Efficient Sequential Monte Carlo Algorithms for Integrated Population Models
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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 counts are only noisily or partially observed, they are typically not sufficiently informative about demographic parameters of interest and must be combined with additional ecological observations within an integrated data analysis. Fitting integrated models can be challenging, especially if the constituent state-space model is nonlinear/non-Gaussian. We first propose an efficient particle Markov chain Monte Carlo algorithm to estimate demographic parameters without a need for linear or Gaussian approximations. We then incorporate this algorithm into a sequential Monte Carlo sampler to perform model comparison. We also exploit the integrated model structure to enhance the efficiency of both algorithms. The methods are demonstrated 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. Supplementary materials accompanying this paper appear online.
KeywordsBayesian inference Capture–recapture Integrated population models Model comparison Sequential Monte Carlo State-space models
This work was supported by The Alan Turing Institute under the EPSRC Grant EP/N510129/1. AB and AF were funded by a Leverhulme Trust Prize.
- Abadi, F., Gimenez, O., Arlettaz, R., and Schaub, M. (2010a). An assessment of integrated population models: Bias, accuracy, and violation of the assumption of independence. Ecology, 91(1):7–14.Google Scholar
- Abadi, F., Gimenez, O., Ullrich, B., Arlettaz, R., and Schaub, M. (2010b). Estimation of immigration rate using integrated population models. Journal of Applied Ecology, 47(2):393–400.Google Scholar
- Bernardo, J. M. and Smith, A. F. M. (2009). Bayesian Theory. Wiley.Google Scholar
- Besbeas, P., Borysiewicz, R. S., and Morgan, B. J. T. (2009). Completing the Ecological Jigsaw. In Modeling Demographic Processes in Marked Populations, pages 513–539. Springer.Google Scholar
- Besbeas, P., Freeman, S. N., Morgan, B. J. T., and Catchpole, E. A. (2002). Integrating mark-recapture-recovery and census data to estimate animal abundance and demographic parameters. Biometrics, 58(3):540–547.Google Scholar
- Breed, G., Costa, D., Jonsen, I., Robinson, P., and Mills-Flemming, J. (2012). State-space methods for more completely capturing behavioral dynamics from animal tracks. Ecological Modelling, 235:49–58.Google Scholar
- Brooks, S. P., King, R., and Morgan, B. J. T. (2004). A Bayesian approach to combining animal abundance and demographic data. Animal Biodiversity and Conservation, 27(1):515–529.Google Scholar
- Carpenter, B., Gelman, A., Hoffman, M. D., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., and Riddell, A. (2017). Stan: A probabilistic programming language. Journal of Statistical Software, 76(1).Google Scholar
- Doucet, A. and Johansen, A. M. (2011). A tutorial on particle filtering and smoothing: Fifteen years later. In Crisan, D. and Rozovskii, B., editors, The Oxford Handbook of Nonlinear Filtering, Oxford Handbooks, chapter 24, pages 656–704. Oxford University Press.Google Scholar
- Gilks, W. R., Thomas, A., and Spiegelhalter, D. J. (1994). A language and program for complex Bayesian modelling. Journal of the Royal Statistical Society. Series D (The Statistician) , 43(1):169–177.Google Scholar
- Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Journal of Basic Engineering, 82(1):35–45.Google Scholar
- King, R. (2011). Statistical Ecology. In Brooks, S., Gelman, A., Jones, G., and Meng, X.-L., editors, Handbook of Markov Chain Monte Carlo, chapter 17, pages 410–447. CRC Press.Google Scholar
- King, R. (2012). A review of Bayesian state-space modelling of capture-recapture-recovery data. Interface Focus, 2:190–204.Google Scholar
- King, R. (2014). Statistical ecology. Annual Review of Statistics and its Application, 1(1):401–426.Google Scholar
- Knape, J. and de Valpine, P. (2012). Fitting complex population models by combining particle filters with Markov chain Monte Carlo. Ecology, 93(2):256–263.Google Scholar
- McClintock, B. T., King, R., Thomas, L., Matthiopoulos, J., McConnell, B. J., and Morales, J. M. (2012). A general discrete-time modeling framework for animal movement using multi-state random walks. Ecological Monographs, 82(3):335–349.Google Scholar
- McCrea, R. S. and Morgan, B. J. T. (2014). Analysis of Capture-Recapture Data. CRC Press.Google Scholar
- Morales, J., Haydon, D., Frair, J., Holsiner, K., and Fryxell, J. (2004). Extracting more out of relocation data: Building movement models as mixtures of random walks. Ecology, 85(9):2436–2445.Google Scholar
- Newman, K. B., Buckland, S. T., Morgan, B. J. T., King, R., Borchers, D. L., Cole, D., Besbeas, P. T., Gimenez, O., and Thomas, L. (2014). Modelling Population Dynamics: Model Formulation, Fitting and Assessment using State-space Methods. Springer.Google Scholar
- Nishimura, A., Dunson, D., and Lu, J. (2017). Discontinuous Hamiltonian Monte Carlo for models with discrete parameters and discontinuous likelihoods. ArXiv e-prints arXiv:1705.08510.
- Parslow, J., Cressie, N., Campbell, E. P., Jones, E., and Murray, L. (2013). Bayesian learning and predictability in a stochastic nonlinear dynamical model. Ecological Applications, 23(4):679–698.Google Scholar
- Peters, G. W., Hosack, G. R., and Hayes, K. R. (2010). Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC). ArXiv e-prints arXiv:1005.2238.
- Plummer, M. (2003). JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. In Proceedings of the 3rd International Workshop on Distributed Statistical Computing. Vienna, Austria.Google Scholar
- Schaub, M., Ullrich, B., Knötzsch, G., Albrecht, P., and Meisser, C. (2006). Local population dynamics and the impact of scale and isolation: A study on different little owl populations. Oikos, 115(3):389–400.Google Scholar
- Sherlock, C., Thiery, A., and Golightly, A. (2015). Efficiency of delayed-acceptance random walk Metropolis algorithms. ArXiv e-prints arXiv:1506.08155.