Abstract
The previous two chapters have presented the state-space model as a general framework for modelling population dynamics and discussed alternative ways of fitting SSMs to data. In this chapter, we address model formulation and model evaluation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
See, for example, http://www.kent.ac.uk/ims/personal/djc24/parameterredundancy.htm.
References
Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Second International Symposium on Information Theory (pp. 267–281). Budapest: Akademiai Kiado.
Anscombe, F.J. (1973). Graphs in Statistical Analysis. American Statistician, 27(1): 17–21
Arlot, S., & Celisse, A. (2010). A survey of cross-validation procedures for model selection. Statistics Surveys, 4, 40–79.
Besbeas, P., Freeman, S. N., Morgan, B. J. T., & Catchpole, E. A. (2002). Integrating mark-recapture-recovery and census data to estimate animal abundance and demographic parameters. Biometrics, 58, 540–547.
Brooks, S. P., Catchpole, E. A., Morgan, B. J. T., & Barry, S. C. (2000). On the Bayesian analysis of ring-recovery data. Biometrics, 56, 951–956.
Brooks, S. P., Friel, N., & King, R. (2003). Classical model selection via simulated annealing. Journal of the Royal Statistical Society B, 65, 503–520.
Brown, D. L. (2010). Climate modelling for animal survival. (Ph.D. thesis, University of Kent).
Buckland, S. T., Burnham, K. P., & Augustin, N. H. (1997). Model selection: An integral part of inference. Biometrics, 53, 603–618.
Burnham, K. P., & Anderson, D. R. (2002). Model selection and inference: A practical information-theoretic approach (2nd ed.). New York: Springer.
Catchpole, E. A., Freeman, S. N., & Morgan, B. J. T. (1996). Steps to parameter redundancy in age-dependent recovery models. Journal of the Royal Statistical Society B, 58, 763–774.
Catchpole. E. A., Freeman, S. N., Morgan, B. J. T., & Harris, M. P. (1998). Integrated recovery/recapture data analysis. Biometrics, 54(1), 33–46.
Catchpole, E. A., Kgosi, P. M., & Morgan, B. J. T. (2001). On the near-singularity of models for animal recovery data. Biometrics, 57, 720–726.
Catchpole, E. A., & Morgan, B. J. T. (1991). A note on Seber’s model for ring-recovery data. Biometrika, 78, 917–919.
Catchpole, E. A., & Morgan, B. J. T. (1996). Model selection in ring-recovery models using score tests. Biometrics, 52, 664–672.
Catchpole, E. A., & Morgan, B. J. T. (1997). Detecting parameter redundancy. Biometrika, 84, 187–196.
Catchpole, E. A., & Morgan, B. J. T. (2001). Deficiency of parameter-redundant models. Biometrika, 88, 593–598.
Catchpole, E. A., Morgan, B. J. T., & Freeman, S. N. (1998). Estimation in parameter redundant models. Biometrika, 85, 462–468.
Celeux, G., Forbes, C. P., Robert, C. P., & Titterington, D. M. (2006). Deviance information criteria for missing data models. Bayesian Analysis, 1, 651–674.
Choquet, R., & Cole, D. J. (2012). A hybrid symbolic-numerical method for determining model structure. Mathematical Biosciences, 236, 117–125.
Cole, D. J. (2012). Determining parameter redundancy of multi-state mark-recapture models for sea birds. Journal of Ornithology, 152(Suppl 2), 305–315.
Cole, D. J., & McCrea, R. S. (2012). Parameter redundancy in discrete state-space and integrated models. (Technical Report UKC/SMSAS/12/012). University of Kent.
Cole, D. J., & Morgan, B. J. T. (2010a). A note on determining parameter redundancy in age-dependent tag return models for estimating fishing mortality, natural mortality and selectivity. Journal of Agricultural, Biological, and Environmental Statistics, 15, 431–434.
Cole, D. J., & Morgan, B. J. T. (2010b). Parameter redundancy with covariates. Biometrika, 97, 1002–1005.
Cole, D. J., Morgan, B. J. T., Catchpole, E. A., & Hubbard, B.A. (2012). Parameter redundancy in mark-recovery models. Biometrical Journal, 54, 507–523.
Cole, D. J., Morgan, B. J. T., & Titterington, D. M. (2010). Determining the parametric structure of non-linear models. Mathematical Biosciences, 228, 16–30.
Cormack, R. M. (1964). Estimates of survival from the sighting of marked animals. Biometrika, 51, 429–438.
de Jong, P. (1988). A cross-validation filter for time series models. Biometrika, 75, 594–600.
Durbin, J., & Koopman, S. J. (2012). Time series analysis by state space methods, 2nd Edition. Oxford: Oxford University Press.
Edwards, D., & Havránek, T. (1985). A fast procedure for model search in multidimensional contingency tables. Biometrika, 72, 339–351.
Engle, R., & Watson, M. (1981). A one-factor multivariate time series model of metropolitan wage rates. Journal of the American Statistical Association, 76, 774–781.
Evans, N. D., & Chappell, M. J. (2000). Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems. Mathematical Biosciences, 168, 137–159.
Frühwirth-Schnatter, S. (1996). Recursive residuals and model diagnostics for normal and non-normal state space models. Environmental and Ecological Statistics, 3, 291–309.
Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D.B. (2003). Bayesian data analysis. Boca Raton: Chapman & Hall/CRC.
Gelman, A., & Meng, X. (1996). Model checking and model improvement. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov Chain Monte Carlo in Practice (pp. 189–201). London: Chapman & Hall.
Gimenez, O., Morgan, B. J. T., & Brooks, S. P. (2009b). Weak identifiability in models for mark-recapture-recovery data. In D. L. Thomson, E. G. Cooch, & M. J. Conroy (Eds.), Modelling demographic processes in marked populations. Environmental and ecological statistics (Vol. 3, pp. 1057–1070). Springer, New York.
Gimenez, O., Viallefont, A., Choquet, R., Catchpole, E. A., & Morgan, B. J. T. (2004). Methods for investigating parameter redundancy. Animal Biodiversity and Conservation, 27, 561–572.
Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–732.
Hart, J. D. (1994). Automated kernel smoothing of dependent data by using time series cross-validation. Journal of the Royal Statistics Society B, 56, 529–542.
Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge University Press.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). New York: Springer.
Hubbard, B. A., Cole, D. J., & Morgan, B. J. T. (2014). Parameter redundancy in capture-recapture-recovery models. Statistical Methodology, 17, 17–29.
Hunter, C. M., & Caswell, H. (2009). Rank and redundancy of multistate mark-recapture models for seabird populations with unobservable states. In D. L. Thomson, E. G. Cooch, & M. J. Conroy (Eds.), Modeling demographic processes in marked populations. Ecological and environmental statistics series (Vol. 3, pp. 797–826). Springer, New York.
Jiang, H., Pollock, K. H., Brownie, C., Hightower, J. E., Hoenig, J. M., & Hearn, W. S. (2007). Age-dependent tag return models for estimating fishing mortality, natural mortality and selectivity. Journal of Agricultural, Biological, and Environmental Statistics, 12,177–194.
Jolly, G. M. (1965). Explicit estimates from capture-recapture data with both death and immigration: Stochastic model. Biometrika, 52, 225–247.
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.
King, R., & Brooks, S. P. (2002). Bayesian model discrimination for multiple strata capture-recapture data. Biometrika, 89, 785–806.
King, R., & Brooks, S. P. (2004). A classical study of catch-effort models for Hector’s dolphins. Journal of the American Statistical Association, 99, 325–333.
King, R., Brooks, S. P., Mazzetta, C., Freeman, S. N., & Morgan, B. J. T. (2008). Identifying and diagnosing population declines: A Bayesian assessment of Lapwings in the UK. Applied Statistics, 57, 609–632.
King, R., Brooks, S. P., Morgan, B. J. T., & Coulson, T. (2006). Factors influencing Soay sheep survival: A Bayesian analysis. Biometrics, 62, 211–220.
King, R., Morgan, B. J. T., Gimenez, O., & Brooks, S. P. (2009). Bayesian analysis for population ecology. London: Chapman & Hall/CRC.
Kirkpatrick, S. (1984). Optimization by simulated annealing: Quantitative studies. Journal of Statistical Physics, 34, 975–986.
Knape, J., Besbeas, P., de Valpine, P. (2013). Using uncertainty estimates in analysis of population time series. Ecology, 94, 2097–2107.
McCrea, R. S., & Morgan, B. J. T. (2011). Multistate mark-recapture model selection using score tests. Biometrics, 67, 234–241.
Millar, R. B. (2009). Comparison of hierarchical Bayesian models for overdispersed count data using DIC and Bayes’ factors. Biometrics, 65, 962–969.
Morgan, B. J. T. (2009). Applied stochastic modelling (2nd ed.). Boca Raton: Chapman & Hall/CRC.
Morgan, B. J. T., Palmer, K. J., & Ridout, M. S. (2007). Negative score test statistic. American Statistician, 61, 285–288.
Neter, J., Kutner, M. H., Nachtsheim, C. J., & Wasserman, W. (1996). Applied linear statistical models (4th ed.). Boston: McGraw-Hill.
Pohjanpalo, H. (1978). System identifiability based on the power series of the solution. Mathematical Biosciences, 41, 21–33.
Rao, C. R. (1948). Large sample tests of statistical hypotheses concerning parameters with application to problems of estimation. Proceedings of the Cambridge Philosophical Society, 44, 50–57.
Schwarz, G. E. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.
Seber, G. A. F. (1965). A note on the multiple recapture census. Biometrika, 52, 249–259.
Seber, G. A. F. (1971). Estimating age-specific survival rates from bird-band returns when the reporting rate is constant. Biometrika, 58, 491–497.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van der Linde, A. (2002). Bayesian measures of complexity and fit (with discussion). Journal of the Royal Statistical Society B, 64, 583–616.
Starfield, A. M., & Bleloch, A. L. (1991). Building models for conservation and wildlife management (2nd ed.). Edina: The Burgess Press.
Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society B, 58, 267–288.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Newman, K.B. et al. (2014). Model Formulation and Evaluation. In: Modelling Population Dynamics. Methods in Statistical Ecology. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0977-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4939-0977-3_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0976-6
Online ISBN: 978-1-4939-0977-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)