The two posterior PDFs in Figure 2 imply very different
calendar age uncertainty ranges.
Not exact matches
So in both cases, one can construct a confidence / credible interval for the carbon - 14
age by well - known methods (that exhibit perfect probability matching), and then simply transform the endpoints of this interval to
calendar years using the calibration curve (which I'll assume is known exactly, since
uncertainty in it doesn't seem to really affect the argument).
However, I'm not convinced that his treatment of calibration curve
uncertainty is noninformative even in the absence of it varying with
calendar age.
Initially I was concerned that the non-monotonicity problem was exacerbated by the existence of calibration curve error, which results in
uncertainty in the derivative of 14C
age with respect to
calendar age and hence in Jeffreys» prior.
An error - free laboratory measurement of modern fraction does not imply that the problem collapses into a deterministic look - up from the calibration curve — even if the curve is monotonic over the relevant
calendar interval — because the curve itself carries
uncertainty in the form of the variance related to the conditional probability of RC
age for a given
calendar date.