I had a Savina placenta sample which of course was miles out of the standard solutions
calibration curve range, and using the equation for the line got a result.
Not exact matches
The measurement process does not allow calendar ages in a
range where the
calibration curve is flat to be distinguished.
Now we'll take the 1000 — 1100 years
range, which asymmetrically covers a steep region in between two plateaus of the
calibration curve.
Actually the
calibration curve beyond the treering
range (ca 12 000 BP) is very decidedly shaky.
For this purpose, it would not be necessary to draw true ages from the full prior, but only well on either side of the selected
range, in order to accommodate possible observation error and the distortion of the
calibration curve.
I've picked periods representing both
ranges over which the
calibration curve is mainly flattish and those where it is mainly steep.
Since the
calibration curve error appears small in relation to 14C determination error, and typically only modestly varying over the 14C determination error
range, I will make the simplifying assumption that it can be absorbed into an increased 14C determination error.
But it also can't provide conclusive evidence for the calendar year having any other value, unless there's a calendar year for which the
calibration curve is nearly vertical, covering the entire
range of carbon - 14 ages that are plausible given the measurement.
Your Fig. 6 shows that the uniform calendar age prior does terribly when the true calendar age is known to be in the
range 1000 - 1100 years, using your hypothetical
calibration curve.
For both variants of the uniform prior subjective Bayesian method, probability matching is nothing like exact except in the unrealistic case where the sample is drawn equally from the entire
calibration range — in which case over-coverage errors in some regions on average cancel out with under - coverage errors in other regions, probably reflecting the near symmetrical form of the stylised overall
calibration curve.
The reason for the form here of Jeffreys» prior is fairly clear — where the
calibration curve is steep and hence its derivative with respect to calendar age is large, the error probability (red shaded area) between two nearby values of t14C corresponds to a much smaller ti
range than when the derivative is small.