Analyzing the Effects of Observation Function Selection in Ensemble Kalman Filtering for Epidemic Models

TL;DR

This paper investigates how the choice of observation functions impacts the accuracy of Ensemble Kalman Filter estimates in epidemic models, emphasizing the importance of correct data interpretation for reliable forecasting.

Contribution

It provides a computational analysis of different observation functions in EnKF for epidemic modeling, highlighting the effects of incorrect assumptions on estimation accuracy.

Findings

Incorrect observation modeling leads to inaccurate estimates.

Choosing appropriate observation functions improves forecast reliability.

Adjusting observation noise covariance can mitigate some modeling uncertainties.

Abstract

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.