Analyzing the Effects of Observation Function Selection in Ensemble Kalman Filtering for Epidemic Models
The Ensemble Kalman Filter (EnKF) is a Bayesian filtering algorithm utilized in estimating unknown model states and parameters for nonlinear systems. An important component of the EnKF is the observation function, which connects the unknown system variables with the observed data. These functions take different forms based on modeling assumptions with respect to the available data and relevant system parameters. The goal of this research is to analyze the effects of observation function selection in the EnKF in the setting of epidemic modeling, where a variety of observation functions are used in the literature. In particular, four observation functions of different forms and various levels of complexity are examined in connection with the classic Susceptible-Infectious-Recovered (SIR) model. Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters. Numerical experiments further illustrate how modifying the observation noise covariance matrix in the filter can help to account for uncertainty in the observation function in certain cases.
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