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.)

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