STATISTICAL METHODS OF TIME SEQUENCING.
Abstract
The problem of ordering archeological artifacts in their correct time-sequence is the motivation for the mathematical developments and the results which are reported. The following model is assumed. For each deposit located there corresponds a population; the artifacts found in the deposit are a sample drawn from that population. Suppose, for example, that varying quantities of different types of pottery are found at several locations. Here, there exists a positive symmetric measure of similarity d sub jk between the jth and the kth population. If the deposits are labeled from 1 to n according to the correct time sequence, then the following holds: (1) d sub jk > d sub ji for i > k > j and d sub jk > d sub ji for i < k < j. The problem of ordering is formulated as follows: Let D be an unknown matrix satisfying (1). Let P be an unknown permutation matrix and let C be an error matrix. The matrix U = PDP' + C is observed. P is to be determined. A procedure to determine P is proposed and its performance is investigated. For some classes of matrices which satisfy (1), the components of the eigenvectors have special rank-order properties. The procedure is based on these properties. The procedure is applied to three matrices computed from archaeological data. The procedure is applied also to matrices whose elements are compoundsed with random errors generated by simulation. It is successful even when the errors have large variances. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 22, 1965
- Accession Number
- AD0625560
Entities
People
- Haim Sternin
Organizations
- Stanford University