dataset. We use the NIMBLE package for R to generate and execute MCMC algorithms, as the algorithmic flexibility it provides facilitates these computational approaches. The use of user- defined distribution functions in NIMBLE allows us to incorporate the filtering algorithms (5) and (6) directly into a hierarchical model specification. The generic discrete HMM filtering procedure described in (5) is used for filtering, or when permitted by the model structure we instead use the closed form likelihood calculation given in (6). NIMBLE also provides the automated parameter blocking procedure (Turek et al., 2015) we use to generate problem-specific parameter blocking strategies for MCMC sampling. We define the efficiency of an MCMC algorithm in terms of the number of effectively independent posterior samples produced per second of algorithm runtime. This metric is denoted as effective samples per second (ESPS), and we will present both the minimum and mean ESPS among all model parameters. This metric balances the tradeoff between computationally fast algorithms which generate highly autocorrelated chains of posterior samples, versus algorithms which are more computationally demanding but result in lower posterior autocorrelation, which provides stronger inferential power. All algorithm runtimes represent the time required to generate 100,000 posterior samples. When possible, we also provide comparisons with MCMC algorithms from the JAGS software package for R. All calculations are produced using single-threaded execution on an Intel Xeon E5-2609 processor (2.40 GHz), running under the Ubuntu Linux operating system. For the Dipper model, use of the filtering MCMC compared to MCMC sampling of all discrete latent states yielded a 60-fold improvement in sampling efficiency in NIMBLE and a 15-fold improvement in JAGS (Figure 1). The sampling efficiencies of both top-level parameters are quite similar under each algorithm (although vary greatly between algorithms), hence the mean and the minimum summary statistics shown in Figure 1 are similar as well. 16 4.1 Dipper Model