Inference for Overlapping Mixture Components in the MEIOM

Develop inference for Gaussian-mixture normalizing-flow settings in which mixture components overlap substantially or mode assignment is uncertain, thereby relaxing the current requirement that observations be assigned reliably to sufficiently well-separated modes; investigate more general base distributions, including full-covariance Gaussian mixtures and potentially non-Gaussian mixture components.

Background

The Gaussian-mixture extension of the Mixed-Effects Influential Outlier Metric currently assumes that mixture components are sufficiently well separated. Under this assumption, each observation can be assigned to a single component and within-component Mahalanobis distances can be approximated by chi-square distributions, which supports the proposed outlier-inference procedure.

The conclusion explicitly identifies as future work the development of inference when components overlap substantially or component assignment is uncertain. It also identifies broader reference distributions—full-covariance Gaussian mixtures and potentially non-Gaussian mixture components—as extensions of the current Gaussian-mixture normalizing-flow framework.