Experiment: Knox case debate with Rolf Nelson

For example, the fact that the suspect and victim are acquaintances is surely not negligible evidence

Screened off by the evidence against Rudy Guede.

a smaller knife would have been compatible with all of the wounds as well as the imprint

(Massei, 170) seems to disagree (although I could be misreading it), but I welcome any counter-arguments. If you want to claim extreme coroner bias or extreme trial-court bias (or both), then eventually you'll want to separate out the hypothesis of bias and make your case for it.

The closest thing to evidence for (the knife being bleached) is that a police officer claimed to have smelled bleach upon opening the drawer that the knife was in. (That doesn't distinguish the knife in question from the others, needless to say.)

I disagree: "Let me state beforehand that it was extremely clean" (Massei, 99)

The innocent explanation is that (Raffaele) had been told about the knife DNA result, and believed it.

I give the odds that he would tell such a lie if guilty as .1, and if innocent as .001; what odds do you give? Why would Raffaele believe the DNA result? He's more likely to believe it's not the murder weapon if he's innocent, and also less likely to lie if innocent.

Similarly, why is Amanda's reaction to the knife drawer even evidence of guilt at all, let alone 10 decibels' worth?

I think if she's innocent, reacting to the knife like that is about .05 likely, and if she's guilty, about .005 likely. What odds do you give? You wouldn't be more likely to react strongly to an otherwise-irrelevant event if you knew it was going to practically end your life?

Where Amanda's DNA was found on the handle suggests someone stabbing rather than cooking with it: meh, shift by 2.

Even if this is so (which I don't have any particular reason to accept), presumably all one has to do to to get one's DNA in this position is shift one's grip on the knife in some way -- as opposed to actually stabbing someone! Isn't the denominator of this ratio quite substantial?

My reasoning: suppose a chef grabs a knife in cooking position ten times and nose-picking position once. Suppose further DNA is only found in one spot. It's probably ten times more likely that the DNA is found in cooking position, and that his unhygienic habit will remain undetected (aside from the giant nasal scars).

But in this situation "knowing the knife isn't a murder weapon" doesn't come close to being necessary for innocence.

I disagree: not necessary, but probable, by a factor of >10 IMHO.

"So unless Raffaele decided to get up after I fell asleep, grabbed said knife, went over to my house, used it to kill Meredith, came home, cleaned the blood off, rubbed my fingerprints all over it, put it away, then tucked himself back into bed, and then pretended really well the next couple of days, well, I just highly doubt all of that."

I'm more concerned by: “This could have happened: Raffaele [killed Meredith] and then, having come back home, pressed my fingerprints — I was asleep — onto the knife", from London Times

So we're probably talking about an order of magnitude increase in the base rate: more like 1/5 instead of 1/50.

I'll posit a factor of three.

(Incidentally, there was never any "first independent report" prior to this one...)

My bad, that was quite confusing of me, I mean the Massei(+Cristiani) report, which is independent of the police lab. Will fix. Thanks!

The sample in question (Trace B) tested negative for blood, as did every other sample taken from the blade.

IMHO irrelevant, Meridith's DNA is incriminating whether it's from blood or tissue, and whether any blood chemicals remained after cleaning in sufficient quantity to test positive.

(Various lab procedural criticisms)

Do you want to formally introduce a hypothesis that, LCN aside, this test was sloppier than the average test at the average lab? (Call this "ddk.slop") If so, one way to numerically assess would be to establish:

1. How sloppy do you think the test was, in terms of percentile? Are 10% of lab tests as or more sloppy than this one? 1%? Less?

2. How certain are you that the ddk.slop and its associated percentile is true? (FWIW I currently think this lab test is less sloppy than average.)

Then we can quantify your estimated shift to the base rate.

My guess is it's probably figured by assuming there are ~500 objects being examined by the lab. However, I would point out that contaminations are unlikely to be independent of each other, and are instead probably correlated via the general level of standards in the laboratory. In other words, if there is a single contamination, there are likely to be others as well (reported or not).

I'm not following this discussion in detail, but I'm glad you guys are having it - I think it's a worthwhile case study, and the flavour of the way it's discussed is informative without getting into the detail of the subject matter.

(2) What is your probability of guilt, conditioned on death having occurred (a) before 21:30? (b) before 22:00?

If we're not taking systemic uncertainty into account, then it's still going to be quite a large probability of guilt. However, I would say that, compared with 23:00, (a) would shift me by about 15:1 on the grounds that the computer evidence would have to be mis-analyzed, or (more likely) Raffaele would have had to manufacture the computer alibi (recall Raffaele is a computer engineer), and (b) by 5:1 on the grounds that the timetable gets a bit tighter than in the 23:00 case.

If we don't take systemic uncertainty into account, then 15:1 isn't much of a shift in the face of numbers like 2500:1 or 200000:1 that you were giving for the knife. On the other hand, if we do take systemic uncertainty into account (as we ultimately must), a shift of 15:1 or even 5:1 would be significant, given your estimate of .95 probability of guilt, or 19:1 odds. Crudely approximating this as 20:1, it would take you down to 4:3 (p = 4/7 = 0.57) or 4:1 (p= 4/5 = 0.8) respectively. I imagine that if you were to believe the 21:26 computer interaction, the pre-22:00 odds could potentially go down to something like 4:3 as well. This indicates that it may be worthwhile to keep pursuing the time-of-death issue.

Keep in mind that I'm currently not yet bothering to weigh the eyewitness testimony at all in my assessment of guilt.

Well, I was already assuming that you didn't believe Curatolo (for one thing, he gives Amanda and Raffaele an alibi for 21:30-23:00!). If you do, that will have to be dealt with separately. But in general, not only is eyewitness testimony among the weakest forms of evidence, but it cuts both ways in this case, as the broken-down car illustrates.

Slippage is a priori unlikely, especially with the ligatures applied (professional opinion), and hence given a level of gastric contents consistent with the meal in question, there's no reason to believe any significant slippage occurred.

I believe the independent court expert more than hearsay that an unknown FRCPath claimed that, even without ligatures, complete slippage is "well-nigh impossible".

Keep in mind, however, that Ronchi's speculation about slippage was based on the mistaken assumption that ligatures had not been applied. So there may not be as much contradiction here as it appears (especially since it isn't clear to me that the FRCPath's opinion necessarily pertained to the non-ligature case, depending on how standard ligatures are).

How much slippage do you think may have occurred?

Here is another source characterizing any lag time over 150 minutes as "extremely delayed". By comparison, "normal" is 50-100 min and "delayed" is 100-150. For half-emptying time, over 200 minutes is "extremely delayed".

This seems to be for small easily-digested test meals, as far as I can tell. No hospital is going to serve a patient a pizza to determine how well their diabetes is under control. ;-)

If you can find a reference to support the idea that a lag time in excess of four or even three hours would not be highly unusual for a small-to-moderate pizza meal eaten by a healthy adult human, I will update appropriately. Conversely, if you can't (and I haven't been able to so far), I don't see how you can derive the level of uncertainty you need to make the Massei theory plausible in the face of all the other data. Even acknowledging the wide variation in lag times depending on the type of meal used in the studies, they are all on the short end; there is no indication, anywhere (that I have come across), of the kind of extremes that we would need at the long end. Not so much as a passing remark. Isn't this a bit suspicious?

I see that large, fried, and/or starchy meals have much larger T(50) times than other meals, and I don't have any lag times for those. Since T(50) times are frequently unexpectedly large, and since lag times correlate in some large but unknown way with T(50) times, I infer a significant probability that lag times are frequently unexpectedly large as well.

I agree, of course; I just don't agree that "frequently unexpectedly large" translates to anything like "regularly in excess of four hours".

Let me float one scenario. I'd presume that starch increases the T(50) time so much because it can take a long time for large amounts of starch to convert to sugar in the stomach. Does almost the entire portion of starch need to get converted to sugar before any starch can go to the duodenum? If so, then the lag time for a large starch meal would be close to the T(50) time...

If we take a leap of faith and use the 317 minutes T(50) for 700 kcal fried pasta but don't believe the starch needs to convert first, then I'd revert to a 1/4 guess for lag time on the basis the ratio decreases as T(50) grows, resulting in 80 +/- 6 minutes, so that model fails for me as well, dang it.

I'll ask Yvain (LW's medical student extraordinaire) if he knows anything about the mechanisms involved and the plausibility of your proposed scenario. At the very least I expect he'll know someone who knows something. (Update: Yvain says he doesn't know any more than we do.)

I'm confused about the notation T(50): does this refer to half-time, or total emptying time? Because the 317 minutes for fried pasta was total emptying time.

I'm open to other suggestions. Unfortunately the gated 81-minute median study isn't currently helpful in this regard, because I have to ask myself, why was this study 81 minutes, instead of the others that were 25 or 10 or 40 minutes? But if we can find out whatever X factor increased it to 81 minutes, then might be able to judge how much of that X factor we had in our case, and whether we had more or less X factor than in the study.

I'll try to find this out from people who have read the study.

Anyway, overall I'll guess 30% for 21:00-21:30, 20% for 21:30-22:00, 25% for 22:00-23:00, 7% for 23:00-23:30.

Not that it's surprising, given the roughness of all these estimates, but there seems to be an inconsistency with your other probabilities: if you believe p = 95% for guilt overall, p = 80% conditioned on before 22:00, and p = 57% conditioned on before 21:30, then you have 40 percentage points' worth of guilt to distribute among the 50% before 22:00, and only 17 of those are taken from the 30% before 21:30; leaving you with 23% to be distributed among the 20% between 21:30 and 22:00, which is impossible.

(EDIT: And also, 55% worth of guilt-probability to be distributed among the 50% post-22:00 probability, likewise impossible.)

Now let's factor in expert testimony. Since none of our models are working very well, and since the literature that I've seen doesn't converge on a single simple model anyway, I think in the end I'll go with the independent expert testimony.

Which testimony? Ronchi didn't give any testimony about lag time, as far as I know.

They also get to factor in the body temperature, which I've been ignoring.

Unfortunately, one of the many scandals of this case is that the body temperature measurement was delayed until 12 hours after the discovery of the body, limiting its usefulness.

My interpretation of Ronchi doesn't depend on the defense appeal; it's simply the common-sense default meaning of what he said, as reported in Massei-Cristiani...

I don't agree with your common-sense default meaning in the English translation, then, although of course the original Italian may be more enlightening.

The term used (in Massei-Cristiani) is svuotamento gastrico, which is a pretty literal counterpart of "gastric emptying". If someone says "X takes Y hours to empty", I view it as the default assumption that they are talking about the time it takes to empty completely (not to start emptying or empty halfway). Do you have a different view?

...and confirmed by general information about average gastric emptying times.

That reasoning seems circular to me: the question of what the times are in this case, is exactly what I'm trying to determine here.

Ronchi is reported by Massei and Cristiani as having said that "gastric emptying" can sometimes take 6-7 hours; we want to know whether he meant total emptying, or just half-emptying (or something else). So I searched and found a reference stating that total emptying (with the meaning unambiguous, explicitly contrasted to other parameters) typically takes 4-5 hours, in contrast to half-emptying, which typically takes 2.5-3 hours. For me this increases the (already high) probability that total emptying, and not half-emptying, was what was meant.

I judge court findings to be much more reliable than claims of the defense attorneys

Here are some factors that you may not be adequately considering:

1. Argument screens off authority. Whatever the appropriate default assumptions about reliability may be, both the court and the defense have explained their arguments in detail (in lengthy documents that are publicly avaliable), while being in a position to know what each other's arguments are. There is unlikely to be much important information not contained in these documents. In particular, if the prosecution case is correct and the defense case isn't, we should expect to be able to determine this from the court's opinion and the appeal documents (without requiring further "rebuttal" from the court), since the court will have heard the defense case already, and should be anticipating the strongest possible defense reply; we should in other words expect to perceive the defense appeals as substantively weak, while perhaps demonstrating legal cleverness. If instead we perceive them as strong, we should regard that as significant evidence in favor of the defense.

2. The argument about "neutrality" could equally well be applied to the prosecution side as much as the court, since the prosecutors (who in Italy supervise the police investigation) are ethically obligated to conduct the investigation in a neutral manner, and to charge only suspects whose culpability is rationally indicated by the evidence. Hence there shouldn't be much difference in reliability between the prosecution and a court which has decided in favor of guilt; yet I presume you wouldn't regard the prosecution as sufficiently reliable to not bother listening to defense arguments. (See also 4. below: in continental European "inquisitorial" systems, judges and prosecutors are traditionally regarded as belonging to the same job category.)

3. People change their minds less often than they think; and the judges are particularly unlikely to revise their opinion during the 90-day interval between the time the verdict is announced and the motivation document is submitted. (They presumably aren't even legally allowed to change the verdict, since the rest of the jury is no longer participating.) Hence the latter is guaranteed to be the work of people trying to defend a decision they've already publicly committed to.

4. Cultural assumptions about how the legal process works (and what is considered acceptable behavior for attorneys and judges) do not necessarily transfer to a foreign country. For example, it's not clear that the Italian system has the concept of a "mistrial" in the sense that you refer to. What it does have is second-level ("appeal") courts which regularly modify or overturn first-level rulings, for various reasons (at a much higher rate than in the American system). My suspicion is that the closest analogue of "a mistrial being declared" is simply the appeal court reversing the first-level verdict -- which is precisely what Knox and Sollecito are currently seeking to have done. So the inference you're wanting to make about the first court's level of even-handedness may not be valid, due to a possible difference in the error-correction mechanism. (Relatedly, a first-level finding of guilt in Italy does not have the same significance as "conviction" in the U.S., but is rather somewhere between indictment and conviction.)

5. Ignoring my own advice above, I could invoke the American assumption that defense attorneys are ethically (and/or legally) obligated not to mislead the court, particularly in official written filings.

Empirically, defense attorneys always side with the defense; I can't think of a case where the defense attorney summed up to the jury with "You know what? I'm convinced, my client is guilty after all."

I expect defense attorneys to make different kinds of arguments when they think their client is guilty than when they think their client is innocent. Don't you?

Though I shouldn't weigh it too highly, a subjective sense that even if the defendants are innocent, this particular defense team has lost credibility, for example with Pasquali's testimony.

We may want to discuss that at some point, then, because I find Pasquali's testimony very compelling (particularly the experiments he conducted).

Of course, I have an analogous sense with regard to Massei and Cristiani, who lose credibility in my view by assigning credence to people like Curatolo and Quintavalle (and indeed by not paying attention to Pasquali and his results).