Environmental and Ecological Statistics

, Volume 21, Issue 2, pp 313–328 | Cite as

Inference for finite-sample trajectories in dynamic multi-state site-occupancy models using hidden Markov model smoothing

  • Ian J. Fiske
  • J. Andrew Royle
  • Kevin Gross


Ecologists and wildlife biologists increasingly use latent variable models to study patterns of species occurrence when detection is imperfect. These models have recently been generalized to accommodate both a more expansive description of state than simple presence or absence, and Markovian dynamics in the latent state over successive sampling seasons. In this paper, we write these multi-season, multi-state models as hidden Markov models to find both maximum likelihood estimates of model parameters and finite-sample estimators of the trajectory of the latent state over time. These estimators are especially useful for characterizing population trends in species of conservation concern. We also develop parametric bootstrap procedures that allow formal inference about latent trend. We examine model behavior through simulation, and we apply the model to data from the North American Amphibian Monitoring Program.


Amphibians Finite-sample trajectory Hidden Markov model Occupancy Trend estimation Wildlife 



We thank Linda Weir of PWRC for providing NAAMP data, and we thank John Monahan, Brian Reich and Len Stefanski for constructive comments and discussion. IJF and KG were supported by Grant DEB 08-42101 from the National Science Foundation.

Supplementary material

10651_2013_256_MOESM1_ESM.pdf (335 kb)
Supplementary material 1 (PDF 335 KB)


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of StatisticsNorth Carolina State UniversityRaleighUSA
  2. 2.USGS Patuxent Wildlife Research CenterLaurelUSA

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