# A Preferential Attachment Model for the Stellar Initial Mass Function

## TL;DR

This paper introduces a new Bayesian computational method to better infer the stellar initial mass function by accounting for observational biases and physical processes, overcoming the limitations of traditional likelihood-based approaches.

## Contribution

It develops an approximate Bayesian computation framework incorporating physical models and observational effects for more accurate IMF inference in astronomy.

## Key findings

- Method accurately recovers true posterior in simulations
- Accounts for observational limitations and physical processes
- Improves inference accuracy over traditional likelihood methods

## Abstract

Accurate specification of a likelihood function is becoming increasingly difficult in many inference problems in astronomy. As sample sizes resulting from astronomical surveys continue to grow, deficiencies in the likelihood function lead to larger biases in key parameter estimates. These deficiencies result from the oversimplification of the physical processes that generated the data, and from the failure to account for observational limitations. Unfortunately, realistic models often do not yield an analytical form for the likelihood. The estimation of a stellar initial mass function (IMF) is an important example. The stellar IMF is the mass distribution of stars initially formed in a given cluster of stars, a population which is not directly observable due to stellar evolution and other disruptions and observational limitations of the cluster. There are several difficulties with specifying a likelihood in this setting since the physical processes and observational challenges result in measurable masses that cannot legitimately be considered independent draws from an IMF. This work improves inference of the IMF by using an approximate Bayesian computation approach that both accounts for observational and astrophysical effects and incorporates a physically-motivated model for star cluster formation. The methodology is illustrated via a simulation study, demonstrating that the proposed approach can recover the true posterior in realistic situations, and applied to observations from astrophysical simulation data.