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A Bayesian approach to identifying and compensating for model misspecification in population models.

James T Thorson, Kotaro Ono, Stephan B Munch

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    |March 28, 2014
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    Summary

    Bayesian semiparametric state-space models using Gaussian processes (GP) improve ecological population estimates when true dynamics are unknown. These models better approximate population growth functions and identify model misspecification.

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    Area of Science:

    • Ecology
    • Statistical Modeling
    • Population Dynamics

    Background:

    • State-space models are vital for estimating population abundance and productivity.
    • A key limitation is the potential mismatch between assumed functional forms and true biological processes, degrading model performance.
    • This mismatch can lead to inaccurate ecological insights.

    Purpose of the Study:

    • To develop a Bayesian semiparametric state-space model using Gaussian processes (GP) to enhance population dynamics estimation.
    • To allow data to inform the population growth function while retaining prior information when data are scarce.
    • To decompose population variability into process error and model error, enabling detection of model misspecification.

    Main Methods:

    • Developed a Bayesian semiparametric state-space model incorporating a Gaussian process (GP) to approximate the population growth function.
    • Utilized simulation modeling to assess the performance of the GP-based approach against conventional state-space models.
    • Analyzed the decomposition of population variability into process and model errors.

    Main Results:

    • The GP model performed comparably to conventional models when the prior matched true dynamics or data were uninformative.
    • GP methods significantly improved estimates of the population growth function when it was misspecified.
    • The magnitude of estimated "model error" effectively indicated instances of model misspecification.

    Conclusions:

    • Bayesian semiparametric state-space models with GPs offer a robust approach for ecological population estimation, particularly when underlying dynamics are uncertain.
    • The ability to quantify "model error" provides a valuable diagnostic for model adequacy.
    • GP methods hold promise for application in various advanced state-space models in ecology.