Abstract
In addition to being crucial to the establishment of archaeological
chronologies, radiocarbon dating is vital to the establishment of time
lines for many Holocene and late Pleistocene palaeoclimatic studies
and paleaeoenvironmental reconstructions. In the early days of
radiocarbon dating an assumption was made that the proportion of
radioactive carbon (14C) in the earth's atmosphere has remained
constant over time. However, due to solar and geomagnetic induced
changes in production rate and ocean circulation changes, it turns out
that there have been quite considerable fluctuations in the levels of
radiocarbon in the earth's atmosphere over time. Thus, in order to
compare radiocarbon age estimates with those derived from other dating
methods such as uranium-series dating, it is necessary to calibrate.
Radiocarbon calibration curves were originally estimated using only
14C measurements on known age tree-rings. More recently, however,
the types of records available for calibration have diversified and a
large group of scientists (known as the IntCal Working Group---IWG)
with a wide range of backgrounds has come together to create
internationally-agreed estimates of the calibration curves. By 2001
the IWG numbered 20+ researchers, but did not include a
statistician. As a result, the early calibration curves were
constructed very simply, with each point separately calculated as a
simple weighted average of all data within a ten or twenty year
bin. This ignored the, often substantial, uncertainty on the calendar
age estimates for each sample in the database.
In 2002, when the IWG began preparations to make an update to the
calibration curves, Caitlin Buck was recruited to the group and asked
to offer advice on statistical methods for curve construction. In
collaboration with Paul Blackwell, she devised a tailor-made Bayesian
curve estimation method which was adopted by the IWG for making all of
the 2004 internationally-agreed radiocarbon calibration curve
estimates.
In our proposed presentation for the Ninth Workshop on Case Studies
in Bayesian Statistics we will report on the development and
implementation of our random walk-based method for the estimation of
radiocarbon calibration curves. In seeking appropriate methods for
curve construction, we were concerned with several specific aspects of
the problem that had not been handled satisfactorily in the past. In
particular, we wanted to be able to take account of the fact that:
- most samples in the IntCal database do not
derive their carbon from a single year of metabolisation;
- many samples in the IntCal database have calendar age estimates that
derive from methods other than tree-ring dating (e.g.\ U/Th dating) and
are, hence, not precisely known (but have measures of uncertainty
associated with them);
- not all samples in the IntCal database have independent calendar
age estimates---some, for example, derive their calendar age estimates
from matching one ``floating'' sequence of dated samples to another
more securely dated one and hence their calendar age estimate is
related to all the others in the same sequence;
- the radiocarbon calibration curve is intended to be our best
estimate of the relationship over time between radiocarbon age and
calendar age and, since this relationship is a continuously varying
one, observations from it are correlated.
In our proposed talk, we will outline the modelling and methods used
to make the 2004 internationally-agreed estimates of the radiocarbon
calibration curves (Buck and Blackwell, 2004; Hughen et al. 2004;
McCormac et al. 2004; Reimer et al. 2004). We will explain how
we took account of all four of the factors listed above (as well as
several other more subtle ones) by formally modelling the relationship
between the data and the calibration curve. The talk will comprise
four main sections:
- first we will formalise what
we mean by a calibration curve;
- second we will outline the
approaches we took to modelling the error structure associated with
the available calibration data;
- third we will outline two
different approaches (one exact and the other approximate) that we
have taken to estimating the curves;
- finally, we will look at
the ways in which our curve estimates are used by the applied
communities with which we work.
At the end of the presentation, we will look to the future. We will
outline the on-going work with which we are involved and seek input
from the other delegates. In particular, we would like suggestions for
improvements to our modelling structures and to our MCMC
implementation.
References:
Buck, C. E. and Blackwell, P. G. (2004).
Formal statistical models for estimating radiocarbon calibration
curves. Radiocarbon, 46(3):1093--1102.
Hughen, K. A., Baillie, M. G. L., Bard, E., Beck, J. W., Bertrand, C. J. H.,
Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon, P. E.,
Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P., Kromer,
B., McCormac, G., Manning, S., Ramsey, C. B., Reimer, P. J., Reimer, R. W.,
Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor, F. W., van der
Plicht, J., and Weyhenmeyer, C. E. (2004).
Marine04---marine radiocarbon age calibration, 0--26 cal kyr BP.
Radiocarbon, 46(3):1059--1086.
McCormac, F. G., Hogg, A. G., Blackwell, P. G., Buck, C. E., Higham, T. F. G.,
and Reimer, P. J. (2004).
SHCal04---Southern Hemisphere calibration, 0--11.0 cal kyr BP.
Radiocarbon, 46(3):1087--1092.
Reimer, P. J., Baillie, M. G. L., Bard, E., Bayliss, A., Beck, J. W., Bertrand,
C. J. H., Blackwell, P. G., Buck, C. E., Burr, G. S., Cutler, K. B., Damon,
P. E., Edwards, R. L., Fairbanks, R. G., Friedrich, M., Guilderson, T. P.,
Hogg, A. G., Hughen, K. A., Kromer, B., G., M., Manning, S., Ramsey, C. B.,
Reimer, R. W., Remmele, S., Southon, J. R., Stuiver, M., Talamo, S., Taylor,
F. W., van der Plicht, J., and Weyhenmeyer, C. E. (2004).
IntCal04---terrestrial radiocarbon age calibration, 0--26 cal kyr
BP. Radiocarbon, 46(3):1029--1058.
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