Specification of informative priors for capture-recapture finite mixture models

Many models involve binomial terms depending on parameters p ∈ [0,1] representing probabilities. That is the case of capture-recapture experiments, where capture and survival of each individual at different occasions are modelled as Bernoulli trials with unknown probabilities. In most actual data applications, the population of interest typically exhibits unaccounted heterogeneity, presumably depending on its partitioning into a finite set of sub-populations, each one having its parameter value. If the sub-population labels are unknown, Finite Mixture Models (FMM) can be exploited to recover the unknown labels and all other model components jointly. Nevertheless, the naive application of finite mixture models within the Bayesian machinery is affected by the so-called label-switching problem. The group-specific parameters are assigned ordering constraints to identify their relative roles to overcome this issue. That is usually achieved by specifying conditionally uniform densities that respect such constraints, preventing the possibility to shape the prior according to available prior knowledge. In this work, we propose two flexible classes of joint priors based on manipulating Beta distributions. The idea is to specify a joint prior that retains the flexibility to induce the desired marginal behaviour while still guaranteeing the desired ordering.