Bayesian inference of Gaussian mixture models with noninformative priors

Abstract: This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of data points. This enables noninformative improper priors such as the Jeffreys prior to be placed on the component parameters. We demonstrate difficulties involved in specifying a prior for the standard Gaussian mixture model, and show how the new model can be used to overcome these. MCMC methods are given for efficient sampling from the posterior of this model.