calculations. For this model (Table 1), the automated procedure converges on the All Scalar al- gorithm, which is the same as its initial state, and which produces overall MCMC Efficiency of about 3. In hindsight this result may not surprise us, since the fully exchangeable nature of the random effects in this model does not induce correlations among the sampled parameters for this particular dataset. Correspondingly, for a large number of un-correlated random effects, and in the absence of multivariate distributions, univariate sampling produces the highest Efficiency. We also note that the All Blocked algorithm, which consists of a single block sampler of dimension 858, has Runtime approximately twice that of the All Scalar algorithm, and produces an overall Efficiency of approximately 0.05. In Figure 4, we present the overall Efficiencies achieved for our suite of example models (excluding the two contrived model structures). The Auto Blocking algorithm consistently out-performs any static algorithm in terms of Efficiency, ranging between roughly a 50% increase to several orders of magnitude of improvement. The exception is the GLMM example, in which Auto Blocking matches the All Scalar algorithm identically. We observe variation in the relative Efficiencies among the Efficiency Gains from Automated Blocking Figure 4: Efficiencies of MCMC algorithms for the suite of example models. 27 0 10 20 30 40 Random Effects Auto Regressive St. Space Indep. Corr. Spatial GLMM Efficiency (effective samples / time) MCMC Algorithm All Block ed Default All Scalar Auto Blocking