Fig 1.
Schematic of the likelihood calibration process.
We start with the prior elicitation and initial input design, followed by iterations of (a) particle filtering, utilising both the simulation model and the embedded model discrepancy (MD), and returning log-likelihood estimates; (b) emulation of the log-likelihood surface; (c) evaluation of the Not Ruled Out Yet (NROY) space using the emulator; (d) generation of a new input design within the NROY space.
Fig 2.
Schematic of the COVID-19 model considered in this paper and an example of the compartmental structure we consider throughout.
Fig 3.
Particle trajectory plots across the ensemble of design points at Wave 10 for the simulated outbreak.
A) Spatial (LTLA-level) plots of the mean number of deaths by day 54, for the data and the fitted model. B) Cumulative deaths at day 54 within each LTLA (ranked in decreasing order of predicted deaths). C) Cumulative deaths over time, aggregated over the 315 LTLAs. D) Hospital cases over time in each NHS region. E) Cumulative deaths over time in each age/region category. F) Cumulative hospital incidence over time by each NHS age/region category. In plot B) the green points are the predicted ensemble means, and the error bars are the 95% prediction intervals. For clarity we show a zoomed-in version of the plot also. The yellow and red points are the observed data coloured by whether they lie inside and outside of the prediction intervals respectively. In plots C–F, the blue dashed lines correspond to the observed data and the black solid lines to the mean trajectories from the particles taken across the ensemble. The ribbons correspond to 50% and 95% prediction intervals. A vertical dashed line corresponds to the end point of the observed data, such that trajectories before the line are generated from the particle filter, and trajectories to the right of the line are simulated forecasts from the model. Source for shapefiles: https://geoportal.statistics.gov.uk from the Office for National Statistics licensed under the Open Government Licence v.3.0. Contains OS data: Crown copyright and database right 2022.
Fig 4.
Particle trajectory plots across the ensemble of design points at Wave 10 for the real UK data up to the first lockdown.
A) Spatial (LTLA-level) plots of the mean number of deaths by day 37, for the data and the fitted model. B) Cumulative deaths at day 37 within each LTLA (ranked in decreasing order of predicted deaths). C) Cumulative deaths over time, aggregated over the 315 LTLAs with death data available. D) Hospital cases over time in each NHS region. E) Cumulative deaths over time in each age/region category. F) Cumulative hospital incidence over time by each NHS age/region category. In plot B) the green points are the predicted ensemble means, and the error bars are the 95% prediction intervals. For clarity we show a zoomed-in version of the plot also. The yellow and red points are the observed data coloured by whether they lie inside and outside of the prediction intervals respectively. In plots C–F, the blue dashed lines correspond to the observed data and the black solid lines to the mean trajectories from the particles taken across the ensemble. The ribbons correspond to 50% and 95% prediction intervals. A vertical dashed line corresponds to the end point of the observed data, such that trajectories before the line are generated from the particle filter, and trajectories to the right of the line are simulated forecasts from the model. Source for shapefiles: https://geoportal.statistics.gov.uk from the Office for National Statistics licensed under the Open Government Licence v.3.0. Contains OS data: Crown copyright and database right 2022.
Fig 5.
Particle trajectory plots across the ensemble of design points at Wave 10 for the real UK data beyond the first lockdown.
A) Spatial (LTLA-level) plots of the mean number of deaths by day 54, for the data and the fitted model. B) Cumulative deaths at day 54 within each LTLA (ranked in decreasing order of predicted deaths). C) Cumulative deaths over time, aggregated over the the 315 LTLAs with death data available. D) Hospital cases over time in each NHS region. E) Cumulative deaths over time in each age/region category. F) Cumulative hospital incidence over time by each NHS age/region category. In plot B) the green points are the predicted ensemble means, and the error bars are the 95% prediction intervals. For clarity we show a zoomed-in version of the plot also. The yellow and red points are the observed data coloured by whether they lie inside and outside of the prediction intervals respectively. In plots C–F, the blue dashed lines correspond to the observed data and the black solid lines to the mean trajectories from the particles taken across the ensemble. The ribbons correspond to 50% and 95% prediction intervals. A vertical dashed line corresponds to the end point of the observed data, such that trajectories before the line are generated from the particle filter, and trajectories to the right of the line are simulated forecasts from the model. Source for shapefiles: https://geoportal.statistics.gov.uk from the Office for National Statistics licensed under the Open Government Licence v.3.0. Contains OS data: Crown copyright and database right 2022.