top-level parameters. We cannot use a reduced data representation under the latent state approach, since for correct inference each of the 11,200 sighting histories must have a corre- sponding sequence of latent state variables. The latent state MCMC required approximately 24 hours to generate 100,000 samples, yielding a minimum sampling efficiency of 0.0027 ESPS and a mean of 0.028 ESPS. This approach can be deemed impractical, as this translates to generating ten effective samples (for the slowest mixing parameter) per hour. Applying the filtering MCMC to a reduced data representation using the 153 unique sighting histories, the complete model likelihood is calculated according to (7), using (5) to calculate the likelihood of each unique history. Computation time is reduced to 20 minutes, which agrees with the expected speedup factor of 11 , 200 153 ≈ 73 . 2. Mixing also improves to produce a minimum sampling efficiency of 0.20 ESPS, a 70-fold improvement relative to the latent state MCMC. This translates to 720 effective samples per hour, which may be considered practical. NIMBLE’s automated blocking procedure converges on seven blocks of parameters, rang- ing between two and five parameters each. These seven blocks include 20 of the 21 param- eters, leaving only one parameter for univariate sampling. It is realistically unlikely that a practitioner would discover this blocking scheme through expert opinion or trial and error. Runtime is comparable using this approach, but the joint sampling of correlated parameters gives a dramatic improvement in MCMC mixing. The minimum sampling efficiency improves by an additional order of magnitude to 2.4 ESPS, or generating over 8,600 effective samples per hour. This represents nearly a 1000-fold improvement over the latent state MCMC. We have studied alternate computational approaches for MCMC sampling of hierarchical models which include embedded discrete HMMs. Traditional MCMC analysis of such mod- els involves sampling the unknown (nuisance) latent states, whereas we propose filtering 5 Discussion 20