LEO-Py: Estimating likelihoods for correlated, censored, and uncertain data with given marginal distributions

Abstract

Data with uncertain, missing, censored, and correlated values are commonplace in many research fields including astronomy. Unfortunately, such data are often treated in an ad hoc way in the astronomical literature potentially resulting in inconsistent parameter estimates. Furthermore, in a realistic setting, the variables of interest or their errors may have non-normal distributions which complicates the modeling. I present a novel approach to compute the likelihood function for such data sets. This approach employs Gaussian copulas to decouple the correlation structure of variables and their marginal distributions resulting in a flexible method to compute likelihood functions of data in the presence of measurement uncertainty, censoring, and missing data. I demonstrate its use by determining the slope and intrinsic scatter of the star forming sequence of nearby galaxies from observational data. The outlined algorithm is implemented as the flexible, easy-to-use, open-source Python package LEO-Py.