• New Methods and Critical Aspects in Bayesian Mathematics for 14C Calibration

      Steier, Peter; Rom, Werner; Puchegger, Stephan (Department of Geosciences, The University of Arizona, 2001-01-01)
      The probabilistic radiocarbon calibration approach, which largely has replaced the intercept method in 14C dating, is based on the so-called Bayes' theorem (Bayes 1763). Besides single-sample calibration, Bayesian mathematics also supplies tools for combining 14C results of many samples with independent archaeological information such as typology or stratigraphy (Buck et al. 1996). However, specific assumptions in the "prior probabilities", used to transform the archaeological information into mathematical probability distributions, may bias the results (Steier and Rom 2000). A general technique for guarding against such a bias is "sensitivity analysis", in which a range of possible prior probabilities is tested. Only results that prove robust in this analysis should be used. We demonstrate the impact of this method for an assumed, yet realistic case of stratigraphically ordered samples from the Hallstatt period, i.e. The Early Iron Age in Central Europe.
    • The Filling of Gaps in Geophysical Time Series by Artificial Neural Networks

      Dergachev, Valentin A.; Gorban, A. N.; Rossiev, A. A.; Karimova, L. M.; Kuandykov, E. V.; Makarenko, G. G.; Steier, Peter (Department of Geosciences, The University of Arizona, 2001-01-01)
      Nowadays, there is a large number of time series of natural data to study geophysical and astrophysical phenomena and their characteristics. However, short length and data gaps pose a substantial problem for obtaining results on properties of the underlying physical phenomena with existing algorithms. Using only an equidistant subset of the data with coarse steps leads to loss of information. We present a method to recover missing data in time series. The approach is based on modeling the time series with manifolds of small dimension, and it is implemented with the help of neural networks. We applied this approach to real data on cosmogenic isotopes, demonstrating that it could successfully repair gaps where data was purposely left out. Multi-fractal analysis was applied to a true radiocarbon time series after recovering missing data.