10.25440/smu.12310106.v1
Zeng TAO
Zeng
TAO
Three essays on Bayesian hypothesis testing and model selection
SMU Research Data Repository (RDR)
2020
DIC
EM Alogorithm
Deviance
Decision Theory
Specification Test
Markov Chain Monte Carlo
Econometric and Statistical Methods
2020-05-15 08:46:48
Thesis
https://researchdata.smu.edu.sg/articles/thesis/Three_essays_on_Bayesian_hypothesis_testing_and_model_selection/12310106
<table><tr>
<td><p>My
dissertation consists of three essays which contribute new theoretical
results to Bayesian hypothesis and model selection.</p>
<br>
<p>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.</p><br>
<p>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.</p>
<br>
<p>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.</p></td></tr></table>