which makes use of state transition matrices and observation matrices We now present the performance of various computational strategies for MCMC estimation applied to the three example capture-recapture models. We do not present posterior results, but instead only the algorithmic efficiencies of each computational approach to generating these. For each, the posterior results of top-level parameters closely agree with existing published analyses of the same datasets and models (Lebreton et al., 1992; K´ ery and Schaub, 2012; Amstrup, McDonald, and Manly, 2010), which provides validation of our computational methodologies. We include results for the following computational strategies MCMC estimation: latent state MCMC (“Latent State”) where model parameters and latent states undergo MCMC sampling, filtering MCMC (“Filtering”) in which we filter over latent states and only top-level parameters undergo MCMC sampling, and a combination of filtering and blocking (“Filtering & Blocking”) in which a customized blocking strategy is used for MCMC sampling of top- level parameters. When appropriate, we also use a reduced representation (“RR”) of the 15 4 Performance Results Z$_{t}$ =       p$_{1}$$_{t}$ 0 0 0 0 p$_{2}$$_{t}$ 0 0 0 0 p$_{3}$$_{t}$ 0 1 − p$_{1}$$_{t}$ 1 − p$_{2}$$_{t}$ 1 − p$_{3}$$_{t}$ 1       . T$_{t}$ =       φ$_{1}$ψ$_{11}$$_{t}$ φ$_{2}$ψ$_{12}$$_{t}$ φ$_{3}$ψ$_{13}$$_{t}$ 0 φ$_{1}$ψ$_{21}$$_{t}$ φ$_{2}$ψ$_{22}$$_{t}$ φ$_{3}$ψ$_{23}$$_{t}$ 0 φ$_{1}$ψ$_{31}$$_{t}$ φ$_{2}$ψ$_{32}$$_{t}$ φ$_{3}$ψ$_{33}$$_{t}$ 0 1 − φ$_{1}$ 1 − φ$_{2}$ 1 − φ$_{3}$ 1      