Fig 7. Sensitivity of β(t) estimation error to the user-specified values of input parameters.

[Panel A] Median RRMSE (Eq (33)) in estimates of β(t) from simulated reported incidence time series (Δt = 1 week, n = 1042), as a univariate function of the factor by which an input parameter was mis-specified. One thousand simulations were performed using fixed values (Table 1) for all data-generating parameters. The simulations accounted for environmental stochasticity [ES] (ϵ = 0.5), demographic stochasticity [DS], and observation error [OE] (p_rep = 0.25, t_rep = 2 weeks). For each simulation, corresponding mock birth and natural mortality time series were created, and β(t) was estimated from the data using the SI method. True (data-generating) values were specified for all input parameters except the focal parameter (indicated by the legend), for which 41 values logarithmically spaced between $\frac{1}{4}$ and 4 times the true value were specified in turn. Each input parametrization yielded 1000 estimates of β(t), whose median RRMSE was calculated (after smoothing with fixed q; see Eq (59)) and displayed as one point in the appropriate graph. [Panel B] Result of repeating the analysis from Panel A in which S₀ was specified with varying amounts of error, but with the initially erroneous value of S₀ updated using the method of peak-to-peak iteration (PTPI; 25 iterations) prior to β(t) estimation. The original result, obtained without PTPI, is presented for comparison.