If radiocarbon measurements are to be used at all for chronological purposes, we have to use statistical methods for calibration. The most widely used method of calibration can be seen as a simple application of Bayesian statistics, which uses both the information from the new measurement and information from the 14C calibration curve. In most dating applications, however, we have larger numbers of 14C measurements and we wish to relate those to events in the past. Bayesian statistics provides a coherent framework in which such analysis can be performed and is becoming a core element in many 14C dating projects. This article gives an overview of the main model components used in chronological analysis, their mathematical formulation, and examples of how such analyses can be performed using the latest version of the OxCal software (v4). Many such models can be put together, in a modular fashion, from simple elements, with defined constraints and groupings. In other cases, the commonly used "uniform phase" models might not be appropriate, and ramped, exponential, or normal distributions of events might be more useful. When considering analyses of these kinds, it is useful to be able run simulations on synthetic data. Methods for performing such tests are discussed here along with other methods of diagnosing possible problems with statistical models of this kind.

/pdf/bayesian-analysis-of-radiocarbon-dates-26ui63c9ae.pdf

Bayesian analysis of radiocarbon dates

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

L'utilisation du programme informatique OxCal permet d'effectuer de nombreuses analyses sur les dates radiocarbones, de la simple calibration a l'analyse de tous les sites archeologiques en donnant des informations sur la stratigraphie et les autres methodes de datation

/pdf/radiocarbon-calibration-and-analysis-of-stratigraphy-the-54f40sv4ez.pdf

Radiocarbon Calibration and Analysis of Stratigraphy: The OxCal Program

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

/pdf/development-of-the-radiocarbon-calibration-program-4frtk6uug3.pdf

Development of the radiocarbon calibration program

https://c14.arch.ox.ac.uk/getPreprint.php?File=BronkRamsey2007.pdf

Deposition models for chronological records

The Bayesian Approach to Statistical Archaeology. Outline of the Approach. Modelling in Archaeology. Quantifying Uncertainty: The Probability Concept. Statistical Modelling. Bivariate and Multivariate Distributions. Bayesian Inference. Implementation Issues. Interpretation of Radiocarbon Results. Spatial Analysis. Sourcing and Provenancing. Application to Other Dating Methods. The Way Forward. References. Index.

/pdf/bayesian-approach-to-interpreting-archaeological-data-33b7qcmxwu.pdf

Bayesian Approach to Interpreting Archaeological Data

A recent and significant improvement in radiocarbon dating has been the increased ability of the radiocarbon laboratories to provide results combining precision with accuracy. This improvement has been accompanied by increasing recognition that the information must be expressed on the calendar, rather than on the radiocarbon, time-scale. Despite the attempts of Ottaway (1987) and Pearson (1987), archaeologists are not sufficiently aware of the statistical problems involved in the transformation from one scale to the other: ‘Some of the trouble lies in the ignorance of radiocarbon consumers; the many attempts to educate them can have only limited success when radiocarbon study depends on statistical concepts and methods far beyond the average archaeologist’s innumerate grasp’ (Chippindale 1990: 203).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0003598X00080534

Combining archaeological and radiocarbon information: a Bayesian approach to calibration

Calibration of radiocarbon results pertaining to related archaeological events

The revised radiocarbon calibration curve, published last year, extends back into the Pleistocene the radiocarbon determinations that can be converted to real calendar years. For determinations of any age, the right judgements and statistical considerations must be followed if the real information held in the determinations is to be found. Here is advice with some worked examples.

Making the most of radiocarbon dating: Some statistical considerations

Archaeological syntheses of western Ecuadorian prehisto7y have been hampered by a lack of reliable absolute chronologies and detailed cultural sequences for many key areas, one of which is northern Manabf Province, known principally as the territory of the Jama-Coaque cultural tradition. This study presents a seven-phase cultural sequence for the Jama River valley of northern Manabf that spans over 3,600 calendar years. A statistical model relating the successive archaeological phases is established, based on prior knowledge of the stratigraphy and ceramic seriation from key archaeological sites throughout the valley. A Bayesian statistical approach is then employed to calibrate 37 radiocarbon determinations for the purpose of estimating calendar dates for the limits of these phases. Apart from its contribution to the prehistory of a poorly studied area, the analysis illustrates the value of a probabilistic Bayesian approach to radiocarbon calibration, especially when the determinations relate to archaeologically predefined phases. It also demonstrates the dangers of uncritically applying generalized periodization schemes to specific sequences of historical development and highlights the need for reassessing Ecuadorian chronology through more precise interregional correlations.

C. D. Litton

Papers

Bayesian Approach to Interpreting Archaeological Data

Combining archaeological and radiocarbon information: a Bayesian approach to calibration

Calibration of radiocarbon results pertaining to related archaeological events

Making the most of radiocarbon dating: Some statistical considerations

Integration of archaeological phase information and radiocarbon results from the jama river valley, ecuador: a bayesian approach