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Abstract Society increasingly demands accurate predictions of complex ecosystem processes under novel conditions to address environmental challenges. However, obtaining the process‐level knowledge required to do so does not necessarily align with the burgeoning use in ecology of correlative model selection criteria, such as Akaike information criterion. These criteria select models based on their ability to reproduce outcomes, not on their ability to accurately represent causal effects. Causal understanding does not require matching outcomes, but rather involves identifying model forms and parameter values that accurately describe processes. We contend that researchers can arrive at incorrect conclusions about cause‐and‐effect relationships by relying on information criteria. We illustrate via a specific example that inference extending beyond prediction into causality can be seriously misled by information‐theoretic evidence. Finally, we identify a solution space to bridge the gap between the correlative inference provided by model selection criteria and a process‐based understanding of ecological systems.
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Spherical Minimum Description Length
We consider the problem of model selection using the Minimum Description Length (MDL) criterion for distributions with parameters on the hypersphere. Model selection algorithms aim to find a compromise between goodness of fit and model complexity. Variables often considered for complexity penalties involve number of parameters, sample size and shape of the parameter space, with the penalty term often referred to as stochastic complexity. Current model selection criteria either ignore the shape of the parameter space or incorrectly penalize the complexity of the model, largely because typical Laplace approximation techniques yield inaccurate results for curved spaces. We demonstrate how the use of a constrained Laplace approximation on the hypersphere yields a novel complexity measure that more accurately reflects the geometry of these spherical parameters spaces. We refer to this modified model selection criterion as spherical MDL. As proof of concept, spherical MDL is used for bin selection in histogram density estimation, performing favorably against other model selection criteria.
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- Award ID(s):
- 1743050
- PAR ID:
- 10088689
- Date Published:
- Journal Name:
- Entropy
- Volume:
- 20
- Issue:
- 8
- ISSN:
- 1099-4300
- Page Range / eLocation ID:
- 575
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/e20080575
