  State-space models are commonly used to describe different forms of
ecological data. We consider the case of count data with observation errors.
For such data the system process is typically multi-dimensional consisting of
coupled Markov processes, where each component corresponds to a different
characterisation of the population, such as age group, gender or breeding
status. The associated system process equations describe the biological
mechanisms under which the system evolves over time. However, there is often
limited information in the count data alone to sensibly estimate demographic
parameters of interest, so these are often combined with additional ecological
observations leading to an integrated data analysis. Unfortunately, fitting
these models to the data can be challenging, especially if the state-space
model for the count data is non-linear or non-Gaussian. We propose an efficient
particle Markov chain Monte Carlo algorithm to estimate the demographic
parameters without the need for resorting to linear or Gaussian approximations.
In particular, we exploit the integrated model structure to enhance the
efficiency of the algorithm. We then incorporate the algorithm into a
sequential Monte Carlo sampler in order to perform model comparison with
regards to the dependence structure of the demographic parameters. Finally, we
demonstrate the applicability and computational efficiency of our algorithms on
two real datasets.
