Figure 9.

Comparison with D-optimal design. This figure compares our set-based <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M55','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M55">View MathML</a> 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 <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M41','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M41">View MathML</a>, triangle <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M39','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M39">View MathML</a> and diamond <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M40','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M40">View MathML</a>. (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 <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M41','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M41">View MathML</a> solid grey line <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M39','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M39">View MathML</a>, dashed grey line <a onClick="popup('http://www.biomedcentral.com/1752-0509/6/21/mathml/M40','MathML',630,470);return false;" target="_blank" href="http://www.biomedcentral.com/1752-0509/6/21/mathml/M40">View MathML</a>. These results show the importance of accurate distribution characterization when designing experiments using the FIM.

Marvel and Williams BMC Systems Biology 2012 6:21   doi:10.1186/1752-0509-6-21
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