The carbondate package contains functions for analysing sets of related radiocarbon (14C) determinations. Suppose we have a set of \(N\) archaeological samples, each of which has a 14C determination \(X_i\). Furthermore, suppose that these samples are known to be related to one another (for example, arising from a particular site, or set of sites, populated by a particular culture). We want to estimate the calendar ages of these samples and investigate changes/variations in the (calendar age) frequency at which the samples arose (as a potential proxy for activity, population size, …):
Each sample has an unknown calendar age \(\theta_i\) (for \(i = 1, \ldots, N\)). Since they are related, the set of calendar ages \(\theta_1, \ldots, \theta_n\) for the samples are assumed to arise from the same shared, and unknown, calendar age density \(f(\theta)\). However, we don’t observe the true calendar ages of the samples: only the 14C determinations \(X_1, \ldots, X_n\). Due to fluctuations in past radiocarbon levels, these 14C determinations need to be calibrated (converted) in order to be understood on the calendar age scale and obtain estimates for each \(\theta_i\). This calibration must be done simultaneously with the summarisation, introducing additional complexity into the overall process.
This library serves two purposes:
We provide two distinct, albeit ideologically linked, approaches to achieve this:
PolyaUrnBivarDirichlet()
and
WalkerBivarDirichlet()
— A non-parametric Bayesian density
estimation approach using a Dirichlet process mixture model (DPMM)
implemented via two different Markov Chain Monte Carlo (MCMC) algorithms
(Heaton 2022). This is a
statistically-rigorous alternative to summed probability distributions
(SPDs) and kernel density estimates (KDE models).PPcalibrate()
— A inhomogeneous Poisson
process/Changepoint approach using Reversible Jump Markov Chain Monte
Carlo (RJ-MCMC) to estimate the changing rate at which the
14C samples occur over calendar time.Separate vignettes are provided to describe each approach. Which approach is more appropriate to apply will be situation dependent, and will be determined by the nature of the underlying shared calendar age distribution \(f(\theta)\):
PolyaUrnBivarDirichlet()
or
WalkerBivarDirichlet()
are likely most suitable.PPcalibrate()
will be more
appropriate.A commonly-used approach to estimate changes in the frequency of past events or the size of populations looks at variations in the rate of archaeological and environmental samples (e.g., charcoal from fires, human/animal bones, or other evidence of occupation) found at a site over time. Time periods with large numbers of samples suggest increased activity, while those with few samples indicate a reduced level of activity. This paradigm is known as dates-as-data (Rick 1987).
The reliability of such a dates-as-data approach is highly dependent upon our ability to estimate the calendar ages of the discoveries. Most archaeological/environmental dates are obtained using radiocarbon. The need for calibration of these 14C samples introduces considerable uncertainties in the resultant calendar ages and complicates the use of dates-as-data, making it more challenging to identify variations in the calendar year density/rates at which samples occur.
In this library, we provide two theoretically-underpinned approaches to overcome these challenges, each of which has its own set of vignettes:
Used appropriately, dates-as-data approaches allow users to borrow strength from more data and hence to identify longer-term trends and less-obvious effects that are not possible with smaller sets of data. This has the potential to provide greater insight into mechanisms and processes. However, like any scientific tool, they must not be used uncritically, or treated as a black-box.
In particular, the reliability of any dates-as-data inference will depend hugely upon the representativeness, or otherwise, of the underlying sampling. Two particular considerations which must be taken into account are:
One must always consider what the sample you are wishing to summarise represents.
The (most-automated) version of the library only requires two vectors:
rc_determinations
rc_sigmas
Note: These values can either be provided as
14C ages, or as F14C concentrations (setting the
flag F14C_inputs = FALSE
or TRUE
accordingly).
All other model parameters will be adaptively chosen based upon these. More experienced users (with external independent information) may however wish to manually set some of the other parameters (see the help files for further information).
The library also provides some joint data (which can be used by either method) as described below
A calibration curve is a mapping providing, for an object of true calendar age \(\theta\), the corresponding radiocarbon age \(\mu(\theta)\). Estimates of such calibration curves are created using reference material for which we have both 14C measurements and independently-known (or estimated) calendar ages. The radiocarbon determination of any individual sample is assumed to be a noisy observation of the calibration curve, i.e., \[ X_i \sim N(\mu(\theta_i), \sigma_{i,\textrm{lab}}^2) \]
Given a undated object for which we obtain a 14C determination one can estimate its calendar age by inverting this mapping. A calibration curve is a required input for all the functions in this package.
The internationally-ratified standard for the radiocarbon calibration curve is known as IntCal, for which regular updates are provided by the IntCal working group:
These products provides pointwise estimates of the mean \(m(\theta)\) and sd \(\rho(\theta)\) of the relevant (NH or SH) calibration curve, which can be integrated out during calibration, i.e.,: \[\begin{align*} \mu(\theta) | \theta & \sim N(m(\theta), \rho(\theta)^2), \textrm{ and} \\ \Rightarrow X_i & \sim N(m(\theta_i), \rho(\theta_i)^2 + \sigma_{i,\textrm{lab}}^2) \end{align*}\]
The curve data intcal20
and shcal20
are
provided in this package. However it is possible to load and use another
calibration curve if you wish.
There are some example 14C data sets provided in the package, each of which contain a number of radiocarbon determinations and uncertainties from real-life cases:
kerr
: 255 radiocarbon determinations collated by
Kerr and McCormick (2014) related to the
building and use of raths in Ireland.
armit
: 2021 radiocarbon determinations collated by
Armit et al. (2014) from archaeological
groups operating in Ireland, to investigate whether a wetter environment
around 2700 cal yr BP led to a population collapse.
buchanan
: 628 radiocarbon determinations collated by
Buchanan, Collard, and Edinborough (2008)
representing the ages of distinct archaeological sites found across
Canada and North America during the time of the palaeoindians.
alces
, bison
, cervus
,
equus
, human
, mammuthus
:
radiocarbon determinations related to a variety of megafauna (and
humans) from Yukon and Alaska (Dale Guthrie
2006). Samples are restricted to those between 25,000–6000
14C yrs BP.
For those new to calibration we provide the introductory vignettes:
To learn more about the functions (and methods) in the library, look at:
These pages provide more details on the methods, and simple examples of their usage.