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Abstract:
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Reaction-diffusion partial differential equation (PDE) models have been used within in a hierarchical Bayesian (HB) framework to understand and forecast a variety of physical and biological processes. To account for imperfect knowledge of the process embodied by the PDE and the discrepancies arising from the numerical approximation of the PDE, process error is included. But, what is the relationship among the numerical solution method, the process error, and the PDE parameter estimates? For example, if a potentially unstable numerical solution method is employed, how will the stability criteria impact the PDE parameter estimates? Here, we explore this question by comparing parameter estimates obtained under different solution methods within an HB framework. We present our findings using a PDE-HB model for observations of carbon dioxide flux through the snowpack in an alpine ecosystem.
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