Stellar Occultations in the Era of Data Mining and Modern Regression Models: Using Gaussian Processes to Analyze Light Curves and Improve Predictions

Gaussian process (GP) regression is a nonparametric Bayesian approach that has been used successfully in various astronomical domains, especially in time-domain astronomy. The most common applications are the smoothing of data for interpolation and the detection of periodicities. The ability to create unbiased data-driven models without a predefined physical model can be a major advantage over conventional regression methods. Prior knowledge can be included by setting boundary conditions or constraining hyperparameter values, while unknown hyperparameters are optimized during the conditioning of the model. We have adapted and transformed previous approaches of GP regression and introduce three new applications for this regression method, especially in the context of stellar occultations: the modeling of occultation light curves, the correction of public JPL ephemerides of minor planets based on publicly available image data of the Zwicky Transient Facility, and the detection of natural satellites. We used data from observations of stellar occultations to validate the models and achieved promising results in all cases, and thus we confirmed the flexibility of GP regression models. Considering various existing use cases in addition to our novel applications, GP regression can be used to model diverse data sets addressing a wide range of problems. The accuracy of the model depends on the input data and on the set boundary conditions. Generally, high-quality data allow the usage of loose boundary conditions, while low-quality data require more restrictive boundary conditions to avoid overfitting.