Assessing convergence of the Markov chain Monte Carlo method in multivariate case

Abstract

The formal convergence diagnosis of the Markov Chain Monte Carlo (MCMC) is made using univariate and multivariate criteria. In 1998, a multivariate extension of the univariate criterion of multiple sequences was proposed. However, due to some problems of that multivariate criterion, an alternative form of calculation was proposed in addition to the two new alternatives for multivariate convergence criteria. In this study, two models were used, one related to time series with two interventions and ARMA (2, 2) error and another related to a trivariate normal distribution, considering three different cases for the covariance matrix. In both the cases, the Gibbs sampler and the proposed criteria to monitor the convergence were used. Results revealed the proposed criteria to be adequate, besides being easy to implement.