Bayesian imputation of COVID-19 positive test counts for nowcasting under reporting lag

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.