Mathematics, statistics and archaeometry: the past 50 years or so

This review of developments in the use of mathematics and statistics in archaeometry over the past 50 years is partial, personal and 'broad-brush'. The view is expressed that it is in the past 30 years or so that the major developments have taken place. The view is also expressed that, with the exception of methods for analysing radiocarbon dates and increased computational power, mathematical and statistical methods that are currently used, and found to be useful in widespread areas of application such as provenance studies, don't differ fundamentally from what was being done 30 years ago

Simulation, Seriation and the Dating of Roman Republican Coins

Seriation was one of the earliest applications of computers to an archaeological problem. Despite the origins of the technique in numismatics, the vast majority of coinage studies manually sequence coin hoards and issues. For many periods, the coin designs or legends can be used to provide a date. For the Republican series, however, detailed sequences rely on the use of coin hoard data. In recent years, Correspondence Analysis has become the de facto seriation routine of choice. For coinage studies, however, where the period of manufacture was very short, a successful seriation would leave one triangle empty in the re-arranged matrix rather than concentrating the largest values on the diagonal as would be the aim in other situations. The aim of this paper is to assess the effectiveness of various easily-available off-the-shelf open-source seriation routines that have been used in archaeology for the analysis of this type of data. Given that we know a great deal about the pattern of production of Republican coinage, it is possible to create simulated coin hoard assemblages to test the various seriation routines and assess which technique is likely to provide the most successful results. This paper presents the results of applying 14 seriation methods to 27 simulated coin hoard data sets, and discusses the results

Central European Early Bronze Age chronology revisited: A Bayesian examination of large-scale radiocarbon dating

In archaeological research, changes in material culture and the evolution of styles are taken as major indicators for socio-cultural transformation. They form the basis for typo-chronological classification and the establishment of phases and periods. Central European Bronze Age material culture from burials reveals changes during the Bronze Age and represents a perfect case study for analyzing phenomena of cultural change and the adoption of innovation in the societies of prehistoric Europe. Our study focuses on the large-scale change in material culture which took place in the second millennium BC and the emergence at the same period of new burial rites: the shift from inhumation burials in flat graves to complex mounds and simple cremation burials. Paul Reinecke was the first to divide the European Bronze Age (EBA) into two phases, Bz A1 and A2. The shift from the first to the second phase has so far been ascribed to technical advances. Our study adopted an innovative approach to quantifying this phenomenon. Through regressive reciprocal averaging and Bayesian analysis of radiocarbon-dated grave contexts located in Switzerland and southern Germany, we modelled chronological changes in the material culture and changes in burial rites in these regions in a probabilistic way. We used kernel density models to summarize radiocarbon dates, with the aim of visualizing cultural changes in the third and second millennium BC. In 2015, Stockhammer et al. cast doubt on the chronological sequence of the Reinecke phases of the EBA on the basis of newly collected radiocarbon dates from southern Germany. Our intervention is a direct response to the results of that study. We fully agree with Stockhammer’s et al. dating of the start of EBA, but propose a markedly different dating of the EBA/MBA transition. Our modelling of radiocarbon data demonstrates a statistically significant typological sequence of phases Bz A1, Bz A2 and Bz B and disproves their postulated chronological overlap. The linking of the archaeological relative-chronological system with absolute dates is of major importance to understanding the temporal dimension of the EBA phases

A survey of statistical problems in archaeological dating

AbstractThis expository paper gives a survey of statistical problems arising in two important and widely used scientific methods of dating archaeological deposits, namely tree-ring-calibrated radiocarbon dates and seriation

The Cultural Project : Formal Chronological Modelling of the Early and Middle Neolithic Sequence in Lower Alsace

Starting from questions about the nature of cultural diversity, this paper examines the pace and tempo of change and the relative importance of continuity and discontinuity. To unravel the cultural project of the past, we apply chronological modelling of radiocarbon dates within a Bayesian statistical framework, to interrogate the Neolithic cultural sequence in Lower Alsace, in the upper Rhine valley, in broad terms from the later sixth to the end of the fifth millennium cal BC. Detailed formal estimates are provided for the long succession of cultural groups, from the early Neolithic Linear Pottery culture (LBK) to the Bischheim Occidental du Rhin Supérieur (BORS) groups at the end of the Middle Neolithic, using seriation and typology of pottery as the starting point in modelling. The rate of ceramic change, as well as frequent shifts in the nature, location and density of settlements, are documented in detail, down to lifetime and generational timescales. This reveals a Neolithic world in Lower Alsace busy with comings and goings, tinkerings and adjustments, and relocations and realignments. A significant hiatus is identified between the end of the LBK and the start of the Hinkelstein group, in the early part of the fifth millennium cal BC. On the basis of modelling of existing dates for other parts of the Rhineland, this appears to be a wider phenomenon, and possible explanations are discussed; full reoccupation of the landscape is only seen in the Grossgartach phase. Radical shifts are also proposed at the end of the Middle Neolithic

Steps towards operationalizing an evolutionary archaeological definition of culture

This paper will examine the definition of archaeological cultures/techno-complexes from an evolutionary perspective, in which culture is defined as a system of social information transmission. A formal methodology will be presented through which the concept of a culture can be operationalized, at least within this approach. It has already been argued that in order to study material culture evolution in a manner similar to how palaeontologists study biological change over time we need explicitly constructed ‘archaeological taxonomic units’ (ATUs). In palaeontology, the definition of such taxonomic units – most commonly species – is highly controversial, so no readily adoptable methodology exists. Here it is argued that ‘culture’, however defined, is a phenomenon that emerges through the actions of individuals. In order to identify ‘cultures’, we must therefore construct them from the bottom up, beginning with individual actions. Chaîne opèratoire research, combined with the formal and quantitative identification of variability in individual material culture behaviour allows those traits critical in the social transmission of cultural information to be identified. Once such traits are identified, quantitative, so-called phylogenetic methods can be used to track material culture change over time. Phylogenetic methods produce nested hierarchies of increasingly exclusive groupings, reflecting descent with modification within lineages of social information transmission. Once such nested hierarchies are constructed, it is possible to define an archaeological culture at any given point in this hierarchy, depending on the scale of analysis. A brief example from the Late Glacial in Southern Scandinavia is presented and it is shown that this approach can be used to operationalize an evolutionary definition of ‘culture’ and that it improves upon traditional, typologically defined technocomplexes. In closing, the benefits and limits of such an evolutionary and quantitative definition of ‘culture’ are discussed