Model selection using Minimal Message Length: an example using pollen data

In this paper we examine the use of the minimum message length criterion in the process of evaluating alternative models of data when the samples are serially ordered in space and implicitly in time. Much data from vegetation studies can be arranged in a sequence and in such cases the user may elect to constrain the clustering by zones, in preference to an unconstrained clustering. We use the minimum message length principle to determine if such a choice provides an effective model of the data. Pollen data provide a suitably organised set of samples, but have other properties which make it desirable to examine several different models for the distribution of palynomorphs within the clusters. The results suggest that zonation is not a particularly preferred model since it captures only a small part of the patterns present. It represents a user expectation regarding the nature of variation in the data and results in some patterns being neglected. By using unconstrained clustering within zones, we can recover some of this overlooked pattern. We then examine other evidence for the nature of change in vegetation and finally discuss the usefulness of the minimum message length as a guiding principle in model choice and its relationship to other possible criteria