Bayesian Model Selection Criteria for Derived Quantities

Emmanuele Lesaffre, KU Leuven and University of Stellenbosch

Co-authors: Bijit Roy, KU Leuven

Abstract: The popular model selection criteria such as AIC, BIC, DIC and WAIC evaluate the appropriateness of the fitted model to the entire data. However, there are circumstances where interest lies in a particular aspect of the fitted model. In our motivating longitudinal growth curve study of newborn babies the aim is to evaluate the pattern of body mass index (BMI) especially at the end of year one. Instead of modeling BMI directly, one could model height and weight and compute BMI, derived from height and weight. Here we discuss model selection criteria that assess the prediction/estimation accuracy of quantities of interest. We propose the Bayesian Focused Information Criteria (BFIC) to assess the estimation accuracy of a model characteristic of interest, and the Derived WAIC (DWAIC) to asses the prediction accuracy of a derived response.