The Kalderon lab at Columbia studies the behavior and regulation of follicle stem cells (FSCs) within the germarium in the adult ovary. They used the MARCM system to generate GFP-labeled clones in dividing cells of young females, from which observations of the number of labeled FSCs in layer 1 (L1) and layer 2 (L2), and the presence or absence of differentiated follicle cells (FCs) after six days were found for a number of different experimental conditions. Among other things, we are interested in estimating the division and differentiation rates of FSCs. This has an interesting stochastic modeling component, which we approached using three-compartment birth-death processes with population size regulation. Models like this have intractable likelihoods, so for statistical inference we resorted to ABC distributional random forests. To better understand the behavior of this approach, we have used a simplified version that mimics the data generation process in terms of a random number of initially labeled FSCs, each of which can divide or differentiate at most once in the course of the experiment. This results in a mixture model that can be analyzed using elementary Markov chain methods and the EM algorithm to estimate division and differentiation probabilities. This is ongoing work with Daniel Kalderon and Léandre Simon (now at EPFL).