
Corona virus spread prediction using kalman filter - ankeshk
https://medium.com/analytics-vidhya/coronavirus-updated-prediction-using-kalman-filter-3ef8b7a72409
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DataDrivenMD
Not 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).

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rmrfstar
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...](https://stats.stackexchange.com/questions/30588/deriving-the-
conditional-distributions-of-a-multivariate-normal-distribution) [2]
[https://www.mathworks.com/help/control/ug/kalman-
filtering.h...](https://www.mathworks.com/help/control/ug/kalman-
filtering.html) [3]
[https://pdfs.semanticscholar.org/bb55/c1c619c30f939fc792b049...](https://pdfs.semanticscholar.org/bb55/c1c619c30f939fc792b049172926a4a0c0f7.pdf)
[4] [https://en.wikipedia.org/wiki/Omitted-
variable_bias](https://en.wikipedia.org/wiki/Omitted-variable_bias)

