Fig 1.
Comparison between the marginal density of the OU SDE at time T = 14, with that obtained through the series approximation upon varying the number of basis n = 3, 5, 10, 15.
Fig 2.
Comparison of the posterior marginal densities of the parameters obtained using the SDE and the SA (with n = 15 basis function). These densities are summarised using a kernel density estimate.
Fig 3.
Influenza dataset: Goodness-of-fit (a); posterior distribution of the latent diffusion paths corresponding to the SDE and SA counterparts (b), with densities summarised by the mean (solid lines) and 95% credible intervals (broken lines); and samples from the posterior distribution of the latent diffusion paths, SDE (c) and SA (d).
Fig 4.
MMD between the joint posterior distributions of the parameters θ and initial values X0 from SDE and SA (for different n).
Table 1.
Runtimes (rounded to nearest integer), in seconds, of MCMC for SA, as a function of the number of basis n, in comparison with the runtime of SDE. These were run on a 3.6 GHz machine with 16 GB memory.
Fig 5.
SIRS model with sinusoidal transmission-potential: Goodness-of-fit (a); posterior distribution of the latent diffusion paths corresponding to the SDE and SA approaches (b), with densities summarised by the mean (solid lines) and 95% credible intervals (broken lines).
Fig 6.
Goodness-of-fit of daily death data (a) and the inferred latent infections (b), produced using the random-walk (magenta lines) and SAd (orange lines). These densities are summarised by the mean (solid lines) and 95% credible intervals (broken lines). The black line indicates the day of lockdown in England 23rd March, 2020.
Fig 7.
Posterior mean (solid lines) and 95% credible intervals (broken lines) for the all England reproduction number Rt,E.
Table 2.
Posterior mean and 95% credible intervals for the age-specific infection-fatality ratio from the random-walk and SAd models of transmission-potential.