Environmental and Ecological Statistics

, Volume 21, Issue 2, pp 313-328

First online:

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

  • Ian J. FiskeAffiliated withDepartment of Statistics, North Carolina State University
  • , J. Andrew RoyleAffiliated withUSGS Patuxent Wildlife Research Center
  • , Kevin GrossAffiliated withDepartment of Statistics, North Carolina State University Email author 

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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