Pragmatic Bayesians: a decade of integrating radiocarbon dates in chronological models

Alex Bayliss Christopher Bronk Ramsey
Centre for Archaeology Research Laboratory for Archaeology
English Heritage University of Oxford
23 Savile Row 6 Keble Road
London W1S 2ET, UK Oxford OX1 3QJ, UK
Alex.Bayliss@english-heritage.org.uk christopher.ramsey@rlaha.ox.ac.uk

Bayesian analysis has been applied routinely to the analysis of chronological information, including radiocarbon dates, for almost a decade. This paper discusses our experiences, both in developing the methods and approaches to be used, and in their practical application to the whole range of archaeological problems. This experience covers a decade of casework encountered by a National Archaeology Service, academic dating projects to study major cultural phases, and work with collaborators from around the world. People working on these problems range from archaeologists with a detailed knowledge of the sites and cultures studied but usually with little statistical background, t physicists and mathematicians who often don't appreciate the nature of archaeological data and approaches. The paper looks at the difficulties encountered in trying to reconcile these very different perspectives, the benefits that come from this integration and at problems that still remain.



Bayesian chronology building: where now?

Caitlin E. Buck
Department of Probability and Statistics
University of Sheffield
Hicks Building, Hounsfield Road
Sheffield S3 7RH, UK
c.e.buck@shef.ac.uk

For more than a decade teams of inter-disciplinary researchers have worked hard to develop a robust and scalable Bayesian framework within which archaeologists can interpret both relative and absolute chronological data. This framework has proven popular and is at the core of Bayesian radiocarbon calibration software such as OxCal (http://www.rlaha.ox.ac.uk/orau/) and BCal (http://bcal.shef.ac.uk/). In this paper I will outline the approach and explain why it has proven to be so generally applicable. I will also look at recent advances and current research in this area and consider which of the up and coming methods are particularly important and might usefully be added to the general toolkits already in use. Finally, I will look to the future and make some suggestions for likely profitable topics of research in Bayesian chronology building in the next few years.



The Synchronization of Civilizations in the Eastern Mediterranean in the Second Millennium BC - natural science dating attempts

Otto Cichocki Max Bichler Maria Gertrude Firneis Walter Kutschera
VIAS - Dendrolab Atominstitut der österreichischen Institut für Astronomie Institut für Radiumforschung und Kernphysik
Institute for Paleontology Universitäten Stadionallee 2 Universität Wien Universität Wien VERA Laboratorium
Althanstr. 14 Türkenschanzstraße 17 Währinger Straße 17
A-1090 Vienna, Austria A-1020 Vienna, Austria A-1180 Vienna, Austria A-1090 Vienna, Austria
otto.cichocki@univie.ac.at

At the end of the first three years of this long-term research program, nine archaeological projects start to combine their dating results with those of four natural science projects to contribute to a controversial debate about chronology.

Max Bichler: Project 4 - Thera Ashes
The general idea of this project is to fix the eruption of the Santorini volcano (during the Late Minoan IA period) within the relative chronologies of this region. Pyroclastic ejecta (fallout from the eruption cloud) formed a layer, relating to this event, within well defined stratigraphic sequences at archaeological sites. Assuming a reliable identification of the ejecta, these layers can be used as a datum line.

Gertrude Firneis: Project 6 - Astrochronology
Two phenomena are defined in ancient Egyptian records: The heliacal rising of Sirius and the last sighting of the Lunar crescent each month. This project has established temporal limits for these astronomical events.

Otto Cichocki: Project 7- Dendrochronology
The dendrochronological investigation of wooden artefacts (construction parts of buildings, coffins, icons, objects of art), especially those made of Cedar wood, is intended to establish floating chronologies for the second millennium. This should allow us to establish the relative temporal range of objects that are relevant to building a relative chronology of certain historical events. If we are able to obtain sufficient nummers and variety of samples, we hope to be able to set up an absolute chronology, starting today and reaching back to the second millennium. If this can be achieved, it will be possible to establish absolute dates of wooden objects (i.e. the age of the last tree-ring of the object, and sometimes the felling date).

Walter Kutschera: Project 8 - 14C Dating
High precision radiocarbon dating with Accelerator Mass Spectroscopy (AMS) allows us to date milligram-size samples. If one wooden piece can be split in several samples (tree-rings of known relative age) wiggle-matching can improve dating results.



Tephrochronology in the North Atlantic region: a review of tephrochronological principles and their application in the reconstruction of Holocene terrestrial palaeoenvironments

Andrew J. Dugmore
Department of Geography
University of Edinburgh
Drummond Street
Edinburgh EH8 9XP, UK
ajd@geo.ed.ac.uk

The development of tephrochronology, a dating technique based on horizons of pyroclastic ejecta or tephra, illustrates a number of key issues that are encountered when constructing chronologies that both built upon, and are applied to, multidisciplinary studies. Tephrochronology is indivisible from volcanic history, and the construction of tephrochronologies requires stratigraphic data that is spatially referenced, mapping of tephra deposits and the determination of characteristic signatures of the tephra, that are frequently defined by chemical compositions. In addition, the relative dating control offered by individual tephras has to be connected to `absolute' time scales. Tephras have been commonly used to provide spot dates and limiting horizons at single sites, but much of the considerable potential for 3-D reconstructions and the spatial analysis of patterns of change through time, has yet to be realised. A key idea is to go beyond the fundamental steps of the identification, correlation and dating of tephra layers, that may actually provide little additional understanding or insight, and develop applications that turn the reporting/description/occurrence of tephra into a effective palaeoenvironmental tool with unique strengths. At its best tephrochronology may add new critical insight at many different levels, and be greater than the sum of its constituent parts.

The 3-D reconstructions that can be created by mapping a series of tephra layers may give uniquely detailed data on changing spatial patterns. Each tephra layer marks a surface at a moment in time; multiple tephra layers constrain the passage of time and define the rate at which change has happened across a landscape. Furthermore, as tephra are formed within hours or days, the distribution of any one tephra through a sediment or in contexts that are not contemporaneous with the initial eruption can be used to identify the pathways taken by sediment through the environment including temporary sediment stores, reworking of sediments and movements of sediments both across landscapes and within profiles. In addition, using tephra isochrones other dating techniques may be combined, tested and applied either at optimum locations or outwith their normal spatial range.



Constructing chronologies of sea level change from salt-marsh sediments

Robin J. Edwards
Department of Geography
University of Durham
Science Laboratories, South Road
Durham DH1 3LE, UK
r.j.edwards@durham.ac.uk

Geologically-based sea-level research spans a wide range of spatial and temporal scales, from global glacial/interglacial variations to local, multi-decadal, decimetre perturbations. Consequently, an accurate knowledge of sea level change can contribute to our understanding of such diverse issues as ice sheet distribution, earth rheology, ocean-atmosphere interaction, palaeoenvironmental change and coastal management. Irrespective of the ultimate research objective, the establishment of a reliable chronology is fundamental to all sea-level studies.

Records of Holocene changes in relative sea-level (RSL) are constructed by studying variations in coastal sedimentary sequences and associated biological components contained within them. In the UK, a multi-proxy approach employing radiocarbon-dated lithostratigraphic and biostratigraphic sea-level indicators is used to establish sea-level index points (SLIs) that fix former positions of RSL in terms of age and altitude. Errors associated with this age and altitude information restrict the resolution of reconstructions. These limitations become increasingly problematic as the temporal scale of the investigation is reduced, particularly when studying fluctuations during the last two or three millennia. Ultimately the error band becomes of comparable magnitude to the sea-level variations of interest, and these difficulties are compounded by the paucity of late Holocene organic deposits suitable for dating. New research seeks to integrate a range of dating tools including pollen chronohorizons, short-lived radionuclides (e.g. Pb210), AMS radiocarbon assays, and archaeological evidence to increase the frequency and distribution of age markers in sedimentary sequences.

The organic-rich salt-marsh sediments of the USA permit high-resolution radiocarbon dating of complete stratigraphic sequences. Wiggle-matched AMS dates from plant macrofossils produce accumulation curves from salt-marsh sediment cores which, when combined with foraminiferal evidence, fix the former position of the marsh surface relative to sea level. Resulting curves of mean tide level change record decimetre and (sub-) century variations of sufficient resolution to permit meaningful comparisons with other climate proxies.



Complicated relations and blind dating: formal analysis of relative-chronological structures

Mads K. Holst
Department of Prehistoric Archeology
University of Aarhus
DK-8270 Hbjerg
Denmark
farkmh@moes.hum.au.dk

Relative chronology serves in archaeology both as a formalized, analytical tool and as a basic, non-formalized, continuously and more or less unconsciously applied approach to handle complex excavation data. The formal use of relative chronology at excavations has largely been focused upon stratigraphical analysis with an expressed ideal of objectivity and a demand of an unambiguousness of the observations used and their chronological implications. This precondition of unambiguousness contrasts the dynamic development and change of interpretations found at excavations, a dynamic, which reflects the uncertainties and ambiguities of the data material. The discrepancy has unfortunate consequences for both approaches. The excavation analysis lacks controllability and the interpretations are in constant danger of being based on logically inconsistent arguments because of problems commanding the complexity and magnitude of the data material. The formal analyses, on the other hand, tend to idealize some observations and suppress others, both potentially leading to a misrepresentation of the factual relative chronological evidence uncovered during excavation.

This paper explores the possibilities of expressing formally the uncertainties and ambiguities of excavation data as well as the chronological implications of observations, which are otherwise left out of the relative-chronological analyses. The formal description allows the construction of network-representations, which may subsequently be subjected to different analyses, first and foremost graph-based. Due to the inclusion of the ambiguities there will rarely be only one possible chronological sorting of the elements, but the network should still represent a more precise model of the relative chronological evidence.



Tephrochronology: applications and problems in dating the palaeoenvironmental archive

John Hunt
Centre for Environmental Change and Quaternary Research (GEMRU)
University of Gloucestershire
Swindon Road
Cheltenham, GL50 4AZ
JHunt@glos.ac.uk

In the absence of historical documentation for signals represented in the stratigraphic record, the traditional first approach towards establishing a chronology is the identification of its broad stratigraphical context, either in terms of biostratigraphy or lithostratigraphy. This `superpositionist' approach usually provides a relative age, and sometimes a first approximation to a numerical age. However, it generally offers limited age information in relation to the potential chronological resolution of a sequence. Furthermore, to achieve a wider, perhaps regional, chronological framework this approach relies upon synchrony of stratigraphical changes that are, in fact, frequently diachronous. For this reason, `absolute' or numerical dating techniques are increasingly relied upon in archaeometric or geoscientific applications.

Falling broadly into two categories, incremental and radiometric, all dating techniques have inherent instrumental or methodological errors to a greater or lesser degree. In a palaeoenvironmental context, dendrochronology, although the most successful and precise of numerical dating techniques, may fail because of gaps in chronologies in certain regions or time frames, or because of erroneous assumptions in linking specific archaeological or other events with the death-age of the tree (i.e. mis-association). Radiometric dating methods such as luminescence typically deal with errors of �5 to �10%, whilst 14C errors usually range from �20 to �300 years in addition to various other errors including those associated with the variability of 14C production and the `radiocarbon plateau' effect. The magnitude of these errors presents difficulties, firstly in isolating cause and effect changes (`leads and lags') in environmental systems, and secondly in constructing a chronology for palaeoenvironmental or archaeo-societal changes occurring over time spans briefer than, or similar to, the error range itself (e.g. the termination of the Pleistocene).

In addition to an approach involving numerical techniques, dating of sequences based upon correlation of synchronous signals is also adopted. Here, either correlative dating serves as the final age control, or is used to transfer an established numerical chronology. The use of synchronous signals is referred to as `event chronology' or `event stratigraphy' or the application of `age-equivalent' stratigraphic markers. Within the Quaternary time frame, magnetostratigraphic methods are commonly applied as age-equivalent markers. Global polarity reversals, dated mainly by the K-Ar method or by the oxygen isotope signal obtained from ocean sediments, are firmly established though they are too infrequent for establishing more than the broadest of chronologies. Secular variations, essentially an event-continuum, also provide a strong correlative chronology, although they require minerogenic sediments and, as with dendrochronology, reference to regional master curves.

Volcanic event stratigraphy is increasingly applied to problems of geochronology. The most successful volcanic approach, tephrochronology sensu lato, is based upon the detection of isochronous deposits of tephra (volcanic `ash') layers. Innumerable observations of explosive eruptive episodes indicate that tephra is deposited rapidly after initial eruption (of the order of hours to weeks). In terms of the longer sediment record, the tephra-forming event is truly instantaneous. Compared with magneto-events for which the `setting-time' is uncertain, these instantaneous volcanic events offer much greater precision in event stratigraphy, along the same lines as extra-terrestrial impact signals. Tephra deposits provide, through the discipline of `tephrochronology', a means of precisely linking sequences or natural or anthropogenic palaeoenvironmental events on a regional and, potentially, global basis. The potential of tephrochronolgy lies in the degree to which it enables the highest resolution time frameworks to be constructed. The opportunities provided by tephrostratigraphy and tephrochronology are multiple, particularly in terms of time slice reconstructions. Examples include: The greatest challenge facing tephrochronology is the fulfilment of this potential. Identification of high resolution sedimentary sequences in palaeoclimatically sensitive areas is vital.

However there are practical difficulties that must be overcome if the full potential is to be realised. These include:

This paper attempts to explore some of these opportunities and difficulties through reporting the results of developing work on analytical methods, and through their application in marine and lacustrine sediments in western Europe. Particular emphasis will be given to the study of (1) issues surrounding the marine radiocarbon reservoir effect in the N. Atlantic, and (2) issues arising from a study of Holocene lacustrine sediments in western Ireland in which 11 tephras have been isolated and analysed. The latter study highlights the potential for distal tephrochronology to identify new volcanic eruptions, unknown/unreported from the proximal record [in this instance, new eruption in Hekla and identification of Jan Mayen island (hitherto thought to be effusive) as an explosive source of tephra].



Bayesian estimation of archaeomagnetic reference curves: applications to dating and chronological interpretation

Phillipe Lanos
Laboratoire d'Archéomagéntisme, UMR 6566 du CNRS "Civilisations Atlantiques et Archéosciences"
Université de Rennes 1
Géosciences-Rennes, Campus de Beaulieu, bât. 15
35042 RENNES, France
Philippe.Lanos@Univ-Rennes1.fr

In this paper, the range of errors that occur at different stages of the archaeomagnetic calibration process are modelled using Bayesian hierarchical models. With such models in place, we are able to derive estimates of the geomagnetic field for archaeological structures such as hearths, kilns or sets of bricks and tiles. The archaeomagnetic data exibit considerable experimental errors (taken into account by hierarchy modelling) and are typically more or less well dated by archaeological context, history or chronometric methods (14C, TL, dendrochronology, etc.). They can also be associated with stratigraphic observations which provide prior relative chronological information. The models we describe in this paper allow all these observations, on materials from a given period, to be linked together.

Further modelling on the calibration curve itself, using penalized maximum likelihood for smoothing univariate or bivariate time series data, finally allows representation of the secular variation of the geomagnetic field over time. The smooth curve we obtain (which takes the form of a penalized natural cubic spline) moreover provides an adaptation to the effects of variability in the density of reference points over time. Since our models take account of all the known errors in the archaeomagnetic calibration process, we are able to obtain a functional confidence envelop on the new curve. With this new posterior estimate of the curve available to us, the Bayesian statistical framework then allows us to estimate the calendar dates of undated archaeological features (such as kilns) based on one, two or three geomagnetic parameters (inclination, declination and/or intensity). Date estimates are presented in much the same way as those that arise from radiocarbon dating. In order to illustrate the models and inference methods used, we will present results based on French, German and Bulgarian data. We will also illustrate the problem of 'circular' reasoning in reference curve building using a specific archaeological example.



Taking Bayes beyond radiocarbon: the potential and problems of Bayesian approaches to other chronometric methods

Andrew R. Millard
Department of Archaeology
University of Durham
South Road
Durham DH1 3LE, UK/TD>
A.R.Millard@durham.ac.uk

The use of Bayesian statistics to combine prior chronological knowledge with radiocarbon dates has been developed and widely applied over the last decade. It has proved a powerful tool for combining information such as stratigraphy or known temporal spacing into statistical analyses of chronological evidence. However, applications of this approach involving chronometric methods other than radiocarbon are very few. The reasons for this vary with the techniques, but consideration of the problems shows that in many cases the potential exists for combining different types of chronological and chronometric information in this way.

This paper examines the potential for application of Bayesian statistics to dendrochronology, uranium-series, amino-acid racemisation, and trapped charge (luminescence and ESR) dating methods. In each case possible mathematical formulations will be explored, and, where these are suitably advanced, illustrated with case studies. In dendrochronology the methods have already been published for matching sequences to master chronologies and interpreting sapwood estimates, however both these procedures could be improved, and the possibility for Bayesian methods in master chronology construction needs to be examined. Closed-system uranium-series dates are easily included into a Bayesian analysis, but matters become more complex in open systems, with isochron dates and with high precision TIMS dates. Amino-acid racemisation dates also look simple, but consideration of how they are calculated reveals that estimation of the rate constant using temperature history reconstruction complicates matters. The two trapped charge methods have much in common when considering their incorporation into a Bayesian framework, particularly in the handling of "systematic" and "random" errors, but ESR dating of tooth enamel faces the additional problem of how to include models for uranium uptake history.



Archaeological methods of creating and documenting chronology: a critical approach

Wolfgang Müller
Austrian Archaeological Institute
Franz Klein Gasse 1
A - 1190 Vienna
Austria
wmueller@oeai.univie.ac.at

The aim of the SCIEM 2000 project is to synchronize civilizations in the Eastern Mediterranean in the 2nd millenium BC. The methods of synchronization will be illustrated in this paper. The basis for these methods is the large number of material cultural remains that have been excavated at Tell el Dab'a, ancient Auaris. This material has been organized and categorized by means of typologies and seriations. The stratigraphy that has now been confirmed for the site of Auaris produces a primary sequence, based on the contexts of artefacts, pottery, etc. The sequences that arise from the material cultural remains are then correlated to the stratigraphic sequence.

The next step is to look for common traits in the material culture of other sites in the area that date to the same period. If links can be confirmed it is possible to create a stratigraphie compar�e (a relative chronology) for the most important sites of the Eastern Mediterranean. The next step should be to "date" at least some parts of this sequence in order to get an absolute chronology. Methods of dating are partly scientific (C14, Dendrochronology etc. ) and partly archaeological. Sometimes the very scarce epigraphic evidence or properties of material culture allow synchronizations with the best established chronology of the ancient world, the Egyptian king list. Egypt is the logical starting point for the construction of a chronological framework because most existing local chronologies are dependent on Egyptian data.

In spite of very encouraging results the profound theoretical and methodological reverberations of the "making of chronology" should not be forgotten. Chronology is made. It is not in the nature of things, but merely a method of describing, understanding and handling time. Excavation produces a kind of monolithical time-block which has to be stroboscopically dissected. We write and talk time in a single-frame mode. The obvious need for discontinuities often results in neglecting long term processes and continuity as a whole. This is particularly important in archaeologies where scholars tend to look for discontinuities in the historical record which are then linked to breaks in the material sequence. Modern quantitative methods enable us to see chronology in a new way: the gradual development of elements of material culture.



Genealogies from time-stamped sequence data

Geoff Nicholls
Department of Mathematics
Auckland University
Private Bag 92019
Auckland, New Zealand
nicholls@math.auckland.ac.nz

We will discuss the problem of recovering genealogical structure, population size and mutation rates from DNA sequence data. The data comes from organisms which lived at different times in a haploid population of fixed size. A typical data set might provide DNA sequences in the mitochondrial hypervariable region I (HVRI) of a few dozen well preserved bones, the ages of which have been assigned using radiocarbon dating. We will describe the observation model, comment on model mispecification issues, and explain briefly how uncertainty in reconstructed parameter values may be quantified via Frequentist or Bayesian sample-based inference.



Applications of formal model choice to archaeological chronology building

Sujit K. Sahu
Faculty of Mathematical Studies
University of Southampton
Highfield
Southampton SO17 1BJ, UK
S.K.Sahu@maths.soton.ac.uk

Statistical methods are now an essential part of the archaeological inference making process. Nowhere is this more important than in the analysis and interpretation of chronological data, especially when information from several sources must be drawn together.

Different statistical models may, however, provide widely different interpretations of the same data. Thus it is often possible to make conflicting re-constructions of archaeological past using different models.

Buck and Sahu (2000) are among the first researchers to recognise this problem. They discussed possible solutions to the problem using some predictive Bayesian model choice criteria. They focussed attention to the problem of relative archaeological chronology building.

Bayesian model choice techniques, however, can be used in virtually all areas of archaeological chronology building where model based statistical techniques are employed. A particular advantage of Bayesian techniques lies in their ability to compare widely different models based on different assumptions and prior information.

In this talk we discuss recent developments in applying formal model choice techniques in archaeological chronology building. We develop computationally intensive model choice methods for archaeological dating problems which allow us to address and measure the uncertainties arising due to the possible mis-specification of the assumed models. We illustrate the methods with two applications.



A statistical framework for analyzing fossil record data

Robert E. WeissSanjib BasuCharles R. Marshall
Department of BiostatisticsDepartment of Statistics Department of Earth and Planetary Sciences
UCLA School of Public HealthNorthern Illinois University Harvard University
Los AngelesDe Kalb20 Oxford St.
CA 90095-1772, USAIL 60115, USACambridge, MA 02138, USA
robweiss@ucla.edubasu@math.niu.edu marshall@eps.harvard.edu

Stratigraphic sections are often sampled at well defined discrete points. Counts of various taxa are recorded at each point. Due to the incompleteness of the fossil record, a particular species may not be observed even when it is extant at a particular sampling point. Sampling intensity can vary across sampling points by orders of magnitude, and depending on extinctions and originations different species can compete to be part of the sample.

We develop a Bayesian analysis framework centered on what we believe is the fundamental statistical model for typical paleontological data. We use this model to estimate the times of appearances and disappearances of a set of taxa from a section in the face of the possibility that failure to find the species beyond its observed stratigraphic range may represent false negatives. We incorporate proper prior information, including an estimated longevity of the species and the probability that it will be observed if extant. We apply our model to mollusc data from the Western United States which has been previously been used to advocate a series of stepped extinctions.