Figure 11

Parameter estimation results for auto-regulatory gene network. Each panel displays MCEM² and SGD MLEs and Poisson method point estimates computed using${\widehat{\mathit{\theta }}}^{\left(0\right)}=(1,1,1,1,1,1,1,1)$ (red, blue, and orange circles, respectively), true parameter values (green circles), and MCEM² 68%, 95%, and 99% confidence ellipses. A, B, C, and D compare the four reversible pairs of reactions in the system. Mean relative errors for MCEM², SGD, and the Poisson method were 52%, 20%, and 30%, respectively. MCEM² 95% confidence ellipses enclosed all true parameter values except${\theta }_5^{\ast }$ and${\theta }_6^{\ast }$; like the birth-death system, their skew indicates that the uncertainties of the parameter ratios are lower than the uncertainties of the parameter magnitudes.