Table 8.

Parameter estimates for the Van der Pol oscillator model with T = 150, true initial condition = random, fitted initial condition = fixed.

	True θ	Mean θ̂	RMSE	rBias	$a\widehat{\mathrm{S}\mathrm{E}}$	MC SD	RDSE	Power/type I error
ζ0	3.00	2.62	0.38	−0.13	0.195	0.257	−0.24	1.00
ζ1	0.50	0.85	0.35	0.70	0.047	0.056	−0.15	1.00
ζ2	0.50	0.84	0.34	0.68	0.047	0.062	−0.24	1.00
μ1	0.00	0.06	0.06	–	0.010	0.011	−0.07	1.00
μ2	0.00	0.01	0.01	–	0.007	0.007	−0.03	0.17
μ3	0.00	0.01	0.01	–	0.010	0.010	−0.07	0.20
λ21	0.70	0.09	0.61	−0.87	0.005	0.041	−0.87	1.00
λ31	1.20	0.15	1.05	−0.87	0.008	0.068	−0.88	1.00
${\sigma }_{e1}^2$	0.50	3.22	2.72	5.44	0.026	0.195	−0.87	1.00
${\sigma }_{e2}^2$	0.50	1.28	0.78	1.57	0.011	0.020	−0.47	1.00
${\sigma }_{e3}^2$	0.50	2.81	2.31	4.61	0.023	0.052	−0.56	1.00
${\sigma }_{b_{\zeta }}^2$	0.50	15.32	14.82	29.64	1.493	0.417	2.58	1.00

% of retained cases = 98%, correlation between true and estimated b_ζ,i = 0.05, true θ = true value of a parameter, mean $\mathrm{\theta ̂}=\frac{1}{H}{\sum }_{h=1}^H{\mathrm{\theta ̂}}_h$, where θ̂_h = estimate of θ from the hth Monte Carlo replication, $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{H}{\sum }_{h=1}^H{({\mathrm{\theta ̂}}_h-\text{true}\theta )}^2}$, rBias relative bias = $\frac{1}{H}{\sum }_h^H({\mathrm{\theta ̂}}_h-\text{true}\theta )/\text{true}\theta$, SE standard deviation of θ̂ across Monte Carlo runs, $a\widehat{\mathrm{S}\mathrm{E}}$ = average standard error estimate across Monte Carlo runs, RDSE average relative deviance of $\widehat{\mathrm{S}\mathrm{E}}=(a\widehat{\mathrm{S}\mathrm{E}}-\mathrm{S}\mathrm{E})/\mathrm{S}\mathrm{E}$, power/type I error = 1 − the proportion of 95% confidence intervals (CIs) that contain 0 across the Monte Carlo replications.