Linear Gaussian State Space Models Table 1 presents results for both parameterizations of the state space model. In the Independent parameterization, the observation noise parameter is the slowest mixing, in all except the All Blocked algorithm. The All Blocked algorithm runs quickly, but is limited by the extremely low algorithmic efficiency of the AR process intercept parameter. The Default algorithm assigns conjugate normal samplers to each latent state, resulting in high algorithmic efficiency but a substantially longer Runtime, which diminishes the overall Efficiency. Auto Blocking (cut height h = 0.8) creates a block of six parameters containing five latent states and the observation noise, and a disjoint block of the two AR process parameters. This combination, unlikely to be discovered though any combination of prior knowledge or trial and error, produces a 40% increase in Efficiency over All Scalar sampling, which is the most efficient static MCMC algorithm. We suspect the intercept and autocorrelation parameters of the AR process to be correlated in the na¨ıve parameterization of the state space model. The All Blocked algorithm once again runs quickly, but is limited by the ESS of the AR process intercept. The Default algorithm is again slow due to conjugate sampling, but similar to the All Scalar algorithm, produces low algorithmic efficiency of the correlated AR process parameters. The Auto Blocking algorithm (cut height h = 0.1) selects the same parameter block as in the Informed Blocking algorithm (AR process intercept and autocorrelation), and additionally a block containing the observation noise and a latent state. The Runtimes are, accordingly, nearly identical, however the ESS of the observation noise, the limiting parameter, increases. Automated blocking produces Efficiency over 20 times higher than the All Blocked algorithm, which is the most efficient static algorithm, and 25% higher than the Informed Blocking algorithm. It is important to note that the automated blocking procedure overcame the sampling inefficiencies introduced by this na¨ıve parameterization, without requiring user intervention. MCMC performance results for the spatial model (Table 1) display several interesting trade-offs in MCMC efficiency. The spatial model contains 148 latent parameters jointly following a multivariate Spatial Model 25