  The K-Mean and EM algorithms are popular in clustering and mixture modeling,
due to their simplicity and ease of implementation. However, they have several
significant limitations. Both coverage to a local optimum of their respective
objective functions (ignoring the uncertainty in the model space), require the
apriori specification of the number of classes/clsuters, and are inconsistent.
In this work we overcome these limitations by using the Minimum Message Length
(MML) principle and a variation to the K-Means/EM observation assignment and
parameter calculation scheme. We maintain the simplicity of these approaches
while constructing a Bayesian mixture modeling tool that samples/searches the
model space using a Markov Chain Monte Carlo (MCMC) sampler known as a Gibbs
sampler. Gibbs sampling allows us to visit each model according to its
posterior probability. Therefore, if the model space is multi-modal we will
visit all models and not get stuck in local optima. We call our approach
multiple chains at equilibrium (MCE) MML sampling.
