  Obtaining up to date information on the number of UK COVID-19 regional
infections is hampered by the reporting lag in positive test results for people
with COVID-19 symptoms. In the UK, for "Pillar 2" swab tests for those showing
symptoms, it can take up to five days for results to be collated. We make use
of the stability of the under reporting process over time to motivate a
statistical temporal model that infers the final total count given the partial
count information as it arrives. We adopt a Bayesian approach that provides for
subjective priors on parameters and a hierarchical structure for an underlying
latent intensity process for the infection counts. This results in a smoothed
time-series representation now-casting the expected number of daily counts of
positive tests with uncertainty bands that can be used to aid decision making.
Inference is performed using sequential Monte Carlo.
