MODIFIED MAHALANOBIS FILTERS FOR GROUPING POTTERY BY CHEMICAL COMPOSITION*

TLDR

The method uses a Mahalanobis filter with X² statistics to group pottery and assign sherds, accounting for correlations, measurement uncertainty, dilution shifts, and other data distortions, thereby replacing PCA or cluster analysis. The procedure is routinely used in the laboratory and, by accounting for dilution, improves assignment and separation of reference groups, equivalent to a compositional data approach with log‑transformed data.

Abstract

A statistical procedure for grouping pottery in provenance studies by chemical data is presented, which now is routinely in use in our laboratory. It is based on the Mahalanobis filter method and X 2 ‐statistics, and can be used for both establishing groups and assigning single sherds to already known groups, thus replacing principal components analysis or cluster analysis and avoiding their problems in grouping pottery. The new method is able to consider correlations, uncertainties of measurement and constant shifts of the data in case of dilution. In particular, considering dilution effects results in both a better assignment to and separation of reference groups and is also equivalent to the compositional data approach, if log‐transformed data are used. Other distortions of data (e.g., mixing of clays) can also be considered.