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Hidden Markov models for extended batch data

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  • Laura L. E. Cowen
  • Panagiotis Besbeas
  • Byron J. T. Morgan
  • Carl J. Schwarz

Abstract

Batch marking provides an important and efficient way to estimate the survival probabilities and population sizes of wild animals. It is particularly useful when dealing with animals that are difficult to mark individually. For the first time, we provide the likelihood for extended batch‐marking experiments. It is often the case that samples contain individuals that remain unmarked, due to time and other constraints, and this information has not previously been analyzed. We provide ways of modeling such information, including an open N‐mixture approach. We demonstrate that models for both marked and unmarked individuals are hidden Markov models; this provides a unified approach, and is the key to developing methods for fast likelihood computation and maximization. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modeling. This allows the simultaneous estimation of population size and immigration, in addition to survival, as well as efficient estimation of standard errors and methods of model selection and evaluation, using standard likelihood techniques. Alternative methods for estimating population size are presented and compared. An illustration is provided by a weather‐loach data set, previously analyzed by means of a complex procedure of constructing a pseudo likelihood, the formation of estimating equations, the use of sandwich estimates of variance, and piecemeal estimation of population size. Simulation provides general validation of the hidden Markov model methods developed and demonstrates their excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically required

Suggested Citation

  • Laura L. E. Cowen & Panagiotis Besbeas & Byron J. T. Morgan & Carl J. Schwarz, 2017. "Hidden Markov models for extended batch data," Biometrics, The International Biometric Society, vol. 73(4), pages 1321-1331, December.
  • Handle: RePEc:bla:biomet:v:73:y:2017:i:4:p:1321-1331
    DOI: 10.1111/biom.12701
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    References listed on IDEAS

    as
    1. Laura Cowen & Carl J. Schwarz, 2006. "The Jolly–Seber Model with Tag Loss," Biometrics, The International Biometric Society, vol. 62(3), pages 699-705, September.
    2. P. Besbeas & S. N. Freeman & B. J. T. Morgan & E. A. Catchpole, 2002. "Integrating Mark–Recapture–Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters," Biometrics, The International Biometric Society, vol. 58(3), pages 540-547, September.
    3. D. Dail & L. Madsen, 2011. "Models for Estimating Abundance from Repeated Counts of an Open Metapopulation," Biometrics, The International Biometric Society, vol. 67(2), pages 577-587, June.
    4. Emily B. Dennis & Byron J.T. Morgan & Martin S. Ridout, 2015. "Computational aspects of N-mixture models," Biometrics, The International Biometric Society, vol. 71(1), pages 237-246, March.
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    Cited by:

    1. Matthew R. P. Parker & Laura L. E. Cowen & Jiguo Cao & Lloyd T. Elliott, 2023. "Computational Efficiency and Precision for Replicated-Count and Batch-Marked Hidden Population Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 43-58, March.
    2. Darshini Jeyasimman & Bilge Ercan & Dennis Dharmawan & Tomoki Naito & Jingbo Sun & Yasunori Saheki, 2021. "PDZD-8 and TEX-2 regulate endosomal PI(4,5)P2 homeostasis via lipid transport to promote embryogenesis in C. elegans," Nature Communications, Nature, vol. 12(1), pages 1-21, December.
    3. Wei Zhang & Simon J. Bonner & Rachel S. McCrea, 2023. "Latent multinomial models for extended batch‐mark data," Biometrics, The International Biometric Society, vol. 79(3), pages 2732-2742, September.

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