Sufficient statistic likelihood construction for age- and time-dependent multi-state joint recapture and recovery data

Two closed-form likelihoods for multi-state joint recapture and recovery data were proposed in King and Brooks (2003); the first incorporated dependence on time and cohort whilst the second included dependence on age and cohort. However, when multi-state joint recapture and recovery data are modelled, it is likely that dependence on age and time will both be potentially of interest and therefore the most useful model formulation will incorporate both of these parameter structures. Within this article the likelihood function required for such a model is derived in terms of a set of sufficient statistics.