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Modelling species abundance in a river by Negative Binomial hidden Markov models

Listed author(s):
  • Spezia, L.
  • Cooksley, S.L.
  • Brewer, M.J.
  • Donnelly, D.
  • Tree, A.
Registered author(s):

    The investigation of species abundance in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, a Bayesian hierarchical model within the class of hidden Markov models is proposed to map the distribution of freshwater pearl mussels in the River Dee (Scotland). In order to model the overdispersed series of mussel counts, the conditional probability function of each observation, given the hidden state, is assumed to be Negative Binomial. Both the transition probabilities of the hidden Markov chain and the state-dependent means of the observed process depend on covariates obtained from a hydromorphological survey. Bayesian inference, model choice, and covariate selection based on Markov chain Monte Carlo algorithms are presented. The stochastic selection of the explanatory variables which are associated with a reduced chance of finding a local mussel population provides new evidence for the causes of the deterioration of a highly threatened species.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313003411
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 71 (2014)
    Issue (Month): C ()
    Pages: 599-614

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    Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:599-614
    DOI: 10.1016/j.csda.2013.09.017
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Konrad Banachewicz & André Lucas & Aad van der Vaart, 2008. "Modelling Portfolio Defaults Using Hidden Markov Models with Covariates," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 155-171, March.
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    3. Cameron, A Colin & Trivedi, Pravin K, 1986. "Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 29-53, January.
    4. Murakami, Junko, 2009. "Bayesian posterior mean estimates for Poisson hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 941-955, February.
    5. Wang, Peiming & Alba, Joseph D., 2006. "A zero-inflated negative binomial regression model with hidden Markov chain," Economics Letters, Elsevier, vol. 92(2), pages 209-213, August.
    6. Paroli, Roberta & Spezia, Luigi, 2008. "Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2311-2330, January.
    7. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
    8. Altman, Rachel MacKay, 2007. "Mixed Hidden Markov Models: An Extension of the Hidden Markov Model to the Longitudinal Data Setting," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 201-210, March.
    9. Filardo, Andrew J, 1994. "Business-Cycle Phases and Their Transitional Dynamics," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 299-308, July.
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