USING COUPLING WITH THE GIBBS SAMPLER TO ASSESS CONVERGENCE IN ANIMAL-MODELS

The coupling method was investigated as a method to assess the converg ence of the Gibbs sampler when drawing marginal inferences with an ani mal model. This method is based on the output of two Markov chains wit h different starting values but the same conditional deviates. The cou pling method shows that the Gibbs sampler has an exponential convergen ce when the variance components are assumed to be known. All the varia bles in the model have the same rate of convergence, and it is closely related with the largest eigenvalue of a matrix derived from the coef ficient matrix of the mixed model equations. Models including the vari ance components as unknowns showed a rate of convergence equal for all the variables, and this rate of convergence was approximately exponen tial. The coupling method provides an estimation of the convergence at the current iteration, and it does not require a post-Gibbs analysis as do the single chain-based methods. The coupling method is less comp utationally demanding than multiple chain methods, because only two ch ains are required to assess convergence.