Hierarchical Bayesian Markov switching models with application to predicting spawning success of shovelnose sturgeon

• Published in: Applied statistics Vol. 58; no. 1; pp. 47 - 64
• Main Authors: Holan, Scott H., Davis, Ginger M., Wildhaber, Mark L., DeLonay, Aaron J., Papoulias, Diana M.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.02.2009; Blackwell Publishing Ltd; Blackwell Publishing; Wiley-Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series C
• Subjects: Acipenser; Animal reproduction; Applications; Bayesian method; Biology; Biology, psychology, social sciences; Eigenvalue; Eigenvalues; Endangered & extinct species; Exact sciences and technology; Fish; Generalized auto-regressive conditional heteroscedasticity; Hierarchical Bayes model; Linear inference, regression; Markov analysis; Markov models; Markov switching; Mathematics; Missouri River; Modeling; Multilevel models; Musical intervals; Oocytes; Parallel computing; Parallel processing; Parametric models; Probability and statistics; Probability theory and stochastic processes; Regression analysis; Rivers; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistical methods; Statistics; Stochastic models; Stochastic volatility; Studies; Sturgeon; Success; Telemetry; Vector-autoregressive models; Missouri River; United States > US; USA, Missouri R; Conditional distribution; Eigenvalue; Probability distribution; Computing; Linear model; Transition matrix; Hierarchical Bayes model; Transition probability; Stochastic volatility; Bayes estimation; Linear regression; Missouri River; Sturgeon; Markov model; Telemetry; Statistics; Heteroscedasticity; Statistical method; Statistical regression; Parallel computing; Regression model; Markov switching; Environment; Hierarchical model; Generalized auto-regressive conditional heteroscedasticity; Application
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/j.1467-9876.2008.00642.x

The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed.