Figure 5

Effects of birth-death dataset size on parameter estimates and MCEM²uncertainty. Each panel displays MCEM² and SGD birth-death MLEs (red and blue circles, respectively) as well as Poisson method point estimates (orange circles) versus the true parameter values (green circles), along with MCEM² 68%, 95%, and 99% confidence ellipses (black curves ranging in size from smallest to largest, respectively). A, B, C, and D display results for datasets of 40, 60, 80, and 100 data points, respectively. The three methods tested identified parameters with comparable accuracy across all datasets. As the numbers of data points increase, the MCEM² MLEs get closer to the truth and the confidence ellipses shrink in size. The green sloped line plots the ratio${\theta }_2^{\ast }/{\theta }_1^{\ast }$, highlighting that the uncertainties of the parameter ratio are lower than the uncertainties of the parameter magnitudes. For all datasets, the 95% confidence ellipse encloses the true parameter values.