Birth-death processes (BDPs) are continuous-time Markov chains that model the number of particles in a system over time. While widely used in population biology, genetics and ecology, statistical inference of the instantaneous particle birth and death rates remains largely limited to restrictive linear BDPs in which per-particle birth and death rates are constant. When individual birth and death rates instead depend on the size of the population as a whole, the model is called a "general" BDP. From state $X(\au ) = k$, transition to state $k+?$ happens with instantaneous rate $\\lambda_k$, and transition to state $k-?$ happens with instantaneous rate $\\mu _k$. \\\\ Researchers often observe the number of particles at discrete times, necessitating data augmentation procedures such as expectation-maximization (EM) to find maximum likelihood estimates.
