Optimizing Prediction with Hierarchical Models: Bayesian Clustering
José M. Bernardo · 2001
A frequent statistical problem is that of predicting a set of quantities given the values of some covariates, and the information provided by a training sample. These prediction problems are often structured with hierarchical models that make use of the similarities existing within classes of the population. Hierarchical models are typically based on a ‘natural’ definition of the clustering which defines the hierarchy, which is context dependent. However, there is no assurance that this ‘natural’ clustering is optimal in any sense for the stated prediction purposes. In this paper we explore the this issue by treating the choice of the clustering which defines the hierarchy as a formal decision problem. Actually, the methodology described may be seen as describing a large class of new clustering algorithms. The application which motivated this research is briefly described. The argument lies entirely within the Bayesian framework.