Statistical Inference for Multi-Pathogen Systems
Figure 4
Inference under scenario II: Temporary cross-immunity.
Inference is carried out for two separate data sets constructed from the same set of parameter values – results are shown in [Left] and [Right] columns for each data set. [Top] Simulated case-data for the two infections are plotted in solid and dashed lines. Log-likelihood profiles for parameters describing the short () [Middle] and the long term (
) [Bottom] interactions. In the insets, we show close-ups of the profiles near the peaks. Plotted
are relative difference in the raw log-likelihood from the reference point set at
, indicated by the horizontal dashed line.
represents the 95% confidence interval – parameter values corresponding to a positive
are within the confidence bound. The gray dots indicate the repeated likelihood estimates (
replicate SMC calculations for each profile point,
particles in each SMC calculation). The profiles are created by fitting a smooth line through the log of the arithmetic mean likelihoods (shown in black dots). The vertical red dashed line is plotted at the actual parameter value used to generate the simulated case-data. Parameters not shown in the graph are taken from Table 1.