  This article introduces the sequential Kalman filter, a computationally
scalable approach for online changepoint detection with temporally correlated
data. The temporal correlation was not considered in the Bayesian online
changepoint detection approach due to the large computational cost. Motivated
by detecting COVID-19 infections for dialysis patients from massive
longitudinal health records with a large number of covariates, we develop a
scalable approach to detect multiple changepoints from correlated data by
sequentially stitching Kalman filters of subsequences to compute the joint
distribution of the observations, which has linear computational complexity
with respect to the number of observations between the last detected
changepoint and the current observation at each time point, without
approximating the likelihood function. Compared to other online changepoint
detection methods, simulated experiments show that our approach is more precise
in detecting single or multiple changes in mean, variance, or correlation for
temporally correlated data. Furthermore, we propose a new way to integrate
classification and changepoint detection approaches that improve the detection
delay and accuracy for detecting COVID-19 infection compared to other
alternatives.
