# Bayesian Approach

Bayesian statistics provide a way of combining different types of information about chronology, to calculate explicit, statistical estimates for the dates of past events. This method has proved particularly effective for the analysis of the complex probability distributions of calibrated radiocarbon dates.

When we calibrate a radiocarbon measurement, we assume that the calendar date of the sample is equally likely to fall at any point on the calibration curve. For one sample, this is a reasonable assumption; but as soon as we wish to calibrate a second measurement from a site, this assumption is no longer valid (if our first sample is of Iron Age date, then it is much more likely that subsequent samples from the same site will also be Iron Age). Our radiocarbon measurements are from the same site – they are related.

Figure 1: Simulated radiocarbon dates from Site A and B, showing the calendar dates of each site from which the radiocarbon simulations were calculated.

The importance of this ‘relatedness’ is illustrated in Figure 1. Consider these radiocarbon dates – when did Site A (upper) start and end? For how long was it is use? What about Site B (lower)? The radiocarbon dates on this graph have in reality been simulated from known points on the calendar scale. So, we know that Site A was in use from 2000 to 1800 BC (for 200 years), and that Site B was in use from 1925 to 1885 BC (for 40 years). Visual inspection, ‘eye-balling’, of graphs of calibrated radiocarbon dates can be really misleading!

What we need is a way to account for the ‘relatedness’ of sets of radiocarbon dates. Bayesian statistics allow us to do this. Imagine, for example, that we have a site. It starts, it continues in use relatively constantly for some period of time, and it then ends.

We then get an assemblage of radiocarbon dates from the site.

But, using the extra, archaeological information that the dates all come from a particular site that was used for a certain period (and that the site started before it ended!), our model can assess how much of the scatter on the radiocarbon dates comes from statistics and how much is real, historical duration.

Furthermore, the model formally estimates when the site began and when it ended!

Figure 2: Bayesian models for the chronologies of Sites A and B, showing the calendar dates of each site from which the radiocarbon simulations were calculated.

By this means, we can construct models that can distinguish between the 200-year duration of Site A and the 40-year duration of Site B (Figure 2).

‘Relatedness’ is only one of many things which archaeologists know about their material before radiocarbon dating. Often a great deal is known about the relative dating of samples – for example, from site stratigraphy, from the typological analysis of a class of finds, or from a seriation of artefact-types in closed assemblages. Sometimes we know from tree-ring counting that one sample is a certain number of years before another, or we know that samples come from a continuously accumulating sediment. We may even have some calendar dates from other sources (e.g. dendrochronology).

In The Times of Their Lives we will exploit all these forms of archaeological evidence about the past, combining them with suites of radiocarbon dates, to illustrate how this methodology allows us to answer questions about the European Neolithic that have previously been beyond the reach of our evidence.

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