Bayesian hypothesis testing in latent variable models

Abstract

Hypothesis testing using Bayes factors (BFs) is known not to be well defined under the improper prior. In the context of latent variable models, an additional problem with BFs is that they are difficult to compute. In this paper, a new Bayesian method, based on decision theory and the EM algorithm, is introduced to test a point hypothesis in latent variable models. The new statistic is a by-product of the Bayesian MCMC output and, hence, easy to compute. It is shown that the new statistic is easy to interpret and appropriately defined under improper priors because the method employs a continuous loss function. The method is illustrated using a one-factor asset pricing model and a stochastic volatility model with jumps.JEL classification: C11, C12, G12.

Bayesian Testing for Asset Volatility Persistence on Multivariate Stochastic Volatility Models

“…  denotes a model which provides a description of the probabilistic behavior of observable data when the null hypothesis H 0 is true. According to the work of Li and Yu [12], the unit root testing problem can be regarded as a decision problem where the action space has only two elements, namely to accept (a 0 ) or to reject (a 1 ) model M 0 as a convenient proxy for model M.…”

“…However, for multivariate SV models considered in this paper, the likelihood function don't have closed-form solution so that K-L loss function also don't have closed-form, hence, can not be applied. Following Li and Yu [12], the continuous divergence function based on   Q   mainly used in EM algorithm is developed to replace K-L divergence function.…”

“…This continued to pose a computational challenge and numerical instability. More recent literature has addressed the point-null hypothesis testing problem, for which Li and Yu [12] has developed a decisional Bayesian hypothesis testing approach to replace the Bayes factor. It was shown that the developed Bayesian test statistic may be implemented under noninformative priors, and was only a log-likelihood ratio as a by-product of Bayesian estimation, hence computationally simple and stable.…”

“…As to unit root testing problem in the univariate SV models, Zhang, Li and Zhang [13] showed that the decisional Bayesian approach by Li and Yu [12] can achieve better finite-sample behaviors than Bayes factor. In this paper, we consider the asset return volatility persistence on multivariate SV models, which are a generalized extension of univariate SV models.…”

“…More details of this issue were developed in the review paper about multivariate SV models by Asai, et al [14]. Also, development of the Bayesian test statistic for testing a unit root is based on the work of Li and Yu [12].…”