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Further details and the R code necessary to calibrate radiocarbon dates are given in the C datasets or age-depth models, it is sometimes useful to characterise each radiocarbon date by an average value, a “best guess” at a single point in time that describes the samples’ age.
A common application is the selection of a subset of dates from a larger database for more rigorous assessment using Bayesian phase models or one of the techniques described in the following texts.
For example, at the time of writing, recent months have seen papers presenting syntheses of millennia of human history in Central Italy (Palmisano et al. The current high level of interest in this kind of work doubtless has many causes, including (a) the fact that available archaeological data have now reached a critical mass, allowing the work to proceed (b) hyper-familiarity by archaeologists with computers and the internet, which now pervade virtually every aspect of modern life, (c) next-generation ancient DNA work which has invigorated interest in demography and population history and (d) a broader shift towards “digital humanities”, positioning archaeology at the interface between scientific research and “Big Data” (for an extended discussion, see Kristiansen ).
In this brave new world, many archaeologists and their collaborators have developed novel methods and theories dealing with the rather complex and intertwined issues of meaningfully summarizing large datasets, but also accounting for the chronological uncertainty and sampling bias inherent to archaeological research.
The choice of smoothing bandwidth is important—if it is too narrow, then spurious wiggles caused by the calibration curve (or rather, the C history of the Earth) will be present; too wide, and the KDE will fail to respond to patterns of interest in the data.
The factors determining the choice of kernel bandwidth are, in essence, similar to the measures taken to mitigate the risk of type I and type II errors in research design: both false positives and false negatives should be avoided if possible, but sometimes a study must run the risk of making one type of error to lower the chance of making a more serious error of the other kind.
That said, many studies still succumb to using point estimates or even histograms of uncalibrated dates because there are few methods that can replace the point estimate when the desired result of the analysis is a time-series, such as temporal frequency distribution or plots of proxy indicators versus time.
Bootstrapping is a potentially important application of point estimation that has not yet been widely discussed in the literature (although see Brown 1000), the bootstrapping process develops a set of results that incorporate the error margin caused by the calibration process.
As many authors have pointed out, using the technique uncritically and as a direct proxy is applicable only to broad trends in very large datasets (Chiverrell et al. This is because the inherently statistical nature of radiocarbon measurements, together with the non-Gaussian uncertainty introduced by the calibration process, causes artefacts in the resulting curve that could be misinterpreted as “signal” but are, in fact, “noise”.
Later in this paper, the technique is used to estimate a conservative confidence interval for models of the frequency of A summed radiocarbon probability function combines two or more probability density functions for a given date range by adding together their probability densities for each year.
As long as each contributing probability density is correctly normalised, the area under the summed probability is equal to the number of items that have been summed.
In this paper, I hope to contribute to this emergent and creative milieu of some universally applicable tools for calibrating radiocarbon dates, examining trends in the data, and mapping out patterns in space and time.
Some of the techniques are new, whereas others have been pioneered elsewhere and reviewed here.