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Bayesian data assimilation for estimating instantaneous reproduction numbers during epidemics: Applications to COVID-19
Fig 2
Validation experiment of the DARt system on simulated data.
First, the ground-truth Rt sequence is synthetic using piecewise Gaussian random walk split by several abrupt change points. The sequence of incident infection jt is simulated based on a renewal process parameterised by the synthetic Rt. The observation process includes applying a convolution kernel that represents the probabilistic observation delay to obtain the expected observation 
and adding Gaussian noise that represents the reporting error to obtain the noisy ‘real’ observation Ct. The inputs (in grey) to the DARt system are the distributions of generation time, observation kernel and simulated noisy observation Ct. The system outputs are the estimated 
, estimated 
and change indicator 
. These outputs are compared with the synthetic Rt, jt and the time of abrupt changes. Also, the observation function is applied to the estimated 
to compute the estimated observation 
with uncertainty, which is compared to the ‘real’ observation.
doi: https://doi.org/10.1371/journal.pcbi.1009807.g002