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Abstract:
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Hierarchical models are being increasingly utilized to implement deterministic physical process models in an inverse fashion; that is, in settings where observed data are utilized to estimate model parameters in the presence of uncertainty. The hierarchical statistical approach generally incorporates a discretized version (e.g., difference equation) of the dynamical process (e.g., differential equation) and allows for the rigorous estimation of latent state variables, model parameters, and variance components. Despite the success of such implementations, little attention has been paid to the precision of the approximated deterministic model itself. Here we implement and compare varying levels of approximated dynamical processes in a hierarchical setting and illustrate by modeling a true ecological process.
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