Variance estimation for integrated population models
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State-space models are widely used in ecology. However, it is well known that in practice it can be difficult to estimate both the process and observation variances that occur in such models. We consider this issue for integrated population models, which incorporate state-space models for population dynamics. To some extent, the mechanism of integrated population models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the observation variance is estimated as zero. In the context of an extended case study involving data on British Grey herons, we consider alternative approaches for dealing with the problem when it occurs. In particular, we consider penalised likelihood, a method based on fitting splines and a method of pseudo-replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper, it is shown that when it occurs, an estimate of zero observation variance is unimportant for inference relating to the model parameters of primary interest. This unexpected finding is supported by a simulation study.
KeywordsBootstrap Cross-validation Cubic splines Grey heron Mark–recovery–recapture data Overfitting Penalised likelihood Plug-in method Process/observation error estimation State-space models Time-dependent parameters
We thank the Associate Editor, Roland Langrock, two anonymous referees, Stephen Freeman, Mark Maunder, Leo Polanski and Martin Ridout for their very helpful comments.
- Besbeas, P., Morgan, B.J.T.: Kalman filter initialisation for integrated population modelling. Appl. Stat. 61, 151–162 (2011)Google Scholar
- Besbeas, P., Borysiewicz, R.S., Morgan, B.J.T.: Completing the ecological jigsaw. In: D.L. Thomson, E.G. Cooch, and M. J. Conroy (Eds.) Modelling Demographic Processes in Marked Populations. Springer Series: Environmental and Ecological Statistics, vol. 3, pp. 513–540. Springer, Berlin (2009)Google Scholar
- Besbeas, P., McCrea, R.S., Morgan, B.J.T.: Integrated population model selection in ecology. University of Kent Technical Report. https://kar.kent.ac.uk/id/eprint/48039 (2015)
- Brooks, S.P., King, R., Morgan, B.J.T.: A Bayesian approach to combining animal abundance and demographic data. Anim. Biodivers. Conserv. 27, 515–529 (2004)Google Scholar
- Kéry, M., Schaub, M.: Bayesian Population Analysis using WinBUGS: A Hierarchical Perspective. Academic Press, Cambridge (2012)Google Scholar
- Maunder, M.N., Deriso, R.B., Hanson, C.H.: Use of state-space population dynamics models in hypothesis testing: advantages over simple log-linear regressions for modeling survival, illustrated with application to longfin smelt (Spirinchus thaleichthys). Fish. Res. 164, 102–111 (2015)CrossRefGoogle Scholar
- Mazzettta, C., Morgan, B.J.T., Coulson, T.: A state-space modelling approach to population size estimation. Technical report, University of Kent Technical Report: UKC/SMSAS/10/025 (2010)Google Scholar
- Patterson, T.A., Parton, A., Langrock, R., Blackwell, P.G., Thomas, L., King. R.: Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges. arXiv:1603.07511v3 [stat.AP] (2017)