THE BAYESIAN APPROACH TO THE INTERPRETATION OF ARCHAEOLOGICAL DATA

Archaeologists are increasingly becoming aware of an approach to data investigation known as Bayesian statistics. In this paper we outline both the philosophical and statistical background to the approach. We show that it provides a logical and coherent framework in which to make inferences on the basis of both data and a priori expert knowledge. We note that adoption of the Bayesian framework is particularly timely since there have been recent dramatic developments in numerical methods which mean that a number of previous implementation problems have now been solved. As a result, many questions of archaeological interest, which require the use of complex statistical models, are being investigated using this methodology. We use a variety of recently published examples from a range of archaeological areas to illustrate the type of questions that can be answered and the nature of the methodologies used, and we make comparisons with the results obtained using more traditional statistical techniques.     

THE FULL-DISTRIBUTION APPROACH TO AGGREGATE REPRESENTATION IN THE INPUT-OUTPUT MODELING FRAMEWORK*

ABSTRACT. This paper presents a probabilistic specification of coefficients in the input- output modeling framework. Although previous works on probabilistic input-output models attribute uncertainty to measurement and sampling errors, this specification derives from systematic variation directly attributable to industrial, institutional, and location factors. Experiments with national input-output data support the existence of such variation. Employing the specification not only yields a more flexible aggregate modeling framework capable of producing interval impact estimates, but also an alternative perspective on such issues as interregional differentiation and structural comparison, the identification of key industrial sectors, aggregation, and spatial variation in production.     

A STATISTICAL APPROACH TO THE CALIBRATION OF FLOATING TREE-RING CHRONOLOGIES USING RADIOCARBON DATES

The bristlecone pine tree-ring calibration of radiocarbon dates, while necessitating changes of up to 700 years in Holocene chronology before 1000 b.c. , offers possibilities of very accurate dating when ¹⁴C determinations from floating tree-ring chronologies are utilized. A statistical approach assuming linear regression is developed and used to position the floating tree-ring chronologies at Swiss neolithic sites, using radiocarbon dates published by Ferguson, Huber and Suess and by Suess. The statistical method gives objective estimated dates with estimates of error related, in a consistent and explicit manner, to the inherent inaccuracies of the radiocarbon dates. Most of the method may readily be tested by standard statistical procedures. For the particular cases considered the assumptions of linearity and parallelism are investigated, and the precision of the estimated dates is comparable with that claimed by Suess and his co-workers. A precise calibration is thus possible without utilizing the short-term fluctuations in the Suess calibration curve. The analysis, while avoiding some assumptions of Suess and his collaborators, offers an explicit procedure for establishing controlled teleconnections with the Ferguson dendrochronology, and supports their emphasis on the importance of radiocarbon dates from floating tree-ring sequences for the construction of precise prehistoric chronologies.     

DISPERSION DIAGRAMS: A NEW APPROACH TO THE DISPLAY OF CARBON-14 DATES

A statistical approach to the display of sets of ¹⁴C dates is suggested. All available dates of any particular culture are used to calculate the two quartiles and the median dates for it. The ‘dispersion’of the dates is then displayed as a bar showing the extreme dates, the quartiles and the median; thus neither individual dates nor their standard deviations are shown. This ‘dispersion diagram’saves much space when the dates of several cultures are to be displayed. The argument is developed that the inter-quartile range, which does not change very much when new dates become available and are added to the set, is a good index of the time span during which a culture flourished, and this range should normally be quoted rather than the mean, median or extreme dates of the culture. With samples of nine or more it can be shown by the Hypergeometric Distribution that there is a 97% chance of two cultures being different if their inter-quartile ranges just fail to overlap, so that this method of display is useful in assessing the overlap of cultures. The fact that the dispersion diagram contains within it a measure of the statistical uncertainties of the individual estimates and therefore can replace the standard deviation of each individual ¹⁴C date is discussed.     

A SYSTEMATIC APPROACH TO THE DEFINITION OF SOURCES OF RAW MATERIAL

This paper argues the importance of the contribution that multivariate statistical techniques can make to the analysis of data from trace element characterization of sources of raw material and of artefacts. A threephase analysis is outlined: for the delimitation of sources of the raw material; the representation of the interrelationships of these sources; and the systematic and explicit allocation of artefactual material within the available universe of source groups. A model is developed using obsidian from New Zealand sources and presented as an example of the method.     

ON STATISTICAL APPROACHES TO THE STUDY OF CERAMIC ARTEFACTS USING GEOCHEMICAL AND PETROGRAPHIC DATA*

The scientific analysis of ceramics often has the aim of identifying groups of similar artefacts. Much published work focuses on analysis of data derived from geochemical or mineralogical techniques. The former is more likely to be subjected to quantitative statistical analysis. This paper examines some approaches to the statistical analysis of data arising from both kinds of techniques, including ‘mixed‐mode’ methods where both types of data are incorporated into analysis. The approaches are illustrated using data derived from 88 Late Bronze Age transport jars from Kommos, Crete. Results suggest that the mixed‐mode approach can provide additional insight into the data.     

THE SUPPLY-DRIVEN INPUT-OUTPUT MODEL: A NEW INTERPRETATION BUT STILL IMPLAUSIBLE

ABSTRACT. In this reply, I argue that the production function proposed by Gruver provides a theoretical foundation for the supply model only in a most trivial case. He proposes a more general alternative which is, however, still very implausible. Furthermore, against Rose and Allison, I argue that small input-coefficient changes provide an insufficient excuse for using the supply model for impact studies, and I show that employment estimates may be quite different depending on the approach used.