Approximate Bayesian Computation for the Stellar Initial Mass Function

Many statistical procedures rely on specification of a likelihood function, but explicitly specifying a likelihood 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. Rather than using a simplified likelihood, approximate Bayesian computation (ABC) provides a framework for performing Bayesian inference in cases where the likelihood is not available, but it is possible (and computationally efficient) to generate a sample from the forward process that mimics the data-generation process. I will introduce and discuss ABC with a goal of illustrating how it can be useful in astronomy focusing on estimation of the stellar initial mass function (IMF). The merit of ABC will be demonstrated through a simplified IMF model where a likelihood function is specified and exact posteriors are available. To aid in capturing the possible 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.

Followed by wine and cheese in Pupin 1402.

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