Model Determination using Predictive Distributions with Implementation via Sampling-Based Methods

Model determination is divided into the issues of model adequacy and model selection and it is proposed to validate conditional predictive distributions arising from single point deletion against observed responses.

Abstract

Abstract Model determination is divided into the issues of model adequacy and model selection. Predictive distributions are used to address both issues. This seems natural since, typically, prediction is a primary purpose for the chosen model. A cross-validation viewpoint is argued for. In particular, for a given model, it is proposed to validate conditional predictive distributions arising from single point deletion against observed responses. Sampling based methods are used to carry out required calculations. An example investigates the adequacy of and rather subtle choice between two sigmoidal growth models of the same dimension.