  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.
