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?:
(1) 21:00 - 21:30 (2) 21:30 - 22:00 (3) 22:00 - ...
Recently, on the main section of the site, Raw_Power posted an article suggesting that we find "worthy opponents" to help us avoid mistakes.
As you may recall, Rolf Nelson disagrees with me about Amanda Knox -- rather sharply. Of course, the same can be said of lots of other people (if not so much here on Less Wrong). But Rolf isn't your average "guilter". Indeed, considering that he speaks fluent Bayesian, is one of the Singularity Institute's largest donors, and is also (as I understand it) signed up for cryonics, it's hard to imagine an "opponent" more "worthy". The Amanda Knox case may not be in the same category of importance as many other issues where Rolf and I probably agree; but my opinion on it is very confident, and it's the opposite of his. If we're both aspiring rationalists, at least one of us is doing something wrong.
As it turns out, Rolf is interested in having a debate with me on the subject, to see if one of us can help to change the other's mind. I'm setting this post up as an experiment, to see if LW can serve as a suitable venue for such an exercise. I hope it can: Less Wrong is almost unique in the extent to which the social norms governing discussion reflect and coincide with the requirements of personal epistemic rationality. (For example: "Do not believe you do others a favor if you accept their arguments; the favor is to you.") But I don't think we've yet tried an organized one-on-one debate -- so we'll see how it goes. If it proves too unwieldy or inappropriate for some other reason, we can always move to another venue.
Although the primary purpose of this post is a one-on-one debate between Rolf Nelson and myself, this is a LW Discussion post like any other, and it goes without saying that others are welcome and encouraged to comment. Just be aware that we, the main protagonists, will try to keep our discussion focused on each other's arguments. (Also, since our subject is an issue where there is already a strong LW consensus, one would prefer to avoid a sort of "gangup effect" where lots of people "pounce" on the person taking the contrarian position.)
With that, here we go...