Separable Nonlinear Least-Squares Parameter Estimation for Complex Dynamic Systems

Table 1

MSE ratios for linear parameters (small samples).

Prior	Low noise				High noise
	SIR	LV	GMA	FHN	SIR	LV	GMA	FHN
Low	8.3	5.8	4.0	2.3	2.8	2.2	2.2	1.3
Medium	3.9	1.8	3.1	1.7	1.4	1.2	1.8	1.2
High	0.9	1.3	0.9	2.0	0.4	1.0	0.6	1.1

The MSE ratios (computed by averaging square errors over Monte-Carlo simulation runs) of NLS and SLS for estimating the linear parameters in various benchmark models and under different experimental setups are displayed (see Section 3.1 for detailed specifications). To identify model names, self-explanatory abbreviations are used. The values in the table are rounded off to one significant digit. The sample size is for the GMA and Lotka–Volterra models, for the FitzHugh–Nagumo system, and for SIR model. The noise levels are and . Values larger than 1 in the table correspond to the cases where SLS performs better than NLS. Note the decreasing pattern in the columns, reflecting the effect of the quality of prior information on the performance of NLS.