Figure 4

Birth-death process MCEM²parameter estimate progression. Green and blue bold lines denote MCEM² parameter estimates${\widehat{\theta }}_1$ and${\widehat{\theta }}_2$, respectively, as a function of iteration number. True parameter values are marked by green and blue horizontal dotted lines. The cross-entropy phase completes in three iterations (gray shaded region), followed by 234 iterations of MCEM until convergence (black vertical line). An additional 100 iterations of MCEM are included to illustrate the diminishing returns from running the algorithm beyond convergence. Although the parameter estimates from the first MCEM iteration are far from the true values, their ratio is nearly correct and this ratio is preserved as the estimates are refined toward the true values.