Over the past year or so, Mark Madsen have been working on a research related the measurement of cultural transmission using frequency seriation methods. This work builds, obviously, on stuff we started back in 1997. Our primary goal has been to explore the link between the processes that produce the archaeological record (cultural transmission structure combined with assemblage accumulation and sampling) and the patterns that frequency seriation exploits for generating chronology. To do this effectively, we had to implement frequency seriation methods in a way that (1) matched the requirements of the method (i.e., the deterministic components) and (2) was automated so that we could begin to computationally evaluate the parameter space established by the processes producing/sampling the record. It is important to recognize that the means by which many people “do frequency seriation” — i.e., through probabilistic tools such as correspondence analysis — do not meet the requirements of the method, namely continuity and unimodality. In this effort, we wrote an iterative algorithm that constructs seriations from their smallest sets (sets of 3 assemblages) and then explores only the solutions that are valid when additional assemblages are added to the ends of the starting sets. While the approach does not solve all the problems inherent in frequency seriation (which has an incomprehensibly large search space when assemblages become >15), it makes it possible to systematically explore solutions for many archaeologically reasonable sets. The technique has led to some useful conclusions about seriation as a whole and has opened up new directions for studying cultural transmission. We will certainly be pursuing these in the months to come.
If you want to read more, we have just published a paper in PLoSOne: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0124942 Mark has set up a discussion session for the paper at Academia.edu: https://www.academia.edu/s/e376baef7d We’d love your feedback!