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.

在包括天文学在内的许多研究领域中，具有不确定，缺失，检查和相关值的数据是司空见惯的。不幸的是，在天文学中经常以特殊方式处理此类数据，从而可能导致参数估计不一致。此外，在实际设置中，目标变量或其误差可能具有非正态分布，这使建模变得复杂。我提出了一种新颖的方法来计算此类数据集的似然函数。这种方法利用高斯copulas来解耦变量及其边际分布的相关结构，从而产生一种灵活的方法来计算存在测量不确定性，检查和缺失数据时的数据似然函数。我通过从观测数据确定附近星系恒星形成序列的斜率和内在散射来证明其用途。概述的算法通过灵活，易于使用的开源Python软件包LEO-Py实现。