# Constraining Stellar Multiplicity with Approximate Bayesian Computation

Since the beginning of modern astronomy, we have known of the existence of binary-star and multiple-star systems. However, we do not know the stellar multiplicity fraction, i.e., the proportion of stellar systems with two or more stars. Astronomers have argued that constraining the value of the multiplicity fraction will improve our theoretical understanding of the Universe. From understanding the birth and evolution of stars to improving the calibration of observational methods, constraining multiplicity will have profound impacts on the field of astrophysics. In this project we implement the advanced statistical algorithm Approximate Bayesian Approximation (ABC) to constrain the value of the stellar multiplicity fraction. The ABC algorithm uses a data simulation to derive a Bayesian posterior distribution without the calculation of the likelihood. We employ the Apache Point Observatory Galactic Evolution (APOGEE) data set of 97,313 stellar objects and the Apache Point Observatory and Kepler Astroseismology Science Constortium (APOKASC) data set of 1,916 stellar objects. We develop and test four forward models, of increasing complexity, to simulate the data-generating process as a function of multiplicity. Using the software package cosmoABC, our forward model and the APOGEE catalog, we derive a posterior distribution of stellar multiplicity. Using our third forward model, we constrain the value of the stellar multiplicity fraction with a 95% credible interval to 0.555 ± 0.051.