
Estimation Results 
Rel err 
Test function SNR 

EL 
MSS 
EL 
MSS 

(A) 100 observations, Δt=0.5, Θ^{(0)} (1,0.1) 
Θ_{1} 
1.00 
± 0.19 
1.56 
± 0.92 
15% 
71% 
SNR: 0.21 
Θ_{2} 
0.101 
± 0.02 
0.156 
± 0.09 
16% 
72% 

(B) 2000 observations, Δt=0.5, Θ^{(0)} =(1,0.1) 
Θ_{1} 
1.00 
± 0.04 
1.00 
± 0.15 
2% 
13% 
SNR: 0.17 
Θ_{2} 
0.101 
± 0.00 
0.101 
± 0.015 
2% 
13% 

(C) 500 observations, Δt=5, Θ^{(0)} =(1,0.1) 
Θ_{1} 
1.01 
± 0.09 
1.02 
± 0.11 
7% 
9% 
SNR: 0.50 
Θ_{2} 
0.101 
± 0.01 
0.102 
± 0.01 
7% 
9% 

(D)100 observations, Δt=10, Θ^{(0)} =(0.6,0.06) 
Θ_{1} 
0.60 
± 0.12 
0.65 
± 0.17 
15% 
21% 
SNR: 0.55 
Θ_{2} 
0.061 
± 0.01 
0.065 
± 0.018 
16% 
22% 


Table 1: Statistics of the estimation results for ImmigrationDeath model. The table shows that the MSS method works well in this example for three out of four
experimental designs and the test functions identify the problematic design. 
50 data sets are simulated using the Gillespie algorithm with initial value v_{0}=10. For each of the 50 data sets an estimation is performed with an exact method (EL) and the
MSS method. The table shows a statistic over the 50 estimates for both the exact and the MSS method: Parameter name (column 1), averages for exact method (column
2), standard deviation of exact method (column 3), averages of MSS method (column 4), standard deviations of MSS method (column 5), relative errors of exact method
(column 6) and MSS method (column 7) and the signal to noise (SNR) test function (column 7). 
The SNR test function indicates a weak SNR in situation (A) and therefore identifies the case in which the MSS approximation is problematic. If this is the case many more
observations are needed to resolve the problem despite still low SNR, situation (B), or another experimental design (C). 