Mixtures of Gaussian Wells: Theory, Computation, and Application.

A primary challenge in unsupervised clustering using mixture models is the selection of a family of basis distributions flexible enough to succinctly represent the distributions of the target subpopulations. In this paper we introduce a new family of Gaussian Well distributions (GWDs) for clustering applications where the target subpopulations are characterized by hollow [hyper-]elliptical structures. We develop the primary theory pertaining to the GWD, including mixtures of GWDs, selection of prior distributions, and computationally efficient inference strategies using Markov chain Monte Carlo.