Plausible parameterization: An approach to fitting weakly identifiable dynamical models
Dynamical population models often encode both mechanistic representations of putative causal processes and observation conditions. When data are rare, the observation process is unknown, or models are misspecified, it may be difficult or impossible to statistically estimate parameters of interest (for instance by maximum likelihood or MCMC). In such situations, what data exist may nevertheless contain sufficient information to exclude some theoretically possible scenarios leading to better understanding of the underlying population dynamic processes and support empirical prediction even if a unique causal explanation cannot be identifed. All three conditions (data scarcity, unknown observation process, and model misspecification) were present in late 2014, when we sought to develop a predictive model for the dynamics of an ongoing epidemic of human Ebola virus disease in West Africa. We therefore developed an ad hoc approach, the method of plausible parameter sets, which seeks to identify the boundaries of ensemble of parameterizations that are consistent with the data. This ensemble may then be used to put bounds on the set of possible future trajectories by enforcing consistency with past observations. This contrasts with, for example, maximum likelihood estimation, which seeks to make statements about the relative probability of alternative hypotheses.
Using the method of plausible parameter sets and a small quantity of data that were reported to be of high quality, I fit a highly parameterized state-space model with discrete time steps to observations of human cases of Ebola virus disease. The ensemble of models that was obtained in this way enabled counterfactual investigation of alternative intervention policies and characterized key attributes of the developing epidemic – for instance the close race between epidemic progression and the roll out of interventions – even though the specific effects of different interventions could not be identified. The model allowed for the possibility that the effective reproduction number was reduced to less than its critical value by late summer, a scenario that seems much more probable in retrospect than it did at that time. By focusing on boundary possibilities and empirically observable quantities rather than maximum likelihood estimates and theoretical quantities, it may be that the method of plausible parameter sets will be of general use in applied ecology, particularly situations where environmental conditions are changing and policy requires immediately actionable science.