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.