# Are Bayesian Statistics Useful to Archaeological Reasoning?

## Article excerpt

An ANTIQUITY paper used the methods of Bayesian statistics to combine radiocarbon and stratigraphic information into a single considered view. But are they different kinds of information, more fairly kept separate?

The article in ANTIQUITY by Buck, Kenworthy, Litton & Smith (1991) used Bayesian statistics to improve a series of radiocarbon dates by incorporating the information available on the position of the measured sample in a stratigraphic sequence. My responses have varied from extreme antipathy to puzzlement. As the article raises important issues in archaeological interpretation, I hope this short response will be useful even if it is obvious that I am still asking questions rather than providing solutions.

The method of the article was based on the formula:

Posterior belief = Prior belief x Standardized Likelihood

The example took measurements of residual radioactivity in a series of organic samples found at different points in a stratigraphic sequence and used Bayesian statistics to combine the numerical information given by the measurements of radioactivity with the unquantified information given in the stratigraphy. By the stratigraphic principle that a higher layer got into position later than a lower layer, the assumption is made that samples taken from higher layers will be younger than samples taken from lower layers. This is a matter not of numerical measurement or certainty but of likelihood, which is more the province of Bayesian than classical statistics. Bayesian methods offer firm and information which other statistics cannot reach.

If the excavated material and structures which can be handled quantitatively were of a historical period, the example could extend to written sources, which, up to now, have been mixed in to the archaeological brew with no methods at all.

Now that the study of excavated material in a historical period is already on the way to quantified methodology, numbers of coins, quantities of pottery, samples of animal bones and plans and dimensions of buildings are often expressed in full statistical form. Dates and sequences can be expressed as probabilities, and tests of significance can give guidance as to whether material from two different archaeological deposits are likely to represent the same past event. Where there is written evidence this is used in a loose way that I consider wrong (Reece 1984); written sources are usually plundered by archaeologists who take statements as fact -- 'the sources say so' -- and apply them to their excavated material provided the 'facts' fit their preconceptions.

This seems to be a classical example inviting a Bayesian approach. Two elements of information exist; one is already well quantified, the other is available and asking to be used, but does not appear in numerical form. If the written sources could be formulated in terms of parameters, variables, estimates and probabilities then the way would be clear for a Bayesian combination. Yet I find I am instinctively opposed and can see three objections:

* It is very rare indeed for the written sources to apply to the exact subject under excavation;

* The two types of subject matter belong to two completely different specialisms and need completely different methods of manipulation and assessment;

* Even where the two sorts of information apply to the same area of study, the written sources are mainly interested in concepts, reasons, and (tendentious) record, while the material seldom, if ever, involves these matters.

A reliable means to combine the information offered by varied sources is surely what most archaeologists hope for; this is what the Bayesian view is said to offer. The central point of the argument is in the nature and extent of the dissimilarity of the elements to be combined.

In the example of dates and layers the physics of radiocarbon is well understood, and the statistical meaning of a determination that follows. …