  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.
