Novel Statistical Model for a Piece-Wise Linear Radiocarbon Calibration Curve

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Abstract
The process of calibrating radiocarbon determinations onto the calendar scale requires the setting of a specific statistical model for the calibration curve. This model specification will bear fundamental importance for the resulting inference regarding the parameter of interest—namely, in general, the calendar age associated to the sample that has been 14C-dated.Traditionally, the 14C calibration curve has been modelled simply as the piece-wise linear curve joining the (internationally agreed) high-precision calibration data points; or, less frequently, by proposing spline functions in order to obtain a smoother curve.We present a model for the 14C calibration curve which, based on specific characteristics of the dating method, yields a piece-wise linear curve, but one which rather than interpolating the data points, smooths them. We show that with this specific model if a piece-wise linear curve is desired, an underlying random walk model is implied as covariance structure (and vice versa). Furthermore, by making use of all the information provided by the calibration data in a comprehensive way, we achieve an improvement over current models by getting more realistic variance values for the calibration curve.