On Model Comparison: Application of Savage-Dickey Density Ratio to Bayes Factor
Olawale B. Akanbi *
Department of Statistics, University of Ibadan, Nigeria.
Olusanya E. Olubusoye
Department of Statistics, University of Ibadan, Nigeria.
Samuel A. Babatunde
Department of Statistics, University of Ibadan, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Bayes factor is a major Bayesian tool for model comparison especially when the model priors are the same. In this paper, the Savage-Dickey Density Ratio (SDDR) is used to derive the Bayes factor to select a model from two competing models under consideration in a normal linear regression with an independent normal-gamma prior. The Gibbs sampling technique for the joint posterior distribution with equal prior precision for both the unrestricted and restricted models is used to obtain the model estimates. The result shows that the Bayes factor gave more support to the unrestricted model against the restricted and was consistent irrespective of changes in sample size.
Keywords: Nested model, prior precision, Savage-Dickey density ratio, Gibbs sampling.