rolf_nelson

Karma: 27

rolf_nelson 23 Feb 2013 19:27 UTC
0 points
on: Experiment: Knox case debate with Rolf Nelson
I finally got around to reading through the appeal motivation and the relevant parts of the Conti-Vecchiotti report, and I find nothing to lend credence to the innocence hypothesis. If anything, I would judge the timing of the double-DNA knife testing seems to move the ‘laboratory contamination’ hypothesis from very very very unlikely to very very very very unlikely.

So in the end, I have to apologize to kompinisto as I have inadvertently wasted both of our time in suggesting this debate; our failure to reach a consensus on an accurate truth in this issue is a mild lose-lose.

rolf_nelson 10 Sep 2011 1:06 UTC
1 point
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson

As it happens, in the present case, the only material found in the small intestine was at the very end, near the ileocecal valve.

I agree, but I don’t know whether other material would have been found if present. Is searching the entire small intestine feasible, and if so was such a search performed? Would food in the middle of the small intenstine after death have continued to digest?

Prof. Umani Ronchi, at the hearings of 04-19-2008 and 9-19-2009, never discussed “an imperfect application of the ligatures” at the duodenal level, but rather the [supposed] failure to ligature the duodenum on the part of Dr. Lalli during the autopsy (p. 23, hearing of 9-19-2009: “given that the ligatures were not applied, given that without the ligatures this sliding toward the bottom can happen, and that an amount of food that had maybe already passed into the duodenum, could even have, due to gravity, could have gotten all the way to the ileocecal valve.”)

Right, like the court, I understand that Umani Ronchi was incorrect about the ligatures.

The missing ligature, in fact, allowed Prof. Ronchi to conclude that the gastric contents, at least in part, had slipped in the duodenum or that the contexts, having already passed into the duodenum, could have slid due to gravity all the way to the ileocecal valve after traveling 5 meters of small intestine. From this, the Court deduced that the autopsy finding regarding the objective fact that the duodenum was empty was unreliable.

From Massei, it appears that Umani Ronchi didn’t “conclude that the gastric contents had slipped”; he concluded instead that either the gastric contents might have slipped, or the stomach had not emptied: “He [Umani Ronchi] could not, however, say whether it [the stomach] had partially emptied” (147) and still gave an overall TOD of 20:50 and 4:50. Thus, logically Umani Ronchi didn’t find a TOD of 20:50+ as proving that the stomach has partially emptied. Of course, you can speculate that Umani Ronchi might have been simply being illogical, but to the degree we trust him as the court-appointed expert, we should weigh his conclusion appropriately.

That said, he obviously did make a mistake for some unexplored reason in concluding the ligatures were absent; and I agree we should lower the estimation of his overall reliability, remembering of course to similarly lower the reliability of experts who you do like every time they make a mistake.

Now, if your mistrust of the defense is sufficiently high, perhaps you’re not willing to draw the same inference I have from this passage.

I do trust the defense; I trust them to not unethically stab their client in the back by drawing attention to any inconvenient pro-prosecution facts in their defense appeal document. Pointing out pro-prosecution facts is the prosecution’s and court’s job, not the defense’s, even in inquisitorial systems, and anyway the defense’s checks are signed by the defendant. That said, where the defense appeal document contains a direct quote, then I’d agree that’s pretty reliable.

Are you willing to acknowledge a significant dependence of your opinion on the presence of material in “earlier” parts of the small intestine?

I don’t think it’s a question of significance, it’s more that we’re dealing with a conjunction: that stomach emptying had to have started, that the full small intenstines were searched, and that post-emptying digestion processes would not have emptied the earlier parts of the small intestine. If we can establish that material isn’t present, and that digestion wouldn’t have destroyed the evidence, and that stomach emptying had to have started, then that would establish the TOD you want (even if slippage can’t be ruled out), but so far I can’t agree by more than an order of magnitude that any of those three are true. Given that I didn’t even know until today that digestion processes continue after death, the odds that I’m going to become more confident than that without reliable sources are pretty small.

Apart from this, another thing this passage implies is that Ronchi’s speculation about slippage was confined to the possibility of it having occurred at the autopsy, with the intestines uncoiled, in a situation where ligatures had not been applied (which we know to be contrary to the actual situation).

Yeah, I’ll have to again pass on giving weight to a defense appeal document’s spin about what must have been going through the mind of a court expert for them to be able to say such incriminating-sounding things against their client. It’s the defense’s job to interpret all testimony in as positive a light for the client as possible.

But we do have data for other situations, and those data are what my prior is based on. What’s your prior, and why is it better?

My prior is much vaguer, and reflects my believing I don’t have enough knowledge to have a more narrow prior. I don’t have an answer to “why it’s better”, it’s the one my brain came up with, and I don’t have anyone else’s brain handy to think with.

Incidentally, I was able to obtain a copy of the Hellmig et al. paper. Here is the study protocol:

For preparation of the solid test meal, 100 mg of 13C-octanoate was dissolved in an egg. After addition of 50 mL of low-fat milk, the egg was scrambled and fried in a pan. The solid test meal was completed by a piece of brown bread (50 g) and butter (20 g).

That’s a bit unexpected to me, that looks less than 300 Calories! I would have expected large lag times to be associated with a large meal.

After an overnight fast a breath sample was collected to define the basic value before the test meal was administered within 10 min. Breath samples were collected every 15 min for the first 120 min, then at 150, 180, 210 and 240 min after ingestion. Patients were again instructed not to drink, eat, smoke or exercise during the test.

Right, so that tends to confirm that there’s no exercise or drinking, and they fast before the test. We already agreed drinking probably doesn’t have a huge effect, but Meredith didn’t fast and she might have gotten some physical activity in.

The range in the Hellmig et al. study was 29-203 minutes.

I assume you mean lag time?

Beyond differences in the test meal, the shorter times may be accounted for by a phenomenon known as “interdigestive duodenogastric reflux”, which is a “sieving” process involving the shuffling of food back and forth between the stomach and duodenum, that takes place during the lag phase. This phenomenon was not known when some of the earlier studies were published, and so there is a significant possibility that those studies detected duodenal activity that the investigators mistook for the end of the lag phase. (HT to LondonJohn at JREF for this observation.)

Doesn’t that paradoxically decrease your confidence that you know everything that’s going on with digestive processes and can accurately predict TOD?

-- or even if the studies consistently had extreme data points in the range of 300, regardless of their averages—then the Massei-Cristiani theory would be in significantly better shape.

I agree, the TOD theory would be in even better shape if that were the case.

Standard formulas predict 57-60 kg from Meredith’s age, sex and height.

Different “standard” formulas give different results. Also, the standard deviation of weight based on a/s/h has to be considered. I’ll go with the estimate of the expert who actually saw the body and what her build was, and consider it unlikely that Lalli’s first estimate of weight would be off by more than 15 pounds.

rolf_nelson 10 Sep 2011 0:55 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson

So to be absolutely clear, then: taking into account all the information you are aware of, and adjusting for systematic uncertainty, what are your current probabilities of guilt conditioned on death having occurred during the following intervals?:

.95 for all the scenarios mentioned, maybe a little less for the 21:00-21:30.

On the contrary, see here for example.

Good find, and it slightly bolsters the case against Knox: contents don’t pass into the duodenum after death (which I expected), and other unspecified parts of digestion continue after death (which I would have bet against). This information slightly increases the probability that the duodenum can empty after death through digestion processes, in which case the duodenum would remain empty no matter what state the stomach is in.

The literature often emphasizes that gastric contents are of limited reliability in determining time of death. However, there is a specific circumstance in this case that make it atypically informative: the fact that the duodenum was completely empty, which by default implies that the entire meal was still in the stomach (modulo slippage issue discussed below)

(snip)

In the situation at hand, we have 100% of the last meal in the stomach, as revealed by the empty duodenum.

But that’s exactly one of the points I’m not confident of. Also even if there is 100% of the meal in the stomach, I still don’t agree that analysis can exclude 21:00-21:30 but include 21:30-22:00 to any large degree of confidence. A model should be robust in its conclusions for us to have confidence in the conclusions; if small, reasonable changes to the model change the conclusions, then we have to limit our level of confidence and weight it with or against corraborating information from elsewhere.

rolf_nelson 12 Aug 2011 3:42 UTC
4 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
Thanks for another well-researched reply, let’s have a couple more posts on this, and then turn to the DNA for a bit.

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.

The problem is that systemic uncertainty works both ways. If I see there being, say, 10 times as much evidence for guilt then there is for innocence, I’ll still cap the probability of guilt at .95 anyway, due to systemic uncertainty. If I change my mind and decided there was 5, or 20, times as much evidence for guilt, the basic conclusion won’t change.

To look at it another way, I expect that if we examine ten pieces of evidence as to whether the Earth is flat, on average one of the pieces can easily point to the Earth being flat at a 10:1 ratio by chance. You would need to either have a much stronger piece of evidence among the first ten pieces, or else have more than one of the pieces point to the Earth being flat, to show that something is true given the first ten pieces of evidence.

How much slippage do you think may have occurred?

There’s a ton of factors here, I’ll guess that if there’s slippage, it’s about 50% that the entire contents would slip; probably our digestion process is evolutionary designed to make the food pass through easily by that stage. Probably another 50% that a suspiciously large amount of food would be found in the small intenstine. I could narrow it down more if I knew how large the volume of the first part of the small intestine to the first bend is, whether the first part of the small intestine was searched, whether the rest of the small intestine was searched, how fast food is evacuated from the duodenum, whether food keeps getting evacuated from the duodenum after the stress of being threatened with a knife occurs, whether peristalsis continues to push food through the small intestine after stress, whether diffusion of food through the small intestine walls continues after stress or even death, and how fast peristalsis and diffusion work.

I’ll add that a search for ‘”empty duodenum” forensics’ suggests to me that, as far as I can tell, almost nobody except for Amanda Knox’s defense has ever cared whether a duodenum was empty or not. That probably puts an upper-bound on how useful this evidence is; if it were reliable, I would expect it come up more often in online appeals-courts decisions, and in trial reporting. I also can’t find any literature on this, which is odd if it’s a useful way to narrow down time of death. So based on the “evidence of absence”, let me propose the following hypothesis:

Vacant Duodenum Hypothesis: “An empty duodenum is not, by itself, definitive proof for or against any time-of-death. The main reason to search the duodenum is in hopes of actually finding food there; no matter what the time-of-death scenario, there is always at least a ¹⁄₁₀ chance that the duodenum will be empty when examined.”

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.

So far, we don’t have data either way about lag times (not median) for a pizza, nor how a follow-up snack affects it. BTW do you know something I don’t about the size of the pizza?

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.

So far there’s no indication of >180 or even >120 either, right? Is the main point of disagreement that if you see the numbers:

10, 25, 23, 82, 48

and if a genie tells you the next number is above 150, then you’re saying “it’s almost certainly between 150 and 180!” and I’m saying “these numbers are all over the place, it’s more likely to be near 150 than near 300, but there’s a signficant chance it’s a lot bigger than 150.”

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.

My bad, I misread the abstract. Doesn’t significantly change the scenarios though.

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.

So are you claiming that Meredith’s weight before losing blood was 57kg, or just pointing out that a weight of 50-55 kg only shifts us by about 10:1?

rolf_nelson 4 Aug 2011 8:24 UTC
3 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson

I would sooner hypothesize that Meredith’s last meal actually took place closer to 19:00 than 18:00, given the vagueness of the testimony on the matter. This puts her within 2 standard deviations, perhaps even 1.5.

If we model the meal start-time as a normal distribution, then it’ll be simple to add it to the model and combine it with the other sources of uncertainty, since two normal distributions sum to a new normal distribution with a variance equal to the sum of the variances. Though now that I mention it, a lot of the other bits of uncertainty might be somewhat log-normal because they might multiply the time rather than add to it.

But, granting a non-normal distribution, it’s really difficult for me to see how it could significantly work against Raffaele, given where the 25th and 75th percentiles are. Probability mass would have to be transferred to the extreme right tail from somewhere else; how do you propose to do this in a way that isn’t specifically tailored to yield the desired bottom line?

To give two contrasting examples, something like female heights (http://www.johndcook.com/blog/2008/07/20/why-heights-are-not-normally-distributed/) would work against Raffaele because outliers are few and extreme, while a gently bimodal distribution like human heights (http://www.johndcook.com/mixture_distribution.html) might work in Raffaele’s favor because of a concentration in the center.

My questions, in that case, are:

(1a) What does your gastric lag-time model look like, such that you don’t get significantly more surprised by going out to 22:00 than 21:00?

Good question. Let me look here at some more papers. One source of uncertainty is that I don’t know if we care in this case about 2% or 10% or something else.

The first completely-ungated study I found in Google shows 10 minutes for a 2% decrease (http://jnm.snmjournals.org/content/32/7/1349.full.pdf).

Second study shows 25 minutes for a 10% decrease (http://jnm.snmjournals.org/content/32/7/1349.full.pdf).

Third study shows 23 minutes using multiple methods (http://jnm.snmjournals.org/content/37/10/1639.full.pdf).

The gated study you cited shows 81.5 minutes using unknown-to-me methods, perhaps the meal was larger or different from the other studies.

So I guess I would reluctantly discard the concept of attempting solely normal distributions, since this already is looking too right-tailed. So this is too complex for me to easily model, I can only say that intuitively even if we use 19:00, then if a genie tells me it’s at least 120 minutes, then I wouldn’t be much more surprised by 150 minutes or 180 minutes. The first three studies above looked like they were behaving at 10, 25, and 23, and then your example jumped to more than 3x the highest figure so far. So jumping again to even 3x of your number wouldn’t be more than a one-in-ten surprise, especially given the numerous factors I’ve itemized.

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

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”.

And note this: “The lag phases after 4 and 10% (v/v) ethanol, beer, and red wine were not significantly different from that of water… the inhibitory effect of ethanol and alcoholic beverages is mainly induced by a prolongation of the gastric emptying phase (without affecting the lag phase)...”

That’s a good point, so I hereby drop the alcohol point altogether for the non-slippage case.

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. ;-)

Just how large do you think the standard deviation is? If you believe in the Massei theory, you have to come up with a lag time of four hours at minimum. I can’t find any evidence that that is anywhere close to being within normal human parameters. Can you?

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.

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.

On the other hand, if you want to believe the time of death was earlier, you run into other problems...

Sounds like a whole other discussion.

So what is your probability distribution for time of death?

Based on just stomach evidence, and ignoring expert testimony, I’d have to say it most likely happened around 19:00. So that’s not very useful.

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.

Factoring in that it wasn’t before 21:00, but still ignoring expert testimony, I’ll have to take an “inside view” and try to generate hypotheses as to why it took so long. I’ll currently guess that for to get us out to 21:00, either the starch needs to convert to sugar first (40%), or else there was slippage after the body was discovered (5%), or that there was slippage when the body was moved by one or more perps before being discovered by the police and “ligatured” (55%). 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. 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.

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. The experts have access to gated medical journals and even some kind of summary chart of different times under different situations in the literature, as well as forensic experience, which I don’t have. They also get to factor in the body temperature, which I’ve been ignoring.

rolf_nelson 4 Aug 2011 8:23 UTC
−1 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
Surely you meant the defense appeal document here?

Yes, typo.

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.

...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.

But even if it did, the appeal documents constitute the defense’s reply to the Massei-Cristiani report, and so I don’t see why they are any less useful than the latter. They rely on the same records that Massei and Cristiani do.

I judge court findings to be much more reliable than claims of the defense attorneys because:
1. The defense attorneys are chosen and paid for by the defense
2. Defense attorneys are ethically obligated to assist the defense, while the court is ethically obligated to neutrally examine the case
3. Court bias can result in a mistrial being declared; defense attorney bias (toward the defense), in contrast, is considered acceptable or even mandatory
4. If the defense is found to wield misinformation to successfully free a guilty client, they’ll gain prestige and be more likely to be hired for more money in the future. If a court wields misinformation, on the other hand, it will be more likely to have negative rather than positive consequences for the court
5. 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.”
6. 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.

rolf_nelson 2 Aug 2011 7:56 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
Just replied here: http://lesswrong.com/r/discussion/lw/6k7/experiment_knox_case_debate_with_rolf_nelson/4liq

rolf_nelson 2 Aug 2011 7:55 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
Great, give me a top-level post when the knife translation is finished, or when you think it’s in a good enough state to back up your claims in the dna discussion.

rolf_nelson 2 Aug 2011 7:46 UTC
0 points
on: Experiment: Knox case debate with Rolf Nelson
Reply to: http://lesswrong.com/r/discussion/lw/6k7/experiment_knox_case_debate_with_rolf_nelson/4jmb

Didn’t realize you updated, looks like we can’t go more than 8 or 9 deep before the RSS feed stops notifying about thread changes.

In terms of narrowing down what Umani Ronchi was actually saying, saying that the prosecution claims something in its appeals document isn’t useful evidence. If there’s a specific quote of Umani Ronchi that the prosecution makes, that might be useful, as long as the quote is clear enough that we can deduce it isn’t being quoted out-of-context.

It sounds like you might disagree with… another of Raffaele’s consultants, Introna, who placed the start of attack between 21:30 and 22:30.

Not according to p. 180 of Massei-Cristiani, where Introna is described as placing it between 21:00 and 21:30.

That’s a good find, and you may be right. I was going by this, but maybe it’s a mistranslation or a misunderstanding:

“[Introna] also observed that the beginning of the attack must have been a moment of tremendous stress for Kercher and may have arrested the digestive process. One could and should obtain a precise indication from this, in the sense that the stress to which the victim was subjected must have started between 21:30 pm and 22:30 pm.” (p. 130)

Raffaele’s appeal document argues for 21:30 − 22:00… I think 21:00-21:30 is most likely, but 21:30-22:00 is not ruled out nearly as strongly in my model as anything after 22:00 is.. the computer evidence provides an alibi up to nearly 21:30.

Again, post-trial prosecution claims that haven’t even gone under cross-examination aren’t useful evidence. If you want an alibi to 21:30, you’ll have to provide better support, which will unfortunately be difficult even if Raffaele is innocent, since computers open files in the background all the time, and so not just the timing but the nature of the file opened will have to be examined.

(although their is no evidence of significant alcohol or drug consumption)

There’s evidence of about one glass (p. 152), so around 10 ml. A dose of 60 ml appears to almost double emptying time in one study (http://alcalc.oxfordjournals.org/content/40/3/187.full.pdf+html), so I’d expect a change of about 10-20% in Meredith’s case. So probably not terribly significant on its own. I know there was no trace of drugs found in her body, and marijuana appears to have a long half-life, so I agree there’s no drug consumption even though Meredith had easy access to marijuana.

Although the paper I cited explicitly stated that the results did not fit to a normal distribution, the percentiles given are fairly well approximated by assuming a mean of 81.5 and a standard deviation of 30. Under these assumptions, the lag time required for the Massei guilt scenario would be at least a five- or six-sigma event.

So to get to even 21:00 from 18:00, you need to go out by more than 90 minutes. Three standard deviations is >.99 probability, so this model doesn’t seem to be accurate, at least not with a normal distribution. So do you want to propose a new model with a greater standard deviation, or propose that it’s not a normal distribution? If the latter, I would expect the deviation from normality to be equally likely to work against Raffaele, as it is to work in his favor.

In the other direction, a 30-minute variance is already too large to provide much evidence in favor of Raffaele’s innocence, especially without further evidence of a 21:30 alibi.

Now I know you doubt that the conditions of the study hold here, but don’t you find this at least a little bit confusing?

I agree that the stomach findings are a mild surprise if we’re talking about 23:00+ like in the Massei narrative, but the first problem is that my surprise is only mild since there are so many factors that affect it, and the second problem is that once I’m slightly surprised by going out to 21:00, I don’t get much more surprised by going out to 21:30 or even 22:00, and so don’t see Raffaele as having an alibi.

As an example, does it surprise you that the abstract of one (unfortunately gated) study (http://www.ncbi.nlm.nih.gov/pubmed/7956593) of fried food gives 317 minutes for total gastric emptying, even though it probably, like other experiments, is unlike Meredith’s case in that it probably involves pre-experiment fasting and no post-meal snack.

But even in the worst-case scenario here, the amount of slippage can’t have been very large, because the stomach contents could easily have constituted the entire meal on their own.

I don’t follow the logic here; isn’t the more important question whether the stomach contents could have equally well constituted just half or ²⁄₃ the meal? Or do you just mean that it’s unlikely more than half of the meal passed through?

To illustrate further, if as much as half of Meredith’s meal had passed into the duodenum, and we assume a normally-distributed half-time with median 127 minutes and standard deviation 40 (the median taken from the study), the finding would still have put her well within the slowest 1% under the prosecution theory (while only in the slowest 10% to 50% under the defense theory).

Yes, your model (if correct) of a non-ligature situation harms the court’s theory about the attack taking place somewhere in the 23:00-23:30 interval, though it fails again to save Raffaele’s computer alibi. Plus, I think you’re underestimating the quantitative level of uncertainty if we don’t know how much she ate, exactly what all she ate, exactly when she started eating, what effect having a post-meal snack has, what effect not fasting has, amount of alcohol consumed, and what effect walking home after eating had, all of which should contribute to a large standard deviation.
What links here?
- rolf_nelson's comment on Experiment: Knox case debate with Rolf Nelson by komponisto (2 Aug 2011 7:56 UTC; 0 points)

rolf_nelson 22 Jul 2011 7:18 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
Let’s talk about the dna some more once you guys have finished translating the relevant parts of the independent report, then, if your argument hinges on details of the independent report rather than just the conclusions.

We’re talking here not about the time it takes for the stomach to emtpy completely, but rather the time it takes for ingesta to begin passing into the duodenum (“T_lag”).

Sounds good. In your case, for one particular meal where the subjects had probably fasted beforehand, the lag is just under ²⁄₃ of the half-time. If you accept Umani Rochi’s half-time of 360-420 minutes, then the lag could be ²⁄₃ of that, or 240+ minutes. Of course, for all I know Umani Rochi could have been referring to the lag time, or the final gastric emptying time, rather than the half-time. Lags could easily be much smaller, or larger, than ²⁄₃ of the half-time in this case.

It sounds like you might disagree with not just with Umani Rochi (a court-appointed expert), and Raffaele’s consultant Vinci, but also with another of Raffaele’s consultants, Introna, who placed the start of attack between 21:30 and 22:30.

Note that stress (such as being attacked) can increase lag time, so we might be talking about the time the attack started rather than the time of death.

In addition to the starchiness of the meal, I would claim that:
1. Alcohol (or drug use) may increase lag time, studies differ as to how significant this is though.
2. Subjects in studies usually fast before the study, which means in the real world I expect lag times to be longer. Meredith also returned home after the meal, which may be more physical activity than the subjects did, though I could be wrong about that.
3. Subjects in studies don’t usually go and eat a snack after the meal, as I believe Meredith did. I would expect this to also increase Meredith’s lag time.
Anyway, what’s your model here: What do you personally estimate the lag to be based solely on digestion (assuming no slippage)? Maybe you can give a mean and a standard deviation, and we can start by modeling it as a normal distribution?

Ronchi claimed that the coroner, Lalli, had failed to seal the duodenum via ligature, as is apparently the standard procedure; this was the basis for his claim that food could have slipped into the small intestine. However, video of the autopsy revealed that Ronchi was wrong, and that Lalli had indeed properly sealed the duodenum. (Sollecito appeal, p. 165)

How much does application of the ligatures reduce the probability of slippage? If ligatures were not applied, how likely do you think complete slippage would be? If they are applied, what are the odds that (1) the slippage occurs before the ligatures are applied, or (2) the slippage occurs anyway after the ligatures are applied, perhaps due to improper application?

rolf_nelson 20 Jul 2011 6:26 UTC
2 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson

So making progress would probably require us to pick a small number of narrowly-defined issues to hash out, one at a time.

Sounds good, like you suggested let’s cover the time of death, and also continue to go deep on the question of lab contamination.

Here’s an important question to assess whether we’ve said anything important yet: has anything I’ve said surprised you?

It hasn’t been predictable, but it hasn’t caused me to shift significantly in favor of innocence or guilt so far. I did learn I was wrong about which knife Amanda reacted strongly to, but that’s within the bounds of how many errors I expected to be making here.

I suspect I could probably get you to agree that it would be extremely unusual for no food to have passed into the duodenum 5 hours after a meal (as required by the prosecution theory), even conditioned on the already unusual fact of none having passed after 150 minutes. However, I can’t predict how far you will lower your probability of guilt as a result.

I haven’t looked into this much. According to Massei, Umani Ronchi, a court-appointed expert, testified that a farinaceous meal takes 6-7 hours for gastric emptying, and additionally that it’s possible some of the food passed into the duodenum but then, after death, slid into the small intestine. Massei also claims that even Vinci agreed with the range of 18:50 − 4:50 for time of death. Did the defence experts take into account the composition of the meal, or testify that sliding of the food after death is unlikely?

I don’t think I would have a problem positing that the expert report constitutes 50:1 evidence in favor of contamination, possibly much more.

The sample in question (Trace B) tested negative for blood, as did every other sample taken from the blade. (Samples from the handle were not tested for blood.) No attempt was made to scientifically determine the actual nature of the alleged biological material.

OK, what are the odds that a small dna trace left by “stabbing + cleaning” would test positive for blood, and what are the odds a small dna contamination to the knife would test positive for blood? (By the way, do you have a specific contamination hypothesis in mind?) In both cases, keep in mind only one “small zone” of the striation was tested for blood, and the rest of the striation was consumed in DNA analysis.

When “quantification” (test to determine whether there was enough DNA to be analyzed) was performed, Traces B and C both yielded a result of “too low”. Stefanoni reported Trace B as a positive result, and Trace C as a negative result, without any justification. There is no documentation in the lab data to support her statement in court that the Trace B sample was in the range of several hundred picograms. Stefanoni also claimed to have executed steps in the quantification procedure that are not documented.

Sounds like she didn’t document everything; how much are you shifting based on this? Part of the problem is I don’t know how much the average technician documents, so I don’t know how usual or unusual this is. If nobody documents everything, but we still see a .02/homicide contamination rate, then Stefanoni’s not documenting doesn’t change anything.

The “amplification” (chemical copying of the sample in order to produce a large enough amount for analysis) was performed only once, despite the fact (admitted by Stefanoni) that it should be repeated in order to be considered reliable.

Can I get a source for Stefanoni’s admission? Is this from the report?

Stefanoni did not perform negative controls, which could have indicated the presence of contamination.

Is this also from the report? Have you translated this part yet?

The sample was analyzed in the same laboratory at the same time as numerous samples containing Meredith Kercher’s DNA.

I gave a .05 chance that, if there was a cross-contamination, it would have been of Meredith’s DNA. Are you giving a different probability?

rolf_nelson 14 Jul 2011 7:11 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
While it remains interesting, we don’t seem to be getting any traction toward significantly changing each other’s mind through this one-on-one debate, should we just cut our losses and end it? I’m open to other suggestions on how to proceed. You haven’t yet presented arguments toward innocence, but if we just follow the same pattern we have been so far we’re probably not going to get anywhere with those either. Probably the only thing we can agree on is that at least one of us is biased on this case. ;-)

If you want to proceed, I’ll ask you whether you agree with my “one contamination in fifty homicides” estimate, and what your probability is that the independent report is basically correct, and whether you would agree with me that this puts an upper bound on the contamination probability. I’ll also continue to try to nail down, line-by-line, where we disagree on the facts of the case, and say that I feel you’re giving too little weight to the statements of lab technicians, police officers, and trial judges, especially when those people were there and we weren’t.

If you don’t want to proceed, then I thank you for humoring me as far as you did with this experiment, and I will express my condolences to all innocent people in jail, whether they include Amanda or not, and hope that justice prevails in this case.

rolf_nelson 12 Jul 2011 4:56 UTC
0 points
in reply to: Wei Dai’s comment on: Experiment: Knox case debate with Rolf Nelson
I don’t currently have a formal calculation. If you’re curious, my current P(guilty) is .95; I’m reluctant to go higher due to the structural uncertainty inherent in any “trial by media”. One way to summarize my current position is that I believe most of the court’s findings (as in the Massei report) seem basically correct, and that correcting for demographics doesn’t look to be nearly enough to swing the needle from guilt to innocence.

rolf_nelson 12 Jul 2011 4:38 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson

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

rolf_nelson 12 Jul 2011 4:18 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
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.

rolf_nelson 12 Jul 2011 4:03 UTC
0 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson

My guess is it’s probably figured by assuming there are ~500 objects being examined by the lab.

Correct, I’m guessing a mean of roughly 500 examinations per homicide investigation.

...if there is a single contamination, there are likely to be others as well (reported or not).

Agree.

rolf_nelson 9 Jul 2011 20:23 UTC
2 points
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
Thanks k, today I’ll give my thoughts on the knife. I’m sure there are some mistakes in my analysis below, but let’s see if we can start to pinpoint areas of disagreement. Let “ddk.lc” be the specific hypothesis that the double-dna knife was accidentally contaminated in the laboratory, and “a.g” be the hypothesis that Amanda is guilty.

I want to estimate the base rate of lab cross-contamination in the late 2000′s. Two observations:
1. Looks like Washington State only admitted to one case of laboratory cross-contamination in homicide cases from around 2001-2003, based on SPI. Maybe there were 2 to 5 that weren’t noticed or otherwise were unreported. Washington State has about 200 homicides/year, I’d guess about ¹⁄₃ go to state labs?
2. Cases of mistaken “cold matches” that are investigated by the police but turn out to be cross-contamination seem to be extremely rare.
Contamination rates have probably declined slightly since 2001-2004, (widespread DNA forensics is relatively new), so I’m guessing a base-rate of about one accidental cross-contamination per 50 homicides.

(Can that base rate be applied to this case? I could lower it a little based on the first independent report [EDIT: Sorry, I mean the trial judges’ sentencing report] affirming the results, on it being a high-profile case, on the defense being allowed to participate in the testing but declining to fully participate, on no “smoking gun” piece of sloppiness found, and on the defense not stressing any history of past contamination. I could raise it a little based on the second independent report criticizing the lab for not following “international protocols” (though I wouldn’t particularly expect them to), and on the low-count DNA. Not having much data here, I’ll stick with the base rate as my “wild-ass guess”.)

Here’s some more WAGs. If there’s a single lab contamination, the odds that it contaminates a likely murder weapon at the cottage is about .002. The odds that the DNA spread is Meredith’s, rather than one of the many people associated with this case or with other cases the lab is processing in parallel, is about .05.

So I assess P(lc) as .02, and P(ddk.lc | lc) as .0001, which gives P(ddk.lc) as .00002, assuming complete innocence.

In contrast, I estimate P(ddk | a.g) is about .05. So if we exclude the large “systemic uncertainty” of my analysis, the DNA evidence on the double-dna knife alone would make me shift by a factor of 2500 to 1 in favor of a.g rather than ddk.lc.

Let me touch on the circumstantial evidence around the knife, with the caveat that there’s even more systemic uncertainty than in my DNA analysis.
1. The knife was on top of the other knives, and matched one of the murder weapons: meh, shift by a factor of 2 to 1 in favor of a.g over ddk.lc.
2. The same knife was bleached, and the other knives weren’t: Shift by a factor of 5 to 1.
3. Raffaele, at one point, claimed that Meredith visited his cottage and pricked herself on the knife: Shift by a factor of 100.
4. Amanda’s reaction to the knife: Shift by 10.
5. Where Amanda’s DNA was found on the handle suggests someone stabbing rather than cooking with it: meh, shift by 2.
6. Amanda wrote in her diary speculating whether Raffaele may have framed her by pressing the knife in her hand while she slept: Shift by 10, this is not something you’d write if you knew the knife isn’t a murder weapon.
So for the non-DNA evidence around the knife I give a slightly larger shift (200000 to 1), but paradoxically I assign it less importance because there’s more systemic uncertainty and more guess-work on my part, compared with the DNA evidence.

rolf_nelson 9 Jul 2011 19:26 UTC
1 point
in reply to: komponisto’s comment on: Experiment: Knox case debate with Rolf Nelson
I tentatively disagree on the interpretation of the experts’ report, ‘reliability’ means a different thing for court DNA procedure vs. Bayesian analysis. I doubt they would say, “this kind of thing is 99% likely to point to the correct suspect, so it is mostly reliable by our standards”.

rolf_nelson 8 Jul 2011 2:04 UTC
2 points
in reply to: komponisto’s comment on: Making an Amanda Knox prediction market

That’s a problem that would presumably exist to some extent on any public forum. I’m not too bothered by it myself; my feeling is that in such a situation one is not necessarily obliged to reply to all comments individually.

We could access-control the main section of a Google Group or a mini-blog, creating a separate area for comments if we like. That would also be convenient because I can easily notice if you’ve posted when I check Google Reader.

Here’s my suggestion: why don’t we try it here first, and see how it works? I’d be interested to see if this kind of thing can work on LW.

That is an excellent reason to do it here, then; go ahead and create a new thread.

Interestingly, I agree with you that the knife and bra clasp are the strongest pieces of prosecution evidence (though I would have put them in the reverse order). However, they’ve been pretty severely punctured by Conti and Vecchiotti in their report. You can read the conclusions of that report here.

If their main point is that the evidence doesn’t meet the standard of scientific rigor, then I might not disagree with them on anything factual. Very little evidence, either way, does meet the standard of scientific rigor. Fingerprints never reach the standard of scientific rigor. DNA testing, as practiced, probably rarely if ever meets the standard of scientific rigor. Eyewitness testimony obviously can never come close to meeting the standard of scientific rigor. Heck, most science doesn’t meet the standard of scientific rigor. We still need to evaluate evidence on its full merits.

So, to confirm that our initial analysis here diverges, around how much are you currently shifting based on the test results for the knife and for the bra clasp? For you, did either one shift P(guilt) by a factor of 100? 10? Not at all? It’s a difficult question to answer in a calibrated way, so if you want to skip that one I’ll understand.

You can guess my hypothesis for why the DNA tests came out the way they did. Do you have a specific alternative hypothesis or hypotheses you want me to consider? Is your main claim here that you believe the knife was accidentally contaminated in the laboratory, and the bra strap was accidentally contaminated in Kercher’s room? Or is there a different alternative hypothesis I should consider first?

I assume we’re not going to quash any evidence, since we’re a court of Bayes and not a court of law? That is, I’m proposing that whenever we want to exclude or diminish evidence, we should have a Bayesian reason for why the evidence doesn’t really alter P(guilt). The proposal is partly because it’s the correct Bayesian thing to do, and partly because trying to divine and mimic Italian criminal procedure and admissability rules would add (IMHO unnecessary) additional complexity.

rolf_nelson 6 Jul 2011 3:37 UTC
0 points
in reply to: komponisto’s comment on: Making an Amanda Knox prediction market
That’d be great! What forum should we use, should we start a Google Group? We can do it here if you like, but I’m concerned about getting distracted by other comments; the original threads got too bulky to hold a coherent conversation. It’s up to you.

For my part, I’m happy to walk through the Micheli report or one of the many lists of evidence against Knox and Sollecito on the Internet, but I would pick as my top three pieces of evidence:
1. The double-DNA knife
2. Sollecito’s DNA on Kercher’s bra strap
3. The mixed-DNA blood
If you could puncture that evidence, then from a “sampling” point of view, even though there is a large amount of additional evidence, I would agree that Knox has a large chance of being innocent.