I've assumed an error standard deviation of 30 14C years, to include
calibration curve uncertainty as well as that in the 14C determination.
However, I'm not convinced that his treatment of
calibration curve uncertainty is noninformative even in the absence of it varying with calendar age.
I think in this respect the Keenan paper must make some fault as
the calibration curve uncertainty must be of the same order in size there as the measurement error.
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).
If the
calibration curve were monotonic and had an unvarying error magnitude, the
calibration curve error could be absorbed into a slightly increased 14C determination error, as both these
uncertainty distributions are assumed Gaussian.
The statistical relationship then becomes, given independence of
calibration curve and radiocarbon determination
uncertainty:
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.
The radiocarbon determination will be more than two standard deviations (of the combined radiocarbon and
calibration uncertainty level) below the exact
calibration curve value for the true calendar date in 2.3 % of samples.
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.
Notice that near the end a large majority of the age determinations the
calibration curve is based on fall outside the indicated
uncertainty envelope of the
curve.
The
curved blue lines in Figure 9 - 1 present the
calibration error, or the
uncertainty in predictions based on the
calibration (technically the 95 percent prediction interval, which has probability 0.95 of covering the unknown temperature), which is a standard component of a regression analysis.