Irmela HERZOG
(Bonn, Germany)
The Harris diagram is a well-known means to reconstruct the chronological sequence of archaeological contexts. Floating sequences, i.e. parallel strands in the diagram pose a problem, because the chronological sequence of the contexts is not fixed by stratigraphic relationships. Often additional dating information is available, for example dendrochronological evidence, radiocarbon data or diagnostic finds. Thus, spot dates and date intervals can be assigned to some of the stratigraphic units. Jürgen Hansohm proposed an algorithm which takes both the stratigraphic relationships and the date intervals of the contexts into account for reconstructing the chronological sequence. The aim of monotone or isotonic regression is to adjust the date intervals in such a way that they concord with the stratigraphic sequence but are as close as possible to the original date intervals. No efficient straight-forward algorithm is known which solves this problem, but Jürgen Hansohm designed an iterative method including an error estimate, and tests show that the outcome is close to the optimal solution. This paper will present some results of this method based on simulated data. The performance of the method will be investigated in terms of different levels of uncertainty: How does the average size of the date intervals influence the result? Does the variability of the interval size play a role in the goodness of fit? In practice, only for some of the stratigraphic units date intervals are known, and there are two ways to deal with the missing data: Either a reduced data set is created including only those stratigraphic units with date intervals, or all stratigraphic units are included in the analysis, and the algorithm assigns date intervals to the contexts which initially had no dates. This paper will present simulation studies to investigate which of the two approaches is best in which situation.
Keywords: monotone regression, stratigraphy, Harris diagram
References: Hansohm, J. 2007, Algorithms and error estimations for monotone regression on partially preordered sets. Journal of Multivariate Analysis 98: 1043 – 1050.