Table 1.

The biases, standard deviations (SD), square roots of average squared errors (RASE) of the parameter estimates for the PDE model (2) using the Bayesian method (BM), the parameter cascading method (PC), and the two-stage method (TS) in the 1,000 simulated data sets when the data noise has the standard deviation σ = 0.02, 0.05. The actual coverage probabilities (CP) of nominal 95% credible/confidence intervals are also shown. The true parameter values are also given the second row.

Noise		σ = 0.02			σ = 0.05
Parameters		θD	θS	θA	θD	θS	θA
True		1.0	0.1	0.1	1.0	0.1	0.1
Bias × 103	BM	−16.5	−0.4	−0.2	−35.6	1.0	0.6
	PC	−29.7	−0.1	−0.3	−55.9	−0.2	−0.5
	TS	−225.2	−0.7	−1.8	−337.8	0.5	0.6
SD × 103	BM	9.1	1.6	0.2	22.2	3.8	0.5
	PC	24.9	3.8	0.5	40.5	6.2	0.8
	TS	91.0	5.9	1.1	140.7	10.2	2.1
RASE × 103	BM	18.81	1.66	0.27	42.0	3.9	0.8
	PC	38.96	3.75	0.54	69.1	6.2	1.0
	TS	243.21	5.91	20.66	365.9	10.2	2.2
CP	BM	93.9%	99.9%	98.8%	74.0%	97.8%	86.4%
	PC	84.3%	96.7%	94.9%	78.1%	96.5%	93.5%
	TS	41.8%	93.6%	72.1%	37.6%	94.0%	93.8%