Journal of Mathematics and Statistics

Assessing Convergence of the Markov Chain Monte Carlo Method in Multivariate Case

Denismar Alves Nogueira, Thelma Safadi, Daniel Furtado Ferreira and Eric Batista Ferreira

DOI : 10.3844/jmssp.2012.471.480

Journal of Mathematics and Statistics

Volume 8, Issue 4

Pages 471-480

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.

Copyright

© 2012 Denismar Alves Nogueira, Thelma Safadi, Daniel Furtado Ferreira and Eric Batista Ferreira. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.