(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.