Fig. 1.

Comparison of Bayesian P-spline models with second-order and first order random-walk prior distributions. Simulated Binomial data for an exponentially increasing prevalence, $\pi \left(t\right)=0.5\times exp(0.05\times t)$, with 5000 tests performed a day. Daily estimates of prevalence (points) and 95% confidence intervals are shown. (A) Model fit for a Bayesian P-spline model with a second-order random-walk prior distribution. (B) Model fit for a Bayesian P-spline model with a first order random-walk prior distribution. (A, B) Central estimates (solid line) are shown with 50% (dark shaded region) and 95% (light shaded region) credible intervals are also shown. Models have been defined up to 60 days, despite the data only going up to 30 days, in order to demonstrate the effect of the model’s prior distribution during periods of no data.