Comment author: rolf_nelson 23 February 2013 07:27:39PM 0 points [-]

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.

Comment author: komponisto 13 August 2011 10:54:14PM *  0 points [-]

[comment split due to length]

Now, to the slippage issue:

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.

As it happens, in the present case, the only material found in the small intestine was at the very end, near the ileocecal valve. At least, that is the implication of the wording of Ronchi's speculation (combined with the absence of any mention by Massei and Cristiani of material nearer to the duodenum):

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.")

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.

(Sollecito appeal, p. 165)

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. However, I'm still interested in the impact it would have on your probability estimates if it were true. Suppose for the sake of argument that there wasn't anything in the small intestine, save a small amount at the ileocecal valve. How would that affect your beliefs? Are you willing to acknowledge a significant dependence of your opinion on the presence of material in "earlier" parts of the small intestine?

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). He wasn't suggesting, in other words, that there may have been slippage due to the body having been moved by the killer(s). And if in fact the only material in the small intestine was at the ileocecal valve, then it is very unlikely indeed that material could have slipped through 5 meters of coiled intestine inside the victim's body, as the slippage hypothesis would in that case require.

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.

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?

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). 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.

\

So far there's no indication of >180 or even >120 either, right?

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

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."

Obviously, it depends crucially on what we know about the process that generated the numbers. Here we're talking about the duration of a physiological process, which is likely to be distributed approximately normally modulo specific pathological conditions. Of those numbers, the most relevant is the 82 (due to the use of a larger test meal with mixed food groups, and its taking place after the phenomenon described below was discovered).

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.)

But furthermore, we also have to reason about the hypothetical sequences of numbers that we didn't see. If the numbers had been

110, 125, 123, 182, 148

to say nothing of

100, 250, 230, 820, 480

-- 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.

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?

I was actually pointing out that an earlier temperature measurement would probably have permitted a narrower confidence interval.

But, since you mention it, 50-55 kg was just Lalli's eyeballed guess; the body was not actually weighed. Standard formulas predict 57-60 kg from Meredith's age, sex and height.

Comment author: rolf_nelson 10 September 2011 01:06:54AM 1 point [-]

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.

Comment author: komponisto 13 August 2011 10:53:32PM *  0 points [-]

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.

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?:

(1) 21:00 - 21:30 (2) 21:30 - 22:00 (3) 22:00 - 23:00 (4) 23:00 - 23:30 (5) after 23:30

(Be sure to check for consistency with your probability distribution for time-of-death and your overall probability of guilt.)

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.

That sounds like a point about priors, rather than systemic uncertainty. What I want to know is the following: if I could show that the time of death was before 21:30, or before 22:00 (etc.), how far would that reduce your current guilt-probability of 95%? (Obviously, if the answer is "negligibly", then there isn't any point in discussing gastric lag time.)

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.

On the contrary, see here for example. (By the way, it's actually Sollecito's defense; the matter is not discussed in Knox's appeal document.)

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). This puts a tighter bound on the time of death than in a more typical situation with some smaller fraction of the meal in the stomach.

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."

I'm not sure how to make sense of this. What matters here is not the emptiness of the duodenum by itself, but rather the conjunction of the empty duodenum with the non-empty stomach. In other words, the phase of digestion -- which is clearly time-dependent, with some phases carrying more information about time than others. See for instance the above-cited textbook, which observes as follows:

  • At autopsy, if 50% of the volume of the last meal is found in the stomach, the last food intake was about 3-4 hours prior to death, with 98% confidence limits not shorter than 1 and not greater than 10 hours.

  • When 90% of the last meal is found in the stomach, the last food intake was probably within the hour prior to death, with 98% confidence limits not more than 3-4 hours.

  • If only 30% of the last meal is found, the last food intake was around 4-5 hours previous to death, with 98% confidence limits not shorter than 1-2 and not longer than 10-11 hours prior to death

In the situation at hand, we have 100% of the last meal in the stomach, as revealed by the empty duodenum. This places us in the second bullet, except with even stronger bounds and higher confidence. (And note, by the way, that 3-4 hours is an upper bound on the 98% confidence interval, not the confidence interval itself. I claim that the 98% confidence interval in this case should actually be more like 2.5 hours.)

[comment split due to length]

Comment author: rolf_nelson 10 September 2011 12:55:06AM 0 points [-]

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.

Comment author: komponisto 05 August 2011 02:28:58PM *  1 point [-]

(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.

Comment author: rolf_nelson 12 August 2011 03:42:14AM 2 points [-]

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?

Comment author: komponisto 03 August 2011 04:22:10PM *  0 points [-]

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.

Surely you meant the defense appeal document here? (I haven't referenced the prosecution appeal, and there wouldn't be much reason to, since it's just a 20-page rant arguing that Amanda and Raffaele are really nasty people and deserve a harsher sentence than the Massei court gave them.)

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

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.

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

There's evidence of about one glass (p. 152), so around 10 ml.

Interestingly, p. 390 says the opposite: that Meredith had not consumed alcohol, according to Lalli. (And indeed it has been suggested by others elsewhere that the alleged small gastric alcohol level could have been due to a fermentation reaction). However, this is unlikely to be an important issue, as you point out.

Of course, this is not the only internal contradiction in the document:

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

[...] "[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)

Indeed, it seems the only way to know for sure which of these passages (if either) is accurate would be to have a transcript of Introna's testimony, which we unfortunately don't have. However, it's pretty clear in any case that Introna would exclude the Massei timeline of post-23:00.

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.

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.

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?

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.

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?

(1b) Why do you believe that model rather than one more similar to mine?

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

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?

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.

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[?]

Only with regard to fried food being the cause; as you'll recall I've already allowed for a total emptying time of 6-7 hours "in some circumstances". Note that this timeline is characterized as "markedly delayed" by the authors. And, once again, the relevant variable for us is lag time, not total emptying time. (If we try to extrapolate, using the fact that 1/2 seems to be an upper bound on the ratio of lag time to total emptying time, with 1/3 being in practice a better estimate, this would yield no more than 158.5 minutes, and probably something more like 105 minutes, in this "markedly delayed" scenario.)

The lag time given in the alcohol study you linked to is 48.1 ± 6.5 minutes (!). (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)...")

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".

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.

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?

In my view, essentially all of the uncertainty arising from the factors you mention is used up simply by postulating a lag time of two hours or more, in contrast to the more typical 50-100 minutes. This view is supported by the sizes of the standard deviations relative to the means in all of the various studies.

On the other hand, if you want to believe the time of death was earlier, you run into other problems (in addition to the improbably extreme lag time for anything after 22:00). From 22:30 onward there was a broken-down car outside the cottage, with a tow truck arriving at around 23:20-23:30. No one associated with this incident (occupants of the car, tow-truck operator, a street witness) reported seeing anyone enter or exit the cottage, or hearing anything coming from inside. (This is of course also a problem for the Massei timeline.) There was activity on Meredith's cell phone at 21:58, 22:00, and 22:13, making it unlikely that death occurred between these times. (Incidentally, it's worth noting the interrupted call home at 20:56, not attempted again afterward, which is extremely consistent with the defense theory of when the attack occurred.) And then, of course, there is the computer activity at 21:10 and (according to the defense) 21:26.

So what is your probability distribution for time of death?

Comment author: rolf_nelson 04 August 2011 08:24:10AM 2 points [-]

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.

Comment author: komponisto 03 August 2011 04:22:10PM *  0 points [-]

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.

Surely you meant the defense appeal document here? (I haven't referenced the prosecution appeal, and there wouldn't be much reason to, since it's just a 20-page rant arguing that Amanda and Raffaele are really nasty people and deserve a harsher sentence than the Massei court gave them.)

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

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.

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

There's evidence of about one glass (p. 152), so around 10 ml.

Interestingly, p. 390 says the opposite: that Meredith had not consumed alcohol, according to Lalli. (And indeed it has been suggested by others elsewhere that the alleged small gastric alcohol level could have been due to a fermentation reaction). However, this is unlikely to be an important issue, as you point out.

Of course, this is not the only internal contradiction in the document:

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

[...] "[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)

Indeed, it seems the only way to know for sure which of these passages (if either) is accurate would be to have a transcript of Introna's testimony, which we unfortunately don't have. However, it's pretty clear in any case that Introna would exclude the Massei timeline of post-23:00.

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.

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.

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?

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.

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?

(1b) Why do you believe that model rather than one more similar to mine?

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

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?

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.

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[?]

Only with regard to fried food being the cause; as you'll recall I've already allowed for a total emptying time of 6-7 hours "in some circumstances". Note that this timeline is characterized as "markedly delayed" by the authors. And, once again, the relevant variable for us is lag time, not total emptying time. (If we try to extrapolate, using the fact that 1/2 seems to be an upper bound on the ratio of lag time to total emptying time, with 1/3 being in practice a better estimate, this would yield no more than 158.5 minutes, and probably something more like 105 minutes, in this "markedly delayed" scenario.)

The lag time given in the alcohol study you linked to is 48.1 ± 6.5 minutes (!). (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)...")

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".

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.

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?

In my view, essentially all of the uncertainty arising from the factors you mention is used up simply by postulating a lag time of two hours or more, in contrast to the more typical 50-100 minutes. This view is supported by the sizes of the standard deviations relative to the means in all of the various studies.

On the other hand, if you want to believe the time of death was earlier, you run into other problems (in addition to the improbably extreme lag time for anything after 22:00). From 22:30 onward there was a broken-down car outside the cottage, with a tow truck arriving at around 23:20-23:30. No one associated with this incident (occupants of the car, tow-truck operator, a street witness) reported seeing anyone enter or exit the cottage, or hearing anything coming from inside. (This is of course also a problem for the Massei timeline.) There was activity on Meredith's cell phone at 21:58, 22:00, and 22:13, making it unlikely that death occurred between these times. (Incidentally, it's worth noting the interrupted call home at 20:56, not attempted again afterward, which is extremely consistent with the defense theory of when the attack occurred.) And then, of course, there is the computer activity at 21:10 and (according to the defense) 21:26.

So what is your probability distribution for time of death?

Comment author: rolf_nelson 04 August 2011 08:23:48AM 0 points [-]

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.

Comment author: komponisto 22 July 2011 03:07:01PM *  0 points [-]

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.

As best I can determine, Ronchi was talking about total emptying time, not half-time (let alone lag time). This is unquestionably what would make the most sense, given not only the term used ("gastric emptying"), but also the averages presented, for example, here:

  • 50% of stomach contents emptied: 2.5 to 3 hours
  • Total emptying of the stomach: 4 to 5 hours

Given this, a total emptying time of 6-7 hours under some cirumstances doesn't seem outside the bounds of possibility. Extrapolating in such a way as to preserve ratios, we could then imagine a half-time of up to 4.5 hours, say. But 2/3 of that would give us 3 hours, or 180 minutes -- not the 4-5 hours we need for the prosecution theory.

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.

Not according to p. 180 of Massei-Cristiani, where Introna is described as placing it between 21:00 and 21:30. Raffaele's appeal document argues for 21:30 - 22:00; this is apparently obtained by averaging the 2-3 hour (from last meal) figure of Lalli and Introna, and the 3-4 hour figure of Ronchi (whose testimony was incorrectly interpreted by Massei and Cristiani, according to the appeal: Raffaele's lawyers cite passages where he appeared to agree that 4 hours is the normal limit). My "disagreement" with Raffaele's lawyers in this context is of little import, for several reasons: (1) I am in perfect agreement with Introna, as reported by Massei; (2) We're talking about confidence intervals anyway; 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; (3) Ronchi, whose estimate figured into their calculation, was talking about total emptying time anyway, not lag time (or even half time).

As for Vinci, he was looking at different criteria for the time of death (not specifically gastric contents), and simply gave a wider range, not an incompatible one. No disagreement here that I am aware of.

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.

Sure; just remember that the computer evidence provides an alibi up to nearly 21:30.

In addition to the starchiness of the meal, I would claim [various ways lag time could be increased beyond study results]

No doubt you've identified some of the ways Meredith's digestive process could have been slowed (although there is no evidence of significant alcohol or drug consumption), in the event that there actually was a lag time of 4-5 hours. The question, however, is how likely such an extraordinary retardation is. According to standard data (see below), it should be a highly unusual event. So how does this information (the fact that a time of death -- or, if you like, attack time -- after 23:00 requires a lag time of over 4 hours) affect your probability of guilt? It seems to me that it should go down noticeably, unless your model was already incorporating both the studies on digestion and the fact that Meredith's duodenum was empty (i.e. you weren't surprised by either datum). (For what it's worth, I think the Massei court erred in this regard by ignoring lag time, and also by using uncertainty as an excuse to smuggle in probability for their preferred conclusion.)

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?

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.

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? To make the Massei narrative reasonable, you would basically have to assume that (1) the 6-7 hours allowed by Ronchi for total emptying of farinaceous meals is typical rather than exceptional; (2) this extrapolates to a typical lag time of 3 hours or more, as in my calculation above; and (3) the variance is large enough to make a 4-5-hour lag time a reasonable exception (in which case we would probably be talking about a total emptying time of 8-9 hours or more). Each of these seems highly doubtful, to say nothing of their conjunction. Regarding (2) in particular, note that the study data suggests that the ratio of lag time to total emptying time is closer to 1/3 than to 1/2 (implying a more concave relationship between elapsed time and percentage of contents emptied; suggesting perhaps that lag time may be short even when total emptying time is long).

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?

I imagine that preventing slippage is at least part of the purpose of the ligatures, and so I assume they reduce the probability significantly. 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. In the unlikely event that the ligatures were improperly applied, we can infer that Meredith may have just passed her lag time, and that a few pieces of food had just started to pass into her duodenum. This is of minimal help to the prosecution, because on their timeline, we should have been long into that stage, and the stomach should not have been nearly as full as it was -- indeed, we should have expected with significant probability that the stomach would be completely empty.

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).

Comment author: rolf_nelson 02 August 2011 07:56:27AM 0 points [-]

Just replied here: http://lesswrong.com/r/discussion/lw/6k7/experiment_knox_case_debate_with_rolf_nelson/4liq

Comment author: komponisto 31 July 2011 02:53:24PM *  0 points [-]

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.

The translation is now nearing completion (the clasp section is finished, and the knife section will be soon). Here, furthermore, are some relevant links:

Comment author: rolf_nelson 02 August 2011 07:55:42AM 0 points [-]

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.

Comment author: rolf_nelson 02 August 2011 07:46:20AM 0 points [-]

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.

Comment author: komponisto 20 July 2011 02:34:24PM *  1 point [-]

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?

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"). (At death, there was 500mL of ingesta in the stomach -- consistent with the meal size -- and nothing in the duodenum.) According to this paper, the median value of T_lag is 81.5 minutes, and the 75th percentile is 102 minutes. (Furthermore, the median time for half the contents to empty ["T_1/2"] is 127 minutes, and the 75th percentile is 168.3 minutes.) The prosecution scenario of death during the 11:00 pm hour would require a T_lag of more than 240 minutes, possibly more than 300. My understanding is that this is basically unheard of, whatever the composition of the meal.

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)

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.

There were four samples on the blade, B,C,E, and G that were tested for blood; the results were all negative. These traces were all presumed to be blood by Stefanoni; it seems reasonable to suppose that if there had been blood on the knife, these would have been the most likely spots in which to have found it.

A positive blood test result would require more than DNA from (white) blood cells -- it would require hemoglobin. So it seems to me that the only way to get a positive blood test result from contamination would be to spill a blood sample on the knife. I estimate the probability of this having happened as being in the range of 0.001.

On the other hand, in the event that the knife had been used for stabbing, and that the victim's DNA remained on the knife, I would estimate a probability northward of 0.9 that at least one of the "presumed blood" traces would have tested positive for blood. (Cf. ChrisHalkides' comment below: "Two experts have publicly stated that the chances of cleaning a bloody knife to the point at which blood is no longer detected but DNA is detected, are small." This agrees with my intuition, and "no more than 0.1" seems a reasonable interpretation of "small".)

Sounds like she didn't document everything;

It's worse than that; what Conti and Vecchiotti describe is suggestive of deliberate misrepresentation if not outright fabrication of results. The "several hundred picograms" quantification result for Trace B appears to have been completely made up. She claimed in court that she had obtained this result using Real Time PCR, but this was not the case: records obtained by Conti and Vecchiotti show that another method ("Qubit Fluorometer") was used, and that the result obtained was "too low" -- the exact same as for Trace C. There was no justification for treating Trace B as a positive result and Trace C as a negative, and in particular no reason for subjecting Trace B to amplification.

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?

Yes (p.61).

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?

This is on p. 79. This section of the report, on Stefanoni's knife results, is next in line to be translated (by my collaborator katy_did, while I'll be simultaneuously doing the clasp section).

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?

Substantially different. Stefanoni is quoted as follows on p. 102 of the report:

"...the knife was analyzed...in the course of these 50 samples attributed to the victim, some were prior to the analysis of the knife, of course, and others subsequent, so in these 50 I don't know if the knife was, I don't know now, a fourth, a third of the way through this flux of analyses..."

This puts me at 0.5 or more. Also note that the number 50 itself gives a probability of 0.1 if we use your estimate of 500 total samples in the lab.

Comment author: rolf_nelson 22 July 2011 07:18:08AM 0 points [-]

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?

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