3.3 Goose Model The multistate Goose model tracks n = 11 , 200 Canadian Geese ( Branta canadensis ) between three distinct locations over k = 4 years. Latent states X = { “site A” , “site B” , “site C” , “dead” } , with observable states Y = { “seen at A” , “seen at B” , “seen at C” , “not seen” } . There ex- ists a large number of identical sighting histories among the 11,200 geese, allowing a reduced representation using only the n ∗ = 153 unique sighting histories. The complete dataset can be found in Amstrup, McDonald, and Manly (2010). Following Amstrup, McDonald, and Manly (2010), we include site-dependent survival probabilities, and both time- and site-dependent geographic transition probabilities and probabilities of detection. We use uninformative priors for all parameters, including Dirichlet priors for each set of geographic transition probabilities. Subsequent works ( e.g. , McCrea and Morgan, 2011) have shown improved fits using more elaborate models for these data, but our purpose is to compare computational efficiency. We desire high efficiency regardless of model fit, so the particular choice of model is tangential to our main points. i assumes all values in 1 , . . . , n in the hierarchical specification below. 14 φ$_{r}$ ∼ Uniform(0 , 1) r = 1 , 2 , 3 { ψ$_{1}$$_{st}$, ψ$_{2}$$_{st}$, ψ$_{3}$$_{st}$ } ∼ Dirichlet( α = { 1 , 1 , 1 } ) s = 1 , 2 , 3 , t = 2 , 3 , 4 p$_{rt}$ ∼ Uniform(0 , 1) r = 1 , 2 , 3 , t = 1 , 2 , 3 , 4 X$_{i}$$_{1}$ = y$_{i}$$_{1}$ X$_{it}$ | X$_{i,t}$$_{−}$$_{1}$ ∼ Categorical( p = T$_{t}$ x$_{i,t}$$_{−}$$_{1}$ ) t = 2 , . . . , k Y$_{it}$ | X$_{it}$ ∼ Categorical( p = Z$_{t}$ x$_{it}$ ) t = 1 , . . . , k