Corona virus spread prediction using kalman filter
medium.comNot being intimately familiar with the limitations of Kalman filters, how susceptible to bias is this approach when hidden states exist? In the case of COVID-19, the asymptomatic cases may be modeled as such, or not, depending on the approach. Also, the incubation and convalescent phase could also present a challenge given that patients can still transmit the virus.
It would be helpful to understand how Kalman filtering approach compares Markov chains, for example.
edit: Could Kalman filters be used to retroactively mark/flag/detect the introduction of a new strain of the same virus? If so, this could prove to be a novel way to quantify the clinically meaningful mutation rate - that is, the rate at which the virus mutates sufficiently to infect a new sub-population (or perhaps re-infect existing ones).
The Kalman filter can be derived as the conditional mean/variance of a multivariate normal. You assume a linear state-space model and walk the equations forward. Those are the key limitations: linear state space; Gaussian innovations. You can derive it other ways, but that's the way I grok it.
You are correct about hidden states. A linear state-space model with omitted variables will suffer the same kinds of bias present in an OLS model with omitted variables [4].
Deriving the equations is a nice way to distract yourself from the apocalypse. [1],[2] should be enough of a toe hold if you are familiar with OLS. Ignore the control term u[n] in the Matlab documentation. Kalman's original paper [3] is also a really nice, although I didn't really get it until I had already approached it as a conditional moment problem.
[1] https://stats.stackexchange.com/questions/30588/deriving-the... [2] https://www.mathworks.com/help/control/ug/kalman-filtering.h... [3] https://pdfs.semanticscholar.org/bb55/c1c619c30f939fc792b049... [4] https://en.wikipedia.org/wiki/Omitted-variable_bias