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Non-parametric regression with observations at imprecise times: Bayesian radiocarbon calibration

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If you have a question about this talk, please contact Richard Nickl.

For accurate radiocarbon dating, it is necessary to identify fluctuations in the level of radioactive carbon (14C) over time. The processes that give rise to these fluctuations are not understood and so a datum-based calibration curve is required. Historic material can provide us with observations of radiocarbon levels at distinct times in the past, but in many cases the precise age of this material is unknown and must itself be estimated.

With some exceptions, the current non-parametric regression literature concentrates on the case where the times at which we observe the function are known precisely. In this talk we will present a general methodology for non-parametric regression, developed as part of this on-going radiocarbon calibration work, which can handle such imprecise time estimates.

In our approach, the underlying function is modelled as a Weiner process with sample paths that are updated, in light of the imprecise data, through use of a Metropolis-within-Gibbs algorithm. This methodology is computationally efficient due to the independent increment property of the process and use of a Brownian bridge.

http://maths.dept.shef.ac.uk/pas/staff_info.php?id=289

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