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Bayesian analysis of radiocarbon dates

Christopher Bronk Ramsey
- 01 Jan 2009 - 
- Vol. 51, Iss: 1, pp 337-360
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TLDR
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) are given.
Abstract
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.

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Keanakākoʻi Tephra produced by 300 years of explosive eruptions following collapse of Kīlauea's caldera in about 1500 CE

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New insights on Late Quaternary Asian palaeomonsoon variability and the timing of the Last Glacial Maximum in southwestern China

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References
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BookDOI

Markov Chain Monte Carlo in Practice

TL;DR: The Markov Chain Monte Carlo Implementation Results Summary and Discussion MEDICAL MONITORING Introduction Modelling Medical Monitoring Computing Posterior Distributions Forecasting Model Criticism Illustrative Application Discussion MCMC for NONLINEAR HIERARCHICAL MODELS.
Journal ArticleDOI

Extended 14C Data Base and Revised Calib 3.0 14C Age Calibration Program

Minze Stuiver, +1 more
- 01 Jan 1993 - 
TL;DR: The age calibration program, CALIB (Stuiver & Reimer 1986), first made available in 1986 and subsequently modified in 1987 (revision 2.0 and 2.1), has been amended anew as mentioned in this paper.
Journal ArticleDOI

Sampling-Based Approaches to Calculating Marginal Densities

TL;DR: In this paper, three sampling-based approaches, namely stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm, are compared and contrasted in relation to various joint probability structures frequently encountered in applications.
Journal Article

Sampling-based approaches to calculating marginal densities

TL;DR: Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the calculation of numerical estimates of marginal probability distributions.
Journal ArticleDOI

Characterizing aquatic dissolved organic matter.

TL;DR: In this article, standards for reporting C-14 age determinations are discussed, and the statistical uncertainty (plus or minus one standard deviation) expresses counting errors, inaccuracies in voltage, pressure, temperature, dilution, and should include errors in C-13 ratios.
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