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?
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?:
(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.)
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.
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.
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.
Thanks for another well-researched reply, let’s have a couple more posts on this, and then turn to the DNA for a bit.
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.
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.”
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?
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.”
My bad, I misread the abstract. Doesn’t significantly change the scenarios though.
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?
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.)
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.)
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.
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:
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]
.95 for all the scenarios mentioned, maybe a little less for the 21:00-21:30.
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.
(snip)
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 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.