Explicitly specifying a likelihood function is becoming increasingly difficult for many problems in astronomy. Astronomers often specify a simpler approximate likelihood - leaving out important aspects of a more realistic model. Estimation of a stellar initial mass function (IMF) is one such example. The stellar IMF is the mass distribution of stars initially formed in a particular volume of space, but is typically not directly observable due to stellar evolution and other disruptions of a cluster. Several difficulties associated with specifying a realistic likelihood function for the stellar IMF will be included.
Approximate Bayesian computation (ABC) provides a framework for performing inference in cases where the likelihood is not available. I will introduce ABC, and demonstrate its merit through a simplified IMF model where a likelihood function is specified and exact posteriors are available. To aid in capturing the dependence structure of the data, a new formation model for stellar clusters using a preferential attachment framework will be presented. The proposed formation model, along with ABC, provides a new mode of analysis of the IMF.