Exact inference for integrated population modelling

Integrated population modelling is widely used in statistical ecology. It allows data from population time series and independent surveys to be analysed simultaneously. In classical analysis the time‐series likelihood component can be conveniently approximated using Kalman filter methodology. However, the natural way to model systems which have a discrete state space is to use hidden Markov models (HMMs). The proposed method avoids the Kalman filter approximations and Monte Carlo simulations. Subject to possible numerical sensitivity analysis, it is exact, flexible, and allows the use of standard techniques of classical inference. We apply the approach to data on Little owls, where the model is shown to require a one‐dimensional state space, and Northern lapwings, with a two‐dimensional state space. In the former example the method identifies a parameter redundancy which changes the perception of the data needed to estimate immigration in integrated population modelling. The latter example may be analysed using either first‐ or second‐order HMMs, describing numbers of one‐year olds and adults or adults only, respectively. The use of first‐order chains is found to be more efficient, mainly due to the smaller number of one‐year olds than adults in this application. For the lapwing modelling it is necessary to group the states in order to reduce the large dimension of the state space. Results check with Bayesian and Kalman filter analyses, and avenues for future research are identified.