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Hierarchical modelling of archaeomagnetic data and curve estimation by moving average technique

Abstract : A Bayesian hierarchical modelling is proposed for the different sources of scatter occurring in archaeomagnetism, which follows the natural hierarchical sampling process implemented by laboratories in field. A comparison is made with the stratified statistics commonly used up to now. The Bayesian statistics corrects the disturbance resulting from the variability in the number of specimens taken from each sample or site. There is no need to publish results at sample level if a descending hierarchy is verified. In this case, often verified by archaeomagnetic data, only results at site level are useful for geomagnetic reference curve building. Typically, a study with at least 20 samples will give an α95i 5 per cent close to the optimal α95i for a fixed site number mi and if errors are random with zero mean (no systematic errors). The precision on the curve itself is essentially controlled, through hierarchical elliptic statistics, by the number of reference points per window and by dating errors, rather than by the confidence angles α95ij at site level (if a descending hierarchy). The Bayesian elliptic distribution proposed reveals the influence of the window width. The moving average technique is well adapted to numerous and very well dated data evenly distributed along time. It is not a global functional approach, but a (linear) local one.
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Philippe Lanos, Maxime Le Goff, Mary Kovacheva, Elisabeth Schnepp. Hierarchical modelling of archaeomagnetic data and curve estimation by moving average technique. Geophysical Journal International, Oxford University Press (OUP), 2005, 160 (2), pp.440-476. ⟨10.1111/j.1365-246X.2005.02490.x⟩. ⟨halshs-00396776⟩

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