Efficient Sequential Monte Carlo Algorithms for Integrated Population Models

Abstract

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.

Bayesian statistics and modelling

“…For a review of these topics and further applications, we direct the reader elsewhere 166,174,175 . Bayesian model-fitting tools, such as MCMC with data augmentation 176 , sequential Monte Carlo or particle MCMC [177][178][179] , permit general state space models to be fitted to the observed data without the need to specify further restrictions -such as distributional assumptions -on the model specification, or to make additional likelihood approximations.…”

Exact Inference for Integrated Population Modelling

“…Whilst it will depend on the age of breeding assumed, this simplifying feature will commonly be the case. See for example Finke et al () for a further illustration.…”

“…Whilst it will depend on the age of breeding assumed, this simplifying feature will commonly be the case. See for example Finke et al (2019) for a further illustration. The extension of equation (18) to the case of more than 2 age classes is in principle straightforward, and dependent on the specifics of the Leslie matrix used in the model.…”

“…Literature surveys of IPM are provided by Schaub and Abadi (2011), and in fisheries science, by Maunder and Punt (2013). For recent research in IPM see for example Besbeas and Morgan (2017), Finke et al (2019) and Lahoz-Monfort et al (2017).…”

Sequential Importance Sampling With Corrections For Partially Observed States

“…In their method they introduced a schedule of intermediate weighting and resampling times between observation times, which guides particles towards the final state. Finke et al (2019) developed a Particle Monte Carlo Markov Chain algorithm to estimate the demographic parameters of a population and then incorporated this algorithm into a sequential Monte Carlo sampler in order to perform model comparison motivated by the fact that a simple importance sampling performs poorly if there is a strong mismatch between the prior and the posterior, which is common when the data is highly informative.…”