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Non‐linear state space modelling of fisheries biomass dynamics by using Metropolis‐Hastings within‐Gibbs sampling

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  • Russell B. Millar
  • Renate Meyer

Abstract

State space modelling and Bayesian analysis are both active areas of applied research in fisheries stock assessment. Combining these two methodologies facilitates the fitting of state space models that may be non‐linear and have non‐normal errors, and hence it is particularly useful for modelling fisheries dynamics. Here, this approach is demonstrated by fitting a non‐linear surplus production model to data on South Atlantic albacore tuna (Thunnus alalunga). The state space approach allows for random variability in both the data (the measurement of relative biomass) and in annual biomass dynamics of the tuna stock. Sampling from the joint posterior distribution of the unobservables was achieved by using Metropolis‐Hastings within‐Gibbs sampling.

Suggested Citation

  • Russell B. Millar & Renate Meyer, 2000. "Non‐linear state space modelling of fisheries biomass dynamics by using Metropolis‐Hastings within‐Gibbs sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(3), pages 327-342.
    • Handle: RePEc:bla:jorssc:v:49:y:2000:i:3:p:327-342
    DOI: 10.1111/1467-9876.00195
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    1. Dunham, Kylee & Grand, James B., 2016. "Effects of model complexity and priors on estimation using sequential importance sampling/resampling for species conservation," Ecological Modelling, Elsevier, vol. 340(C), pages 28-36.
    2. Christoph Berninger & Almond Stocker & David Rugamer, 2020. "A Bayesian Time-Varying Autoregressive Model for Improved Short- and Long-Term Prediction," Papers 2006.05750, arXiv.org, revised Feb 2021.
    3. Ruth King & Stephen P. Brooks & Chiara Mazzetta & Stephen N. Freeman & Byron J. T. Morgan, 2008. "Identifying and diagnosing population declines: a Bayesian assessment of lapwings in the UK," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(5), pages 609-632, December.
    4. Ji-Hoon Choi & Jae-Bong Lee & Sang-Chul Yoon & Do-Hoon Kim, 2021. "A Bioeconomic Analysis of the Sandfish ( Arctoscopus japonicus ) Management Policies of the Eastern Sea Danish Fishery in Korea," Sustainability, MDPI, vol. 13(14), pages 1-14, July.
    5. Gimenez, Olivier & Rossi, Vivien & Choquet, Rémi & Dehais, Camille & Doris, Blaise & Varella, Hubert & Vila, Jean-Pierre & Pradel, Roger, 2007. "State-space modelling of data on marked individuals," Ecological Modelling, Elsevier, vol. 206(3), pages 431-438.
    6. Ruiz, Javier & Prieto, Laura & Astorga, Diana, 2012. "A model for temperature control of jellyfish (Cotylorhiza tuberculata) outbreaks: A causal analysis in a Mediterranean coastal lagoon," Ecological Modelling, Elsevier, vol. 233(C), pages 59-69.
    7. Min-Je Choi & Do-Hoon Kim, 2020. "Assessment and Management of Small Yellow Croaker ( Larimichthys polyactis ) Stocks in South Korea," Sustainability, MDPI, vol. 12(19), pages 1-17, October.
    8. Axel Finke & Ruth King & Alexandros Beskos & Petros Dellaportas, 2019. "Efficient Sequential Monte Carlo Algorithms for Integrated Population Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(2), pages 204-224, June.
    9. Roa-Ureta, Ruben H. & Santos, Miguel N. & Leitão, Francisco, 2019. "Modelling long-term fisheries data to resolve the attraction versus production dilemma of artificial reefs," Ecological Modelling, Elsevier, vol. 407(C), pages 1-1.
    10. Su, Zhenming & Peterman, Randall M., 2012. "Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error," Ecological Modelling, Elsevier, vol. 224(1), pages 76-89.
    11. Russell B. Millar, 2004. "Sensitivity of Bayes Estimators to Hyper-Parameters with an Application to Maximum Yield from Fisheries," Biometrics, The International Biometric Society, vol. 60(2), pages 536-542, June.
    12. I. B. J. Goudie & M. Goudie, 2007. "Who captures the marks for the Petersen estimator?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(3), pages 825-839, July.
    13. Chaloupka, Milani & Balazs, George, 2007. "Using Bayesian state-space modelling to assess the recovery and harvest potential of the Hawaiian green sea turtle stock," Ecological Modelling, Elsevier, vol. 205(1), pages 93-109.

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