Objective prior distributions for Jolly-Seber models of zero-augmented data

Statistical models of capture-recapture data that are used to estimate the dynamics of a population are known collectively as Jolly-Seber (JS) models. State-space versions of these models have been developed for the analysis of zero-augmented data that include the capture histories of the observed individuals and an arbitrarily large number of all-zero capture histories. The number of all-zero capture histories must be sufficiently large to include the unknown number N of individuals in the population that were ever alive during all sampling periods. This definition of N is equivalent to the "superpopulation" of individuals described in several JS models. To fit JS models of zero-augmented data, practitioners often assume a set of independent, uniform prior distributions for the recruitment parameters. However, if the number of capture histories is small compared to N, these uniform priors can exert considerable influence on the posterior distributions of N and other parameters because the uniform priors induce a highly skewed prior on N. In this article, I derive a class of prior distributions for the recruitment parameters of the JS model that can be used to specify objective prior distributions for N, including the discrete-uniform and the improper scale priors as special cases. This class of priors also may be used to specify prior knowledge about recruitment while still preserving the conditions needed to induce an objective prior on N. I use analyses of simulated and real data to illustrate the inferential benefits of this class of prior distributions and to identify circumstances where these benefits are most likely to be realized.