Efficient sequential Monte Carlo algorithms for integrated population models

In statistical ecology, state-space models are commonly used to represent the
biological mechanisms by which population counts - often subdivided according to characteristics such as age group, gender or breeding status - evolve over time. As the population counts are typically only noisily or partially observed, the information from the count data alone is not sufficient for sensibly estimating demographic parameters of interest. Thus, the count data are combined with additional ecological observations to form an integrated data analysis. Unfortunately, fitting integrated models can be challenging, especially if the constituent state-space model is non-linear/non-Gaussian. We first propose an efficient particle Markov chain Monte Carlo algorithm to estimate demographic parameters without the need for resorting to linear or Gaussian approximations. We then incorporate this algorithm into a sequential Monte Carlo sampler in order to perform model comparison with regards to the dependence structure of demographic parameters. In particular, we exploit the integrated model structure to enhance the efficiency of both algorithms. We demonstrate the methods on two real data sets: little owls and grey herons. For the owls, we find that the data do not support an ecological hypothesis found in the literature. For the herons, our methodology highlights the limitations of existing models which we address through a novel regime-switching model.