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 settingof 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.
The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data. Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating the effects of observation function selection when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired observation functions of different forms in connection with the classic Susceptible-Infectious-Recovered (SIR) model , we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions . 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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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
popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting
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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
Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating
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in the EnKF in the settingof epidemic modeling, where a variety of observation functions are used in the literature. In particular, four
when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired
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and various levels of complexity are examined
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, we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions