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Pragmatic Bayesians: a Decade of Integrating Radiocarbon Dates into Chronological Models
Abstract
This chapter is an account of the experiences of the two authors in routinely applying Bayesian statistics to sets of radiocarbon dates. Whereas Buck (Chapter 1) gives an account of the development of the mathematical models, this chapter is concerned with their implementation and routine use. Since the early 1990s radiocarbon data from a large number of archaeological sites have been analysed using Bayesian methods and this chapter provides an overview of the subject from an archaeological perspective. Using examples largely taken from English Heritage projects, the chapter demonstrates the usefulness of the technique, some of the pitfalls and problems encountered and areas for future research. The problems that arise when trying to apply rigorous mathematical methods to very complex models are discussed in relation to the developments of the computer program OxCal. Other perspectives on archaeological chronology building are given by Holst (Chapter 6) and Cichocki et al. (Chapter 4).
... Both the definition of the question and the examination of the quality of the date (stratigraphy and sample selection strategy) are the first steps in the construction of a chronological model. The understanding of these steps and the correct formulation of them is crucial for the correct elaboration of the model (Bayliss & Bronk Ramsey, 2004). When working with published radiocarbon dates, a work prior to any modelling attempt should be focused on a strict evaluation of the taphonomy of each dated site. ...
... The main benefit of combining 14 C information with stratigraphy is that while radiocarbon data have probability distribution, stratigraphy, in a mathematical sense, provides non-probabilistic logical statements (Steier & Rom, 2000). However, the main issue of using Bayesian statistics for archaeological chronology cannot be ignored, and this is that absolute Bayesian strictness is almost impossible to achieve (Bayliss & Bronk Ramsey, 2004). It can produce posterior distributions that are highly influenced by the priors, and in addition there is no correct way to select a prior, since this depends directly on personal abilities to convert a subjectivity into a mathematical prior formulation. ...
... While A model is a model agreement index used to see if the model as a whole is not likely given the data, A overall is an individual agreement index product of the individual agreement indices. For both indices, values below 60% generally indicate a high probability that there is a problem with the model (Bayliss & Bronk Ramsey, 2004). ...
The purpose of the last chapter in the book is to draw things together from a historical perspective. The first section opens with a few words about how Luca Cavalli-Sforza and I began working in collaboration on the Neolithic transition in Europe and then introduces the early simulation study of the spread of the Linearbandkeramik (LBK) in central Europe, which we did at Stanford in 1973. The second section considers some of the processes that are involved in transitioning in space and time from late hunting and gathering to early forms of agro-pastoralism. The third section returns to the LBK and the recent gains that have been made in its simulation study by a research group in Paris. The fourth section then turns to a broader discussion of simulation studies and research on the transition to agriculture.
... The application of accelerator mass spectrometry (AMS) 14 C dating, which enables analysis of small samples and thus production of larger and relevant datasets (e.g. dating especially short-lived plant materials or specific treerings of direct relevance to specific contexts); improved 14 C calibration curve resolution; and, in particular, the use of Bayesian chronological methods (e.g., [58][59][60][61]) enabling the incorporation of archaeological and other information about sample and site temporal relationships, have collectively transformed the ability to resolve dates in archaeology including for later 15 th through earlier 17 th century Northeast North America [62][63][64][65]. In particular, two methods, ideally combined, have been transformational, enabling a revolution in temporal resolution for archaeological sites in the region: (i) 14 C dating fixed time series of specific tree-rings, even from wood samples preserving short tree-ring sequences (<50 rings), and placing these into calendar time via correlation against the 14 C calibration curve (so-called 14 C 'wiggle-matching' [66,67]); and (ii) integration of prior archaeological or ethnohistoric information about stratigraphic and temporal relationships within a site's history and the temporal constraints on the likely overall maximum duration of such village sites, to greatly constrain and refine 14 C dating using Bayesian methods (e.g. ...
... Dendrochronological calibration of radiocarbon dates to account for fluctuations in atmospheric radiocarbon concentrations; accelerator mass spectrometry (AMS) dating, allowing analysis of small samples while increasing both accuracy and precision of dates; and, as noted above, Bayesian analyses of large suites of radiocarbon dates have all combined to make the building of site and regional chronologies less subjective and more robust in recent decades (e.g. [58][59][60][61][91][92][93][94]). While widespread in several areas of world archaeology for over two decades, applications of these developments to the 15 th to 17 th century Indigenous archaeological record in eastern North America is only in its initial stages (e.g. ...
The timeframe of Indigenous settlements in Northeast North America in the 15th-17th centuries CE has until very recently been largely described in terms of European material culture and history. An independent chronology was usually absent. Radiocarbon dating has recently begun to change this conventional model radically. The challenge, if an alternative, independent timeframe and history is to be created, is to articulate a high-resolution chronology appropriate and comparable with the lived histories of the Indigenous village settlements of the period. Improving substantially on previous initial work, we report here high-resolution defined chronologies for the three most extensively excavated and iconic ancestral Kanienʼkehá꞉ka (Mohawk) village sites in New York (Smith-Pagerie, Klock and Garoga), and a fourth early historic Indigenous site, Brigg’s Run, and re-assess the wider chronology of the Mohawk River Valley in the mid-15th to earlier 17th centuries. This new chronology confirms initial suggestions from radiocarbon that a wholesale reappraisal of past assumptions is necessary, since our dates conflict completely with past dates and the previously presumed temporal order of these three iconic sites. In turn, a wider reassessment of northeastern North American early history and re-interpretation of Atlantic connectivities in the later 15th through early 17th centuries is required. Our new closely defined date ranges are achieved employing detailed archival analysis of excavation records to establish the contextual history for radiocarbon-dated samples from each site, tree-ring defined short time series from wood charcoal samples fitted against the radiocarbon calibration curve (‘wiggle-matching’), and Bayesian chronological modelling for each of the individual sites integrating all available prior knowledge and radiocarbon dating probabilities. We define (our preferred model) most likely (68.3% highest posterior density) village occupation ranges for Smith-Pagerie of ~1478–1498, Klock of ~1499–1521, Garoga of ~1550–1582, and Brigg’s Run of ~1619–1632.
... Finally, to securely evaluate the relationship between dated samples and their archaeological context, models using Bayesian statistics are crucial. The accuracy of these models strongly depends on the kind of data that are introduced: e.g., the number of samples dated, the 'prior' information (e.g., stratigraphy), and the error range of the 14 C dates [51]. Moreover, a precise chronology is also strictly related to the quality and preservation of the archaeological record. ...
Radiocarbon dating is the most widely applied dating method in archaeology, especially in human evolution studies, where it is used to determine the chronology of key events, such as the replacement of Neanderthals by modern humans in Europe. However, the method does not always provide precise and accurate enough ages to understand the important processes of human evolution. Here we review the newest method developments in radiocarbon dating ('Radiocarbon 3.0'), which can lead us to much better chronologies and understanding of the major events in recent human evolution. As an example, we apply these new methods to discuss the dating of the important Palaeolithic site of Bacho Kiro (Bulgaria).
... The radiocarbon dates were calibrated to a 95.4% probability range, using the SHCal20 Southern Hemisphere atmospheric curve (Hogg et al. 2020). Bayesian modeling utilizes a statistical approach to interpreting radiocarbon dates, incorporating assumptions known as priors, to constrain the resulting calibrated probability distributions for groups of dates (Bayliss and Bronk Ramsey 2004;Bronk Ramsey 2015). Bayesian modeling of prior assumptions alongside radiocarbon dates can be used to obtain improved chronological resolution for sites and events, e.g., the timing of Inka expansion. ...
Estadio de Quillota (EDQ) is the largest known pre-Columbian cemetery site within the Aconcagua Valley of Central Chile. Despite its importance, existing chronological data for EDQ are limited and questions remain regarding the prehistory of the Valley, particularly around the adoption and intensification of maize agriculture, as well as the timing of Inka influence reaching the region. Seventeen new AMS radiocarbon dates presented here indicate two distinct phases of use at EDQ: An earlier phase (339–196 cal BC to cal AD 128–339), and a later phase (cal AD 1280–1387 to cal AD 1413–1458). Accompanying stable isotope (δ ¹³ C and δ ¹⁵ N) analyses of human bone collagen (n=22) demonstrate diachronic dietary changes corresponding to these phases, with a reliance on terrestrial C 3 resources during the earlier period, followed by a heavy dependence on C 4 -based (maize) resources during the later use. Bayesian modeling of the dates from Late Period contexts suggests Inka influence arrived in Central Chile by ca. cal AD 1400, decades before the date cited in traditional chronologies, AD 1471. Inka expansion likely occurred here with an initial phase of interaction and exchange preceding a later phase of integration. This finding supports growing evidence that the traditional chronology of the Inka Empire requires reconsideration.
... Bayesian statistical techniques provide an alternative method to interrogate these datasets. Bayesian methods have been used to address both new and long-standing chronological questions (Bayliss, 2009;Bayliss & Bronk Ramsey, 2004;Culleton et al., 2012;Hamilton & Kenney, 2015;Kennett et al., 2014;Pluckhahn et al., 2015;Turck & Thompson, 2016). Bayesian methods, in contrast to traditional statistical techniques, rely on probability curves, a priori information, and numerous, iterative permutations. ...
Important methodological advances have led to the availability of high-resolution datasets relating to environment, settlement, and chronology in archaeological studies. Such advances in resolution can lead to new understandings, but they also create new issues. In this chapter, we discuss synthetic datasets and their utility in identifying and understanding large-scale population movements. We focus on the 14th and 15th century AD Savannah River Valley as a case study given its position as one of the earliest, synthetic explorations of the multi-faceted relationship between settlement, mobility, climate, and culture in the archaeological literature of the Eastern Woodlands. We begin by outlining some of the history of synthetic approaches to settlement and demographic analysis in Eastern North America and discuss how this tradition of study has successfully and productively made the leap to the digital realm in recent years, using the Digital Index of North American Archaeology (DINAA) as an example. We then demonstrate how the types of data indexed by DINAA can be used to identify regional population shifts and investigate the demographic and social trajectories in play. This approach provides an alternative to traditional methods of identifying episodes of migration, such as the various analyses applied to artifact assemblages or to ancestral remains. Due to the nature of the archaeological record in this region, which we will return to, these more traditional analytical approaches are not always applicable or available. Using newly created digital datasets, we present evidence for a large-scale immigration to the neighboring coastal region of Georgia, using methods that we believe can be widely and productively applied elsewhere to document large-scale population movements.
... Additional uncertainty from the calibration of raw dates to calendar dates can further widen the age span due to the presence of numerous wiggles and plateaus in the calibration curve leading often to multi-decadal, multi-centennial age ranges (40-60 or even several hundred years). A series of 14 C dates with known stratigraphy can be finetuned using Bayesian modeling approaches, as the a priori information on the stratigraphic position of the samples and their association can help us to adjust imprecision generated by the calibration curve (Bayliss 2007(Bayliss , 2009Bayliss and Bronk Ramsey 2004;Bayliss et al. 2007;Buck et al. 1991Buck et al. , 1996. The age given by written historical sources dating the site use between 1577 and 1692 and the typochronology of artifacts recovered serves as extra a priori information on the association of the 14 C dated samples and are built into the model itself as constraints (Buck et al. 1991(Buck et al. , 1996Gulyás et al. 2018). ...
One of the most influential rulers of the sixteenth century, Sultan Suleyman I, passed away and was buried temporarily near the fortress of Szigetvár in SW Hungary in 1566. Later, a memorial place was erected on the site in the second half of the sixteenth century. The complex was surrounded by a palisade system and a moat on its northern side. The site was fully destroyed in 1692, and the exact location vanished with time. Recent investigations of historical sources complemented by geophysical, archeological, and geoarcheological investigations managed to identify the location of the site, and probe corings revealed the moat system. This study presents the results of complex chronological, sedimentological, and geochemical investigations done on the sediments accumulated in the moat. Based on geoarcheological data, two major changes could have been noted in the nature of the deposit marking erosion and transportation of soil from the banks of the moat. Elevated concentrations of Fe and K, and high MS values mark the effects of fire on the deposit and accumulation of flue ash. A rise in heavy metals in these horizons is attributable to anthropogenic sources related to the destruction of the site. Chronological data comes from dateable artifacts reposited and ¹⁴ C dates of charred cereal seeds. A Bayesian age model built using ¹⁴ C ages constrained by written historical data on site use helped us to determine the age of moat construction and the referred erosion-accumulation events. The older event was dated around 1670, which is in line with historical records of the first siege of Szigetvár. The second event postdates 1684 and thus must correspond to the time of the site’s final siege and later destruction.
... The dating of mounds has been addressed by Erens et al. (2015) where the centre of the mound was sampled with an auger. Optical luminescence and C14 dating should both be undertaken and combined with Bayesian modelling to increase confidence that results are not aberrations caused by bioturbation (Bayliss and Ramsey 2004;Ramsey 2009). ...
Using multidisciplinary literature, this paper takes a multispecies approach to human-termite interactions across the tropics to demonstrate how termites exploit ecological effects of human behaviours and in turn provide humans with significant ecosystem services. These provisions are deeply entangled within cultural practices and ideologies. Conceptualisations of human and landscape fertility, and the role of termites in facilitating life, create gendered interactions that are manifested in ecological knowledge and praxis relating to termites and termite mounds. The strong association between termites and farmers in particular, may offer insights into past human settlement patterns and their relationships with ecosystems. This paper proposes the use of geomorphology, thin-section ceramic petrography, and stable isotope analysis to investigate these relationships across the tropics. A multispecies approach creates new possibilities for a diachronic understanding of human ecology and raises important questions for the Anthropocene and the future of farming in the tropics.
... Borić and others 2018; Sanjuan and others 2018). The strati graphical information either in terms of Harris matrices (trenches) or depth information (sediment profiles) could then be used to inform Bayesian models (Bayliss and Ramsey 2004;Blaauw and Christen 2011). Summarizing activity plots based on all 14 C and OSL dates from the riverine hinterland would then allow for using kernel density estimation (KDE) within a Bayesian framework (Ramsey 2017). ...
Rivers have always been a magnet for human settlement, providing resources, such as water, food, and energy, and communication and travel routes. Climate- and human-made changes to the environment can easily affect the fragile balance between the 'natural' and the 'urban', causing droughts, floods, and other changes in riverine systems that challenge economic, environmental, and social sustainability. This is especially true in semiarid regions and in times of rapid climate change and human-driven deterioration of the environment. Therefore a deeper understanding is needed of the evolution of urban-riverine relationships within long-term historical frameworks. This article presents an integrative and interdisciplinary programme for research, which although exemplified by one case study-the city of Gerasa/ Jerash and its hinterland in modern Jordan-can be applied to other locations and regions with benefits.
Reconstructing the biological profile of a skeletal sample is essential for defining a particular demographic group or classifying isolated remains. These results allow us to complete the population pyramid of a settlement, analyse mortality trends and relate individuals of a particular sex or age-at-death category to possible funerary rituals, lifestyles and/or states of health and disease. In this work, we carry out a paleodemographic analysis of a singular tomb: the chalcolithic burial site of Camino del Molino, Murcia, SE Spain. The tomb hosted 1348 individuals (30.7% non-adults and 69.3% adults) over two contiguous funerary phases, spanning a large part of the third millennium BC, which makes it a reference site for knowledge of the Recent Prehistoric populations. For this purpose, we estimated different paleodemographic parameters (life tables, mortality rates and sex ratios) and compared them to model life tables of preindustrial populations and data from other contemporary peninsular series to evaluate possible demographic anomalies. The results suggest that Camino del Molino was home to individuals of all ages and sex. However, there is a clear under-representation of newborns and nursing/ breastfeeding infants and an over-representation of 5-15-year-old individuals. These findings could indicate potential issues related to diet/weaning, disease and early inclusion in the economic activities of the group.
Project Location: The project area is located in the former
Ballona Lagoon, a prehistoric wetland complex in west Los
Angeles that is known collectively as the Ballona. That area is
today bounded, roughly, by Playa del Rey to the west, Marina
del Rey to the north, the Ballona Escarpment (a high bluff )
and Del Rey Hills/Westchester Bluffs to the south, and Interstate
405 to the east. It is located approximately 0.5 km
east of the Pacific Ocean, near Santa Monica Bay, along that
section of the coast; 1.3 km west of the Baldwin Hills; and
1.6–2.6 km north of Los Angeles International Airport. Ballona
Creek, a drainage that is now channelized, crosses the
project area; Centinela Creek, a spring-fed drainage, once
ran along the southern portion of the project area, along the
base of the Ballona Escarpment.
Project Description: Statistical Research, Inc., (SRI) conducted
research—including testing, evaluation to determine
eligibility for listing in the National Register of Historic Places
(NRHP), and data recovery—at eight sites in the Ballona
(CA-LAN-54/H, CA-LAN-62/H, CA-LAN-193/H, CALAN-
211/H, CA-LAN-1932/H, CA-LAN-2676/H, CALAN-
2768/H, and CA-LAN-2769/H) (hereinafter in this
volume, the prefix “CA-” and the suffix “/H” will be omitted).
Of those eight sites, five were recommended eligible for
listing in the NRHP: LAN-54, LAN-62, LAN-193, LAN-
211, and LAN-2768. Data recovery was conducted at those
five sites (Altschul 1991; Altschul et al. 1991; Altschul et al.
1998a; Altschul et al. 1999; Altschul et al. 2003; Keller and
Altschul 2002; Van Galder et al. 2006; Vargas and Altschul
2001a; Vargas et al. 2005). Research designs and plans of work
were developed and implemented (after review by regulatory
agencies). In addition, related research in the Ballona included
a paleoenvironmental study of the area (Volume 1 of the Playa
Vista Archaeological and Historical Project [PVAHP] series),
analyses and results of material classes and subsistence data
(Volume 3 of the series), and bioarchaeology (Volume 4 of the
series). The final volume in the series (Volume 5) synthesizes
the work presented in other volumes and offers detailed discussions
and modeling of the Native Californians, including
the Gabrielino/Tongva, who lived in the Ballona for thousands
of years. Volume 5 also includes detailed mortuary-analysis
ethnohistoric studies for the Ballona. This volume (Volume
2 of the series) presents the methods and results of the data
recovery at the five sites. In addition, it details the inventory
of the entire project area and documents additional sites that
either were found not eligible for listing in the NRHP or
were not evaluated.
Project Summary: This volume of the PVAHP series presents
the methodology and approach to large data recovery at
complex sites in an alluvial context, the results of the chronostratigraphic
reconstruction, and the descriptive results
of the data recovery, with emphasis on midden-constituent
analysis and feature typology. The long-term occupation in
the Ballona, from 8,000 years ago through the Mission and
early Historical periods, has been well documented through
these excavations. The large-scale excavations yielded large
data sets with complex temporal and spatial contexts that
are discussed in detail in this volume. This project is among
the very large-scale and rigorous studies of Native American
adaptations in the southern California coastal region, especially
for the Mission period Gabrielino/Tongva territory.
The data presented here illustrate both stability and change
in cultural systems extending back 8,000 years, including
denser occupations during the Protohistoric and Mission
periods. The most-pronounced changes occurred at the
beginning and end of the Intermediate period and at the
start of the Protohistoric and Mission periods.
This paper highlights some of the main developments to the radiocarbon calibration program, OxCal. In addition to many cosmetic changes, the latest version of OxCal uses some different algorithms for the treatment of multiple phases. The theoretical framework behind these is discussed and some model calculations demonstrated. Significant changes have also been made to the sampling algorithms used which improve the convergence of the Bayesian analysis. The convergence itself is also reported in a more comprehensive way so that problems can be traced to specific parts of the model. The use of convergence data, and other techniques for testing the implications of particular models, are described.
Statistical analysis is becoming much more widely used in conjunction with radiocarbon dating. In this paper I discuss the impact of Bayesian analysis (using computer programs such as OxCal) on archaeological research. In addition to simple analysis, the method has implications for the planning of dating projects and the assessment of the reliability of dates in their context.
A new formalism for describing chronological models is introduced here: the Chronological Query Language (CQL), an extension of the model definitions found in the program OxCal.
New methods of Bayesian analysis can be used to overcome some of the inherent biases in the uncertainty estimates of scientific dating methods. Most of these methods, including ¹⁴ C, uranium series and thermoluminescence (TL), tend to favor some calendar dates over others. ¹⁴ C calibration overcomes the problem where this is possible, but a Bayesian approach can be used more generally.
People usually study the chronologies of archaeological sites and geological sequences using many different kinds of evidence, taking into account calibrated radiocarbon dates, other dating methods and stratigraphic information. Many individual case studies demonstrate the value of using statistical methods to combine these different types of information. I have developed a computer program, OxCal, running under Windows 3.1 (for IBM PCs), that will perform both 14 C calibration and calculate what extra information can be gained from stratigraphic evidence. The program can perform automatic wiggle matches and calculate probability distributions for samples in sequences and phases. The program is written in C++ and uses Bayesian statistics and Gibbs sampling for the calculations. The program is very easy to use, both for simple calibration and complex site analysis, and will produce graphical output from virtually any printer.
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 chronology study of the cemetery of Marquises of Jin is valuable to improving the chronological table of Marquis of Jin family. It is also helpful for improving the chronological table of the Zhou Dynasty. The samples were measured at Peking University (PKUAMS). We also made an interlaboratory check with Isotrace to ensure the accuracy. By careful analysis of archaeological information, we built different models and calibrated by OxCal. The calibration results, both sampling contexts and estimations, are in very good agreement with the historical record. Because the dates of some events correspond to the special part of the curve, the calibration gets very high precision. The calibration result of tomb M93 suggests that its host is Marquis Shangshu instead of Marquis Wen.
This paper summarizes radiocarbon measurements of mainly botanical samples from the Iceman (“Ötzi”) and from his discovery site, an Alpine glacier at the Austrian-Italian border. The results were obtained by accelerator mass spectrometry (AMS) at 3 different laboratories (Vienna, Austria; Uppsala, Sweden; Gif-sur-Yvette, France) between 1992 and 1997. All the dates, except 2, are consistent with the time period 3360–3100 BC, as previously determined from bone and tissue samples from the Iceman himself. The 2 exceptional dates from wooden artifacts suggest that the site of the Iceman was used as a mountain pass for millennia prior to and after the lifetime of “Ötzi”.
For a 2nd sample complex, we studied logs from the beginning of salt mining in the world's oldest salt mines at Hallstatt in Upper Austria. ¹⁴ C AMS measurements were performed in Vienna on spruce samples found in the prehistoric mines and from a log-house on the surface. Data evaluation included “wiggle matching” of different sets of tree rings. The results suggest that salt mining in the Hallstatt region took place in the 14th–13th century BC, well before the so-called Hallstatt period.
We discuss in some detail the chemical pretreatment of the samples and the data evaluation. We also present a comprehensive survey of ¹⁴ C dates available in the literature concerning both botanical remains from the vicinity of the Iceman and from the earliest salt mining in Hallstatt.
This chapter provides an overview of a topic that is likely to become increasingly important as greater numbers of researchers adopt formal statistical models for constructing chronologies. Other chapters in this volume (1, 2, 3, 10 and 11) use single statistical models, but in the future, as researchers attempt to draw together coherently information from different sources, they will almost certainly develop several alternative models for a single problem. Different statistical models may, however, produce very different interpretations of the same data and thus give rise to conflicting reconstructions of the past. In such situations, we need a robust way to investigate which models are best supported by the data. This chapter outlines recent developments in the application of formal Bayesian model choice techniques to archaeological chronology building and illustrates these tools using two examples, one from absolute and the other from relative chronology building problems. A particular advantage of Bayesian model choice techniques lies in their ability to compare widely different models based on differing assumptions and prior information.