## Three essays on Bayesian hypothesis testing and model selection

My dissertation consists of three essays which contribute new theoretical results to Bayesian hypothesis and model selection. Chapter 2 shows that the data augmentation technique undermines the theoretical underpinnings of the deviance information criterion (DIC), a widely used information criterion for Bayesian model comparison, although it facilitates parameter estimation for latent variable models via Markov chain Monte Carlo (MCMC) simulation. Data augmentation makes the likelihood function non-regular and hence invalidates the standard asymptotic arguments. A robust form of DIC, denoted as RDIC, is advocated for Bayesian comparison of latent variable models. RDIC is shown to be a good approximation to DIC without data augmentation. While the later quantity is difficult to compute, the expectation – maximization (EM) algorithm facilitates the computation of RDIC when the MCMC output is available. Moreover, RDIC is robust to nonlinear transformations of latent variables and distributional representations of model specification. The proposed approach is applied to several popular models in economics and finance. While DIC is very sensitive to the nonlinear transformations of latent variables in these models, RDIC is robust to these transformations. As a result, substantial discrepancy has been found between DIC and RDIC. Chapter 3 proposes a new Bayesian approach to test a point null hypothesis based on the deviance in a decision-theoretical framework. The proposed test statistic may be regarded as the Bayesian version of likelihood ratio test and appeals in practical applications with three desirable properties. First, it is immune to Bartlett’s paradox. Second, it avoids Jeffreys-Lindley’s paradox, Third, it is easy to compute and its threshold value is easily derived, facilitating the implementation in practice. The method is applied to three real examples in economics and finance. Empirical results confirm the strength of the test over the Bayes factor and reject the wellknown three factor Fama-French model. Chapter 4 proposes a Bayesian method for assess the model specification of an econometric model after it is estimated by Bayesian MCMC methods. The proposed approach does not required an alternative model be specified and is applicable to a variety of models, including latent variable models for which frequentist’s methods are more difficult to use. It is shown that the proposed statistic and its threshold values are easy to compute. The method is illustrated using the Fama-French asset price model and dynamic stochastic general equilibrium (DSGE) model. |