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In this paper, a new and convenient $\chi^2$ wald test based on MCMC outputsis proposed for hypothesis testing. The new statistic can be explained as MCMCversion of Wald test and has several important advantages that make it veryconvenient in practical applications. First, it is well-defined under improperprior distributions and avoids Jeffrey-Lindley's paradox. Second, it'sasymptotic distribution can be proved to follow the $\chi^2$ distribution sothat the threshold values can be easily calibrated from this distribution.Third, it's statistical error can be derived using the Markov chain Monte Carlo(MCMC) approach. Fourth, most importantly, it is only based on the posteriorMCMC random samples drawn from the posterior distribution. Hence, it is onlythe by-product of the posterior outputs and very easy to compute. In addition,when the prior information is available, the finite sample theory is derivedfor the proposed test statistic. At last, the usefulness of the test isillustrated with several applications to latent variable models widely used ineconomics and finance.

A New Wald Test for Hypothesis Testing Based on MCMC outputs