Figure 9

Comparison with D-optimal design. This figure compares our set-based ${\mathcal{P}}_V$ experimental design to FIM D-optimal design when using measurements that are characterized by Gaussian distributions. (a) Figure illustrating different possible Gaussian distributions for each of the three original measurement sample times (t₁ = 2, t₂ = 4 and t₃ = 6). The three distributions for each sample time are characterized by left shifted, center shifted, and right shifted means. (b) Time index of predicted time points given the number of additional measurements that can be made. The figure shows a comparison of time point selection for the following: solid squares--set-based method, circle $-{\mathit{\theta }}_{ML}^{\left\{c_2,c_4,c_6\right\}}$, triangle $-{\mathit{\theta }}_{ML}^{\left\{c_2,l_4,l_6\right\}}$ and diamond $-{\mathit{\theta }}_{ML}^{\left\{l_2,l_4,l_6\right\}}$. (c-d) Parameter estimations after adding one or two additional data measurements, respectively; black dot--θ*, solid black line--set-based method, dashed black line $-{\mathit{\theta }}_{ML}^{\left\{c_2,c_4,c_6\right\}}$ solid grey line $-{\mathit{\theta }}_{ML}^{\left\{c_2,l_4,l_6\right\}}$, dashed grey line $-{\mathit{\theta }}_{ML}^{\left\{l_2,l_4,l_6\right\}}$. These results show the importance of accurate distribution characterization when designing experiments using the FIM.