fried the hard drive.

Now since then the appeals team has published what certainly appear to be detailed computer activity logs recovered from Sollecito's fixed laptop that confirm their alibi for the entire night, from 21:00 or so right through to 6am the next morning. So that pretty much rules out even the most tangential involvement in the murder, since they were at home from before it happened to long, long after it was all over.

The pro-guilt response to this could be summarised as (and I quote no particular person) "(long silence) um (long silence) THEY DID IT ANYWAY THEY'RE GUILTY GUILTY GUILTY!". I'm completely serious. We've been asking for some time now for any pro-guilt poster to present even one remotely plausible story for how Knox and Sollecito could possibly have been guilty given the facts we now know and not one of them has managed to do so.

A couple have started out on one, but they rapidly ran aground on the plain fact that Meredith almost certainly died before 21:30 and Knox and Sollecito were almost certainly at home until long after 21:30. There's no way to get around that. It's no longer a matter of whether there's proof beyond reasonable doubt Knox and Sollecito did it, it's a question of whether it's even conceivable that they did do it, and the pro-guilt crowd can't even convincingly argue that it's conceivable.

Yet despite this, not one pro-guilt poster has come forward and said "Well in that case, maybe they didn't do it, I guess I was wrong". Given that several of them are people who've posted at the JREF for some time, that's pretty sad.

The reason why they haven't is, I think, twofold. One, (and there is some hard evidence for this) people who believe Knox are guilty generally aren't the most rational tools in the box to start with. Two, they have immersed themselves in their echo chamber at perugiamurderfile.org where they constantly reinforce each other's falsified factual beliefs about the case, and constantly misrepresent pro-innocence arguments to each other so that they only ever encounter straw man versions of them on their home turf

 

[Charlie Wilkes]

Wow what a list of docs! Thanks. That is something to work through.

___

Charlie if you reading this, I think you should give everything in the case. Possibly have a warning before you link to something explicit. One of the arguments is being made is that the court had access to information we didn't and thus we can't question their judgement. In SCO v. IBM which was the first "webified" trial I was involved in, one of things that was most valuable was Groklaw came into existence as a warehouse of all of the evidence submitted to the court. That allowed people who knew anything to comment on conversations they had been present for (i.e. essentially hearsay) which then resulted in primary witnesses getting notified and they ended up deposing themselves.

For example SCO made claims about code in Lion's, Lions on Unix and where he got it. Much to everyone's surprise John Lions was still alive and actually wrote into Groklaw with "BS I got it from....." and there were dozens of examples of this. It was devastating for SCO's case to constantly have their "facts" (really wild guesses) refuted.

My approach has been to make this material available as the need arises. The raw data is simply too much, and a lot of it is irrelevant.

There is also some material that I cannot share for obvious reasons. I have gone through the Nov. 2-3 2007 video and edited out frames that show Meredith's body. Even with the edits, however, the video is jarring and unpleasant, more so than still photos of the crime scene. I asked this group if I should make it available, and the consensus was that it would be better to make it available by private request, which is what I have done.

I want to avoid having this material end up on youtube or on sites that present such content as ghoulish entertainment. I therefore try to limit distribution while at the same time making information available to those who have a serious interest in the case. So far it has worked. Nobody has abused my trust or misused the information.

 

[Charlie Wilkes]

This story has all the earmarks of having come in over the transom. There are no names, dates, times, judge, or much of anything to verify the truth or non truth of the story. Despite it originating locally with this paper, there is no byline indicating nobody at this paper even wants to take credit for this. There are no attempts to even get a quote or reaction from the prosecution or defense team or any effort made to show how the story was independently verified.

My opinion is that this is a pure smear job.

I have the impression that it comes down to one individual making a claim that is not corroborated by cell phone records.

 

[bobc]

I was thinking about the Bayesian approach, and begun to wonder what the actual rate of wrongful convictions is. Without considering the facts of the particular case, it seems sensible to set the a priori probability of the guilt of a defendant for a specific case at the general rate of reliable convictions.

I imagined the rate of wrongful convictions might be something like 5 in 1000 cases. After doing some research the answer I found surprised me.

So I'd like to ask,

1) what is your unresearched view of the wrongful conviction rate?
2) According to research, what is the best estimate for wrongful conviction rate? We would need to take into the type of crime, as well as the jurisdiction, but there must be some numbers to get a reasonable estimate.

 

[bobc]

There's a term called t(lag), which is the time it takes for food you have swallowed to start moving from the stomach to the duodenum. It's distinct from t(1/2) which is the time for half the food in a meal to get out of the stomach into the duodenum. T(lag) distribution is a normal distribution on the right hand side of the graph, and depending on the meal and the person it can be as short as minutes or as long as three or just maybe even four hours.
...
Meredith Kercher, a normal, healthy young woman ate a meal of pizza followed by apple crumble no later than 18:30. All of that meal was still in her stomach when she was murdered. The prosecution case was that she was murdered at 23:30. If you do the math, that's just not possible.

So if Meredith arrived home at 21:00, what is a reasonable probability that t(lag) was > 2.5 hours and no food had moved out of the stomach? My research suggests that t(lag) is < 90 minutes to high probability.

According to your math, Meredith is most likely to have died before she reached home, while she was watching a movie with friends. The math doesn't work for you either.

It seems like the stomach evidence is impossible either way, so perhaps it should be disregarded completely.

[1] "Lag Phase in Solid Gastric Emptying: Comparison of Quantification by Physiological and Mathematical Definitions "
http://jnm.snmjournals.org/cgi/content/abstract/34/10/1701

 

[Chris_Halkides]

gritsforbreakfast on the frequency of wrongful convictions

I was thinking about the Bayesian approach, and begun to wonder what the actual rate of wrongful convictions is. Without considering the facts of the particular case, it seems sensible to set the a priori probability of the guilt of a defendant for a specific case at the general rate of reliable convictions.

I imagined the rate of wrongful convictions might be something like 5 in 1000 cases. After doing some research the answer I found surprised me.

So I'd like to ask,

1) what is your unresearched view of the wrongful conviction rate?
2) According to research, what is the best estimate for wrongful conviction rate? We would need to take into the type of crime, as well as the jurisdiction, but there must be some numbers to get a reasonable estimate.

bobc,

That is a very difficult number to estimate. I would have guessed at least 1%, I suppose (unresearched). Scott Henson's treatment is a good place to start. If I understand him correctly, the estimates he has are 1.5% and 3.3%.

 

[bobc]

bobc,

That is a very difficult number to estimate. I would have guessed at least 1%, I suppose (unresearched). Scott Henson's treatment is a good place to start. If I understand him correctly, the estimates he has are 1.5% and 3.3%.

Yes, that is the research I found. 3% error rate would be way too high in my profession! It surely is a serious cause for concern, at least in Texas.

Making the assumption that the Knox case is a "DNA based conviction" (which could be disputed) and the less well-founded assumption that Texan legal and forensic processes are applicable to Italy, that would suggest the a priori probability of Knox being guilty is ~0.97.

So the question to Bayesians: if a priori is 0.97, and the probability of Knox being guilty solely based on case details is judged to be 0.05, what is the resulting probability?

 

[RoseMontague]

Yes, that is the research I found. 3% error rate would be way too high in my profession! It surely is a serious cause for concern, at least in Texas.

Making the assumption that the Knox case is a "DNA based conviction" (which could be disputed) and the less well-founded assumption that Texan legal and forensic processes are applicable to Italy, that would suggest the a priori probability of Knox being guilty is ~0.97.

So the question to Bayesians: if a priori is 0.97, and the probability of Knox being guilty solely based on case details is judged to be 0.05, what is the resulting probability?

I think the rate that the first court is overturned at one of the appeal levels is probably a better estimate of an error rate in Italy. Perhaps after this case has gone through all three steps could you use a rate similar to the one you are using.

 

[Kevin_Lowe]

So if Meredith arrived home at 21:00, what is a reasonable probability that t(lag) was > 2.5 hours and no food had moved out of the stomach? My research suggests that t(lag) is < 90 minutes to high probability.

According to your math, Meredith is most likely to have died before she reached home, while she was watching a movie with friends. The math doesn't work for you either.

It seems like the stomach evidence is impossible either way, so perhaps it should be disregarded completely.

[1] "Lag Phase in Solid Gastric Emptying: Comparison of Quantification by Physiological and Mathematical Definitions "
http://jnm.snmjournals.org/cgi/content/abstract/34/10/1701

Not this again? I mean, as talking points go, it's really stupid.

Meredith was seen alive by her friend Sophie until about 21:00. She was found dead at home, which was five minutes walk or so from where Sophie parted with her, so she was alive until at least 21:05.

If you knew nothing else about Meredith's time of death except the state of her stomach and the time of her last meal, you would say that Meredith died between 18:30 and 21:30, or just maybe as late as 22:30 depending on which source you use and how far down the tail of the distribution you are willing to go.

Put the two facts together and any time before 21:05 is impossible and any time after 21:30 is really unlikely.

Rational people do not argue that if the chance of X happening is one in one hundred or one in one thousand, and X appears to have happened, that this is such an absurd outcome that we should just throw everything we know about human biology out the window. Until and unless you come up with a hypothesis which a rational person should prefer to the hypothesis that Meredith just happened to have a long t(lag) time and so she still had no food in her duodenum 150 minutes after she ate, a rational person is going to go with the hypothesis that conforms with the way the universe actually works.

That is to say, the hypothesis that she ate at 18:30 or so, and died very shortly after 21:05.

 

[bobc]

I think the rate that the first court is overturned at one of the appeal levels is probably a better estimate of an error rate in Italy. Perhaps after this case has gone through all three steps could you use a rate similar to the one you are using.

Well no, that is a different thing. That is the rate of convictions, not the rate of wrongful convictions.

Also I think you would also need to filter on murder cases that hinge on DNA evidence.

 

[bobc]

Not this again? I mean, as talking points go, it's really stupid.

Meredith was seen alive by her friend Sophie until about 21:00. She was found dead at home, which was five minutes walk or so from where Sophie parted with her, so she was alive until at least 21:05.

If you knew nothing else about Meredith's time of death except the state of her stomach and the time of her last meal, you would say that Meredith died between 18:30 and 21:30, or just maybe as late as 22:30 depending on which source you use and how far down the tail of the distribution you are willing to go.

Put the two facts together and any time before 21:05 is impossible and any time after 21:30 is really unlikely.

Rational people do not argue that if the chance of X happening is one in one hundred or one in one thousand, and X appears to have happened, that this is such an absurd outcome that we should just throw everything we know about human biology out the window. Until and unless you come up with a hypothesis which a rational person should prefer to the hypothesis that Meredith just happened to have a long t(lag) time and so she still had no food in her duodenum 150 minutes after she ate, a rational person is going to go with the hypothesis that conforms with the way the universe actually works.

That is to say, the hypothesis that she ate at 18:30 or so, and died very shortly after 21:05.

Rational people would address my point, and not instead attack a strawman, with a few ad homs thrown in.

It is your argument that a probability of the actual events can be derived from stomach emptying times, are you now denying this?

Also you seem to be selectively believing the autopsy evidence. If the police investigation is "unethical and incompetent" as you put it, why would you believe the part that is convenient to your argument? Also YOU re-raised the stomach evidence, not me.

The maximum t(lag) found by experiment, is less than 90 minutes. Your conclusion is therefore unsupported.

 

[Kevin_Lowe]

Yes, that is the research I found. 3% error rate would be way too high in my profession! It surely is a serious cause for concern, at least in Texas.

Making the assumption that the Knox case is a "DNA based conviction" (which could be disputed) and the less well-founded assumption that Texan legal and forensic processes are applicable to Italy, that would suggest the a priori probability of Knox being guilty is ~0.97.

So the question to Bayesians: if a priori is 0.97, and the probability of Knox being guilty solely based on case details is judged to be 0.05, what is the resulting probability?

If 95% of fuzzballs are blue, and it's 95% likely the fuzzball I hold in my hand is red, what is the resulting probability that the fuzzball I hold in my hand is red?

How about I rephrase your question for you? Suppose you had actually asked "If 97% of those tried are guilty, but in this case we found a piece of evidence which only has a 5% chance of existing if the defendant is guilty, and a 100% chance of existing if the defendant is innocent, what is the resulting probability that they are innocent?".

Let's call this hypothetical evidence a computer log alibi, to stick with the Knoxian theme.

I won't subject you to equations. Imagine we tried 100 people this way. We try 97 guilty people, and 0.05 of them have a computer log alibi going for them, so 4.85 or so of the 100 would be guilty but have a computer log alibi anyway. We try 3 innocent people and all of them have computer log alibis.

So in our pool of people with the evidence going for them, 4.85 (nominally) are guilty and 3 are innocent. So the odds of innocence with this evidence on your side are about 38%. That means those 7.85 defendants should go free, since 38% is reasonable doubt in anyone's language. However at the same time rational people should think it more likely than not each of them did it, and you wouldn't walk down a dark alley with those people.

However I think in this case the real prior probability of Knox and Sollecito participating in an unprecedented three-way sex murder is a lot lower than the prior probability of a randomly selected defendant being guilty of whatever they are in for. The Mignini theory is a zebra hypothesis, and hence substantially more unlikely than most everyday prosecution theories.

 

[bobc]

Any idiot can unpack their new toys and and try to use them the first time without reading the instructions. It takes a vey special kind of idiot to proceed to destroy 4 drives in a row before they figure out that they are doing something wrong.

In a forensic context, trashing one drive would be pretty bad, but trashing 4 is surely incompetent, particularly as there are off the shelf systems for extracting forensic computer data.

 

[bobc]

If 95% of fuzzballs are blue, and it's 95% likely the fuzzball I hold in my hand is red, what is the resulting probability that the fuzzball I hold in my hand is red?

How about I rephrase your question for you? Suppose you had actually asked "If 97% of those tried are guilty, but in this case we found a piece of evidence which only has a 5% chance of existing if the defendant is guilty, and a 100% chance of existing if the defendant is innocent, what is the resulting probability that they are innocent?".

Let's call this hypothetical evidence a computer log alibi, to stick with the Knoxian theme.

I won't subject you to equations. Imagine we tried 100 people this way. We try 97 guilty people, and 0.05 of them have a computer log alibi going for them, so 4.85 or so of the 100 would be guilty but have a computer log alibi anyway. We try 3 innocent people and all of them have computer log alibis.

So in our pool of people with the evidence going for them, 4.85 (nominally) are guilty and 3 are innocent. So the odds of innocence with this evidence on your side are about 38%. That means those 7.85 defendants should go free, since 38% is reasonable doubt in anyone's language. However at the same time rational people should think it more likely than not each of them did it, and you wouldn't walk down a dark alley with those people.

However I think in this case the real prior probability of Knox and Sollecito participating in an unprecedented three-way sex murder is a lot lower than the prior probability of a randomly selected defendant being guilty of whatever they are in for. The Mignini theory is a zebra hypothesis, and hence substantially more unlikely than most everyday prosecution theories.

I see yet again you fail to address a simple point, and instead attack some convoluted strawmen of your own devising.

There are those who say you are just a clever troll, is that true?

 

[Kevin_Lowe]

Rational people would address my point, and not instead attack a strawman, with a few ad homs thrown in.

It is your argument that a probability of the actual events can be derived from stomach emptying times, are you now denying this?

...

The maximum t(lag) found by experiment, is less than 90 minutes. Your conclusion is therefore unsupported.

I've rearranged your post to make it more comprehensible. People keen to see the original can scroll up or click on the little arrow.

Let me guess, you've cherry-picked one study where the highest t(lag) value was 90m and you're presenting this as evidence that the highest t(lag) value ever known to science was 90m? Do I really need to explain to you the error here?

We've cited multiple studies to back up our case. A t(lag) of 150m is highly unlikely but not unheard of. A t(lag) of 300m is crazy.

Also you seem to be selectively believing the autopsy evidence. If the police investigation is "unethical and incompetent" as you put it, why would you believe the part that is convenient to your argument?

This argument is also pretty strange if you think about it. It's the prosecution's job to prove their case beyond reasonable doubt. I don't think you can rescue proof-beyond-reasonable-doubt by arguing that yes the prosecution evidence proves that the defendant is innocent if the prosecution evidence is any good, but that since the prosecution evidence might be rubbish that there is proof beyond reasonable doubt anyway.

Also, review The Fallacy of Composition.

Also YOU re-raised the stomach evidence, not me.

My point is merely that we've seen the Chewbacca Defence used repeatedly to try to discredit the stomach contents evidence in the past, and no matter how many times you guys try it, it's still just the Chewbacca Defence.

 

[Kevin_Lowe]

I see yet again you fail to address a simple point, and instead attack some convoluted strawmen of your own devising.

You asked your question wrong. I gave you a gentle nudge in the direction of the answer to the question you actually asked. Then I gave you a mathematically precise answer to something resembling your question the way you would have asked it if you had a rough idea what Bayes' Theorem was.

There are those who say you are just a clever troll, is that true?

It's true that there are people who say it. Those people say all sorts of stupid things though. I wouldn't listen to those people.

 

[Dan O.]

If you try to hypothesize Meredith's death before 21:00, you suddenly have to deal with a conspiracy between Meredith's English friends and Rudy Guede. (or that one of the English girls dressed as Meredith walking past the CCTV camera to establish that Meredith was walking home alone ran into Rudy in front of the cottage and invited him inside.)

Conspiracy theories are for some reason a forbidden topic so nobody is willing to explore this possibility. Therefore we take it as given that Meredith died after 21:00.

 

[Charlie Wilkes]

Try sticking the board in an old microwave.

It is interesting that the consultant's report basically sweeps the problem under the rug. He picks up the story at the point where the professor swaps the circuit boards. He doesn't inquire as to what happened to damage them in the first place. At the end of his report, he exonerates everyone, saying he found no evidence that anyone did anything wrong or inappropriate.

It's the kind of exercise that typifies how this case has been handled from start to finish - a lot of fancy verbiage to hide the fact that the people in charge of this case are bungling idiots.

 

[Chris C]

If you try to hypothesize Meredith's death before 21:00, you suddenly have to deal with a conspiracy between Meredith's English friends and Rudy Guede. (or that one of the English girls dressed as Meredith walking past the CCTV camera to establish that Meredith was walking home alone ran into Rudy in front of the cottage and invited him inside.)

Conspiracy theories are for some reason a forbidden topic so nobody is willing to explore this possibility. Therefore we take it as given that Meredith died after 21:00.

Actually, there is 0 proof that was Meredith that walked by the CCTV camera. Though I personally believe it was Meredith, there still is no proof. After all there was a car parked in that driveway. It could have been someone in that car. Someone from that car either walked in front of that camera or they where in fact in the apartment.

 

[Chris_Halkides]

final answer?

Yes, that is the research I found. 3% error rate would be way too high in my profession! It surely is a serious cause for concern, at least in Texas.

Making the assumption that the Knox case is a "DNA based conviction" (which could be disputed) and the less well-founded assumption that Texan legal and forensic processes are applicable to Italy, that would suggest the a priori probability of Knox being guilty is ~0.97.

So the question to Bayesians: if a priori is 0.97, and the probability of Knox being guilty solely based on case details is judged to be 0.05, what is the resulting probability?

bobc,

It is not clear to me, but the 3.3% value may not be a final estimate. I think it would depend on how many convictions have been examined. I am of the impression that many have not been. My own readings on false confessions, faulty eyewitness testimony, and erroneous or fraudulent forensics makes me wonder whether the number of false convictions is higher than I would have suspected, say, five years ago.

It is interesting that in Texas the number of fires classified as arson has gone from about 60% to about 40% over a number of years, IIRC. During the last, very roughly, 25 years or so, arson investigation has become more scientific in its methods, and previously-thought indicators of arson are now known to be no such thing. Disclaimer: correlation is not the same as causation. For the purposes of a mathematical exercise, using a value of 3.3% is fine by me, but there is a limit to how seriously I take it.