Table 9.

Parameter estimates for the Van der Pol oscillator model with T = 300, 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	2.78	0.22	−0.07	0.156	0.335	−0.53	1.00
ζ1	0.50	0.88	0.38	0.76	0.040	0.081	−0.51	1.00
ζ2	0.50	0.87	0.37	0.74	0.039	0.078	−0.50	1.00
μ1	0.00	0.09	0.09	–	0.007	0.009	−0.18	1.00
μ2	0.00	0.01	0.01	–	0.005	0.005	−0.12	0.38
μ3	0.00	0.01	0.01	–	0.007	0.008	−0.12	0.44
λ21	0.70	0.07	0.63	−0.89	0.004	0.048	−0.92	0.99
λ31	1.20	0.13	1.07	−0.89	0.006	0.081	−0.93	0.98
${\sigma }_{e1}^2$	0.50	3.33	2.83	5.67	0.019	0.214	−0.91	1.00
${\sigma }_{e2}^2$	0.50	1.29	0.79	1.58	0.007	0.019	−0.60	1.00
${\sigma }_{e3}^2$	0.50	2.82	2.32	4.64	0.016	0.052	−0.69	1.00
${\sigma }_{b_{\zeta }}^2$	0.50	15.69	15.19	30.39	1.521	0.474	2.21	1.00

% of retained cases = 100%, 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.