Mixture Models for Dependent Observations

Parametric mixture models appropriate for data presented in homogeneous blocks of varying sizes from several unidentified source populations are considered. For most applications, the data elements within each block are dependent. Models are proposed for multivariate normal data incorporating two types of dependence, exchangeability of elements within blocks, and a Markov structure for blocks. The consequences of assuming exchangeability, when in fact the Markov structure holds, are explored. Computational problems for each model are considered, and results of a simple test of the exchangeability hypothesis for LANDSAT data are presented.