Assumptions baked into the VMS carbon dating

[oshfdk]

Again, why?  Even if the Author acquired that bifolio in the same buying/begging/stealing/rummaging transaction as the other folios, it does not follow that they were all manufactured at about the same time.   Vellum is a non-perishable commodity, like timber, leather, copper, or vitriol, so a merchant's stock could well have new vellum mixed with decades-old vellum.  Especially considering that the Author was happy to take off-cuts and grossly defective sheets.  Are you perchance assuming that the Author made the vellum himself?

No, my interpretation would apply to any situation when you take 4 random samples from any large collection of fungible (not unique) manufactured items bundled together in the past. Would similarly apply to a bunch of timber blocks or undated copper coins. If three items are found to be definitely from 1390-1460 and also have a large common range of 1404-1450 and the fourth item by measurement alone is 50% 1310-1350 and 50% 1390-1438, I would say it's extremely more likely that the fourth item is from 1390-1438 and it's quite likely that the whole bundle is from 1404-1438, just the by way human society works. It's possible and likely that a pile of rocks in the forest have completely unrelated timelines each. For human manufactured and human consumed items the general rule is that if something can be used, it will be used, if something can be sold, it will be sold, and if something stays neglected for a long time, there is a reason for this too (missing owner, lost or forgotten items belonging to the same owner ). Human manufactured fungible items are produced by someone who wanted either to use or to sell them, and each person buying them likely had intention to use or resell them. Making no assumptions about the manuscript and the parchment, just the fact of it being a bunch of goods bundled together, affects the probability of a common time and place of origin significantly, compared to items randomly sampled from different places.

The above only applies to fungible items. Obviously, this doesn't works for collectibles, but I don't think raw parchment of low quality is a collectible in any sense.

But in this case that single-interval summary would be rather uninformative, even misleading, because the distribution has two well-separated humps with non-trivial areas.  Thus a better summary is to split the gray distribution into two curves and find the 68.2% or 95.4% intervals R,S for each hump.  The areas of the humps for the f68 sample seems to be about 0.445 and 0.555. Then we can say that the date is within the R interval with 0.445 x 0.954 probability and within the S interval with 0.555 x 0.954 probability.

Thank you for the explanation, I think I understand how the values were computed, but I'm still not sure what these numbers imply for the probability for the item to be from the first range or the second.

To make it simple, consider the graph below. The yellow bar is the distribution of measured samples, to greatly simplify computations let's assume it's uniform between the min and the max values. If I understand the computation above, in this particular case the probability distribution would simply be the shapes A and B and the probabilities would be proportional to the areas of A and B, is this correct? The areas are comparable, I'd even say A is a bit larger than B, so the percentages are roughly equal and range a gets a bit more than 50%.

However, if we look at the distribution of the measured samples (yellow band), we find that most of them cannot be produced from range a at all. Shape A only reaches up about 20-25% into the sample distribution, so then we will have to understand how 75+% of the registered samples were produced? 

In this case I can imagine, the more correct metric of the probabilities of range a vs range b would be which part of the sample range is covered by each period, so, for range a it's c / (c + d), which produces a small number like ~18%.

I suppose the difference lies in the question being asked, but I'm not sure I understand what the question is in either case.