Bayesian inference in hierarchical Stellar systems

Abstract

A methodology for Bayesian inference in binary stellar systems based on the No-U-Turn sampler Markov chain Monte Carlo algorithm is presented, providing a precise and efficient estimation of the joint posterior distribution of the orbital parameters. The Bayesian methodology allows to directly incorporate prior information about the system to constrain the solution and estimate orbital parameters that cannot be determined due to lack of observations or imprecise measurements. The incorporation of prior information of the parallax and the primary object mass is extensively studied to determine the individual masses of the components of single-lined visual-spectroscopic binary systems. This study is made by analyzing the posterior distributions and their respective projection in the observation spaces. The methodology is extended for the Bayesian inference in hierarchical stellar systems of any multiplicity, architecture, and lack of observation sources. Finally, a methodology to determine the optimal measurements time in binary and hierarchical systems is proposed based on the maximum entropy sampling criterion. This methodology makes direct use of the estimated posterior distribution to provide a temporal characterization of the information gain of new observations of the system and estimates a probability distribution of the optimal measurement time.