Statistical Science

Multivariate State Hidden Markov Models for Mark-Recapture Data

Devin S. Johnson, Jeff L. Laake, Sharon R. Melin, and Robert L. DeLong

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State-based Cormack–Jolly–Seber (CJS) models have become an often used method for assessing states or conditions of free-ranging animals through time. Although originally envisioned to account for differences in survival and observation processes when animals are moving though various geographical strata, the model has evolved to model vital rates in different life-history or diseased states. We further extend this useful class of models to the case of multivariate state data. Researchers can record values of several different states of interest, for example, geographic location and reproductive state. Traditionally, these would be aggregated into one state with a single probability of state uncertainty. However, by modeling states as a multivariate vector, one can account for partial knowledge of the vector as well as dependence between the state variables in a parsimonious way. A hidden Markov model (HMM) formulation allows straightforward maximum likelihood inference. The proposed HMM models are demonstrated with a case study using data from a California sea lion vital rates study.

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Statist. Sci., Volume 31, Number 2 (2016), 233-244.

First available in Project Euclid: 24 May 2016

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Capture-recapture Cormack–Jolly–Seber hidden Markov model multivariate partial observation state uncertainty


Johnson, Devin S.; Laake, Jeff L.; Melin, Sharon R.; DeLong, Robert L. Multivariate State Hidden Markov Models for Mark-Recapture Data. Statist. Sci. 31 (2016), no. 2, 233--244. doi:10.1214/15-STS542.

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Supplemental materials

  • Supplement A: Notation summary and additional sea lion analysis details. Contains additional tables that summarize notation used throughout the paper and provides additional details and results for the analysis of sea lion data in Section 3.
  • Supplement B: R code used to analyze sea lion data. Contains the R code used to run the sea lion example analysis in Section 3. The most up-to-date version of the marked package can be installed directly using the R package devtools with the command: devtools::install_github("jlaake/marked/ marked"). However, in order to install this version, users need to ensure that their machines are equipped to compile R packages with source code (namely, Fortran and C++). Using the R console, the command, install.packages("marked"), will install a precompiled binary version from CRAN.