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.
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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.
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 split due to length]
Now, to the slippage issue:
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):
(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.
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:
\
The range in the Hellmig et al. study was 29-203 minutes.
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.
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.
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?
Right, like the court, I understand that Umani Ronchi was incorrect about the ligatures.
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.
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.
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.
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.
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:
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.
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.
I assume you mean lag time?
Doesn’t that paradoxically decrease your confidence that you know everything that’s going on with digestive processes and can accurately predict TOD?
I agree, the TOD theory would be in even better shape if that were the case.
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.