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.     

A NEW APPROACH TO MODELING THE IMPACT OF DISRUPTIVE EVENTS

This paper develops a new methodology to predict the interregional and interindustry impacts of disruptive events. We model the reactions of economic agents by minimizing the information gain between the pre‐ and postevent pattern of economic transactions. The resulting nonlinear program reproduces, as it should, the pre‐event market equilibrium. The methodology is tested further by means of a comparison of this base scenario with two regional production shock scenarios and two interregional trade shock scenarios. The outcomes show a plausible combination of partially compensating demand, supply, and spatial substitution effects, which justifies the further development, testing, and application of this new approach.     

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.     

ANALYZING THE IMPACT OF PUBLIC CAPITAL STOCK USING THE NEG WAGE EQUATION: A SPATIAL PANEL DATA APPROACH

ABSTRACT This paper examines the relationship between the level of public infrastructure and the level of productivity using panel data for the Spanish provinces over the period 1985–2004, a period that is particularly relevant due to the substantial changes occurring in the Spanish economy at that time. The underlying model used for the data analysis is based on the wage equation, which is one of a handful of simultaneous equations which when satisfied correspond to the short‐run equilibrium of New Economic Geography (NEG) theory. This is estimated using various spatial panel models with either fixed or random effects to allow for individual heterogeneity. Using these models, we find consistent evidence that productivity depends directly on the public capital stock endowment of each province, but also there is evidence of negative spillover effects from changes in capital stock in neighboring provinces.     

TOWARDS A NEW APPROACH TO ARCHAEOMAGNETIC DATING IN EUROPE USING GEOMAGNETIC FIELD MODELLING*

We introduce a new approach to producing secular variation curves for archaeomagnetic dating, using global geomagnetic field modelling techniques. Using published palaeosecular variation curves for five European locations as input, and a previous global model for regularization, we produce a model for the period ad 0–1900, which reproduces the input curves within their 95% confidence intervals, and successfully fits data from other regions in Europe. Our global model performs as well as a previous regional model, but additionally ensures consistency with physical constraints. We show that the curves currently used for dating are not mutually consistent, and therefore that in the future this new approach will provide more reliable curves for archaeomagnetic dating.     

THOUGHTS ON THE UTILITY OF A BIVARIATE‐SPLITTING APPROACH TO OLMEC CERAMIC DATA INTERPRETATION*

A recently resolved debate centred on the interpretation of a major set of INAA data that was based on Olmec ceramics from Mexico. In an attempt to answer questions arising from the debate, this paper discusses the effect of numbers of samples chosen for data interpretation. It also presents interpretations of the ceramic data set based on a bivariate data‐splitting approach and compares the results of this with the multivariate analysis approaches employed by the initial publishers of the data.     

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.