On Model Comparison: Application of Savage-Dickey Density Ratio to Bayes Factor

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.

Likelihood Ratio Search Procedure for Optimum Number of States in a Hidden Markov Manpower Model

“…The proposed search procedure utilizes the likelihood ratio statistic in pairwise comparison test to locate the HMMM that has the optimum number of hidden states among a number of HMMMs ordered according to a desired property. Though there are many methods of model comparison, see, for example [17,18], the likelihood ratio test is chosen because it is considered as the only statistical test which can be used to directly compare the goodness-of-fit of two models [2,19]. The HMMM is first specified and estimated.…”