# Are Bayesian Statistics Useful to Archaeological Reasoning?

By Reece, Richard | Antiquity, December 1994 | Go to article overview

# Are Bayesian Statistics Useful to Archaeological Reasoning?

Reece, Richard, Antiquity

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.

• Questia's entire collection
• Automatic bibliography creation
• More helpful research tools like notes, citations, and highlights

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Project items
Notes

#### Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

#### Cited article

Are Bayesian Statistics Useful to Archaeological Reasoning?
Settings

Typeface
Text size
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience.
Full screen

## Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

## Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.