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Astronomical data often suffer from noise and incompleteness. We extend thecommon mixtures-of-Gaussians density estimation approach to account forsituations with a known sample incompleteness by simultaneous imputation fromthe current model. The method, called GMMis, generalizes existingExpectation-Maximization techniques for truncated data to arbitrary truncationgeometries and probabilistic rejection processes, as long as they can bespecified and do not depend on the density itself. The method accounts forindependent multivariate normal measurement errors for each of the observedsamples and recovers an estimate of the error-free distribution from which bothobserved and unobserved samples are drawn. It can perform a separation of amixtures-of-Gaussian signal from a specified background distribution whoseamplitude may be unknown. We compare GMMis to the standard Gaussian mixturemodel for simple test cases with different types of incompleteness, and applyit to observational data from the NASA Chandra X-ray telescope. The python codeis released as an open-source package at https://github.com/pmelchior/pyGMMis

Filling the gaps: Gaussian mixture models from noisy, truncated or incomplete samples