Topic status: We're looking for students to study this topic.
Multivariate mixture models provide a model-based approach to classification. For example, they have been used to determine ecoregions, which encompass similar environmental factors and conditions. As with other classification algorithms, the aim is to predict the most appropriate boundaries between regions, and the likelihood that each pixel belongs to each region (softclassification). In addition, the mixture model also provides a description of typical values and range of each environmental attribute within each ecoregion. When a mixture model is fit within the Bayesian paradigm, there is an option to include other information (such as expert knowledge) via an informative prior model. To date, almost all applications of Bayesian mixture models have focused on conjugate priors, namely the inverse Wishart for covariance matrices.
This project will explore other choices for the prior on covariance matrices, including various forms of mathematical decomposition.