Hypothesis testing, specification testing and model selection based on the MCMC output using R - LI, Yong (Institutional Knowledge at Singapore Management University, 2019)
This chapter overviews several MCMC-based test statistics for hypothesis testing andspecification testing and MCMC-based model selection criteria developed in recentyears. The statistics for hypothesis testing can be viewed as the MCMC version ofthe “trinity” of test statistics based in maximum likelihood (ML), namely, the likelihoodratio (LR) test, the Lagrange multiplier (LM) test, and the Wald test. The model selection criteria correspond to two predictive distributions. One of them can be viewed asthe MCMC version of widely used information criterion, AIC. The asymptotic distributions of the test statistics and model selection criteria are discussed. The test statisticsand model selection criteria are applied to several popular models using real data,one of which involves latent variables. The implementation is illustrated in R withthe MCMC output obtained by R2WinBUGS.